Fluid transport technology

Section 2: Basic Knowledge of Fluid Flow I. Continuity Equation 1. Steady Flow Systems Based on the changes in various parameters as fluid flows through piping systems, fluid flow can be classified as steady flow or unsteady flow. If the values of various physical quantities in a flow system change only with position and not with time, it is called steady flow. If the values of various physical quantities in a flow system change not only with position but also over time, it is called unstable flow. In continuous operation processes in industrial production, as long as the production conditions are under proper control, the fluid flow is generally stable. The start-up and shutdown processes in continuous operation, as well as the batch operation process, belong to unsteady flow. The fluid flow discussed in this chapter is a steady-flow process. Observe more closely the flow of fluid in a constant-level tank system equipped with an overflow device ； The flow of fluid when the liquid level in the tank continues to drop in the absence of fluid replenishment. 2. Continuity equation: The system of steady flow is shown in Figure 1-10; the fluid fills the pipe and flows continuously in from section 1- and out from section 2-. Taking the inner wall of the pipe and cross-sections 1- and 2- as the calculation domain, and unit time as the basis for calculation, according to the law of conservation of mass, the mass flow rate of fluid entering cross-section 1- is equal to the mass flow rate of fluid exiting cross-section 2-. That is, qm1 = qm2 (1-1). Since qm = uA, where qm represents the mass flow rate of the fluid – that is, the mass of fluid that passes through the effective cross-sectional area of the pipe per unit time, in kg/s ； u — average flow velocity of the fluid at any cross-section of the pipe, m/s ； A —— Effective cross-sectional area of the pipeline, m2 ； ——Density of the fluid, kg/m3. Therefore, qm = u1A1 and 1 = u2A2 2 (1-2). If this equation is applied to any cross-section of the pipe, then qm = uA = constant (1-3). These equations indicate that in a steady-flow system, the mass flow rate of the fluid through each cross-section of the pipe remains constant; however, the fluid velocity at each cross-section varies depending on the cross-sectional area of the pipe and the density of the fluid. If the fluid is incompressible, that is, = constant, then qv = uA = constant. (Equation 1-4) Here, qv represents the volumetric flow rate of the fluid, which is the volume of fluid that passes through the effective cross-sectional area of the pipe per unit time, in m3/s ； The above equation shows that for an incompressible fluid, not only is the mass flow rate equal across all cross-sections, but the volume flow rate is also equal. Moreover, the pipe cross-sectional area A is inversely proportional to the fluid flow velocity u; the smaller the cross-sectional area, the greater the flow velocity. If an incompressible fluid flows within a circular pipe, then, as shown by equation (1-5), the flow velocity u of the incompressible fluid in the pipe is inversely proportional to the square of the pipe’s inner diameter d2. Equations (1-1) to (1-5) are known as the continuity equations for the steady flow of fluid in a pipe. The continuity equation describes the variation of flow velocity at various cross-sections of a pipe in a steady-flow system when the flow rate remains constant, and this pattern is independent of the layout of the pipes as well as whether there are fittings, valves, or conveying equipment installed in them. 【Example 1-1】 In the series-connected pipe system shown in Figure 1-10, the specifications of the smaller pipe are φ57×3 mm, while those of the larger pipe are φ89×3.5 mm; both pipes are seamless steel pipes. The average flow velocity of water in the smaller pipe is 2.5 m/s, and the density of water can be taken as 1000 kg/m3. Find: (1) The flow velocity of water in the large pipe ； ⑵Volumetric flow rate and mass flow rate of water in the pipeline. Solution: (1) The diameter of the small tube is d1 = 57 – 2×3 = 51 mm, and u1 = 2.5 m/s. The diameter of the large tube is d2 = 89 – 2×3.5 = 82 mm, with a flow rate of m/s. (2) The mass flow rate qm = qv = 0.0051×1000 = 5.1 kg/s. II. Bernoulli’s equation: In chemical manufacturing, Bernoulli’s equation serves as the fundamental basis for solving problems related to fluid transport; therefore, it and its applications are extremely important. The Bernoulli equation can be obtained from the energy balance of a steady-flow system. (1) Energy in flow systems: There are various forms of energy involved in flow systems, including internal energy, mechanical energy, work, heat, and energy losses. If the system does not experience any temperature changes or heat exchange and its internal energy remains constant, then the only forms of energy present in the system are mechanical energy, work, and energy losses. Energy is classified according to its properties into the energy inherent in the fluid itself and the energy exchanged between the system and the outside world. 1. The energy possessed by a fluid – mechanical energy (1) Potential energy. Potential energy is the energy that a fluid has when it is in a gravitational field. If a fluid with mass m (kg) is at a vertical distance z (m) from the reference horizontal plane, its potential energy is mgz (J), while the potential energy per unit mass of the fluid is gz (J/kg). Potential energy is a relative value, and a reference level must be specified for its calculation. (2) Kinetic energy: Kinetic energy is the energy possessed by a fluid as it flows at a certain speed. The kinetic energy of a fluid with mass m (kg), when its flow velocity is u (m/s), is (J); the kinetic energy per unit mass of fluid is (J/kg). (3) Static pressure energy: Static pressure energy is the energy possessed by a fluid due to its specific pressure. Every point within a fluid has a certain pressure. If a small hole is made in the wall of a pipe through which liquid is flowing and a vertical glass tube is connected to it, the liquid will rise to a certain height inside the glass tube; this height of the liquid column represents the static pressure of the fluid at that section of the pipe. In a piping system, the fluid pressure at a certain cross-section is p. For the fluid to flow through that cross-section, it must do work to overcome this pressure; as a result, the fluid enters the system with energy equivalent to this work, and this energy of the fluid is known as static pressure energy. The static pressure energy of a fluid with mass m (kg) is pV (J), while the static pressure energy per unit mass of fluid is (J/kg). 2. Representation of pressure: The pressure measured with absolute vacuum as a reference is called absolute pressure. The pressure measured relative to atmospheric pressure is called gauge pressure or vacuum level. If the system pressure is higher than atmospheric pressure, the excess amount is known as gauge pressure, and the instrument used to measure it is called a pressure gauge ； If the system pressure is lower than atmospheric pressure, the amount by which it is lower is referred to as vacuum level, and the instrument used to measure this is called a vacuum gauge. It can be seen that the relationship between them is such that the vacuum level is clearly the negative value of the gauge pressure; the higher the vacuum level of the fluid inside the device, the lower its absolute pressure. The relationship between absolute pressure, gauge pressure, and vacuum can be shown in Figure 1-11. Note: ① To avoid confusion, when pressure is expressed as gauge pressure or vacuum, it should be indicated in parentheses; if not specified, it is assumed to be absolute pressure ； ②The basis must be consistent when calculating pressure. ③Atmospheric pressure is based on the reading of the barometer at that time and location. Think about the conversion of pressure between different units of measurement. 3. Energy exchanged between the system and the outside world: In practical flow systems, the energy exchanged between the system and the outside world mainly consists of useful energy and lost energy. (1) External work: When a fluid transport machine is installed in the system, it performs work on the system, that is, it converts external energy into the mechanical energy of the fluid. The energy obtained per unit mass of fluid from the conveying machinery is called the external work, denoted by We, with the unit of J/kg. The additional work We is an important parameter for selecting fluid transfer equipment; it can be used to determine the effective power Pe of such equipment, namely Pe = We / qmW (1-6) (2). Energy loss: Due to the viscosity of the fluid, various resistances must be overcome during flow, which results in energy losses. The energy lost per unit mass of fluid as it flows to overcome resistance is denoted by Σhf, and its unit is J/kg. (II) Bernoulli’s equation: As shown in Figure 1-12, an incompressible fluid flows steadily within a system, with the fluid being transported from section 1- to section 2- via a pump. According to the law of energy conservation in a steady-flow system, the energy input to the system should equal the energy output from the system. The energy input into the system includes its own energy brought in when entering through section 1-, as well as the energy obtained from the conveying machinery. The energy output by the system includes its own energy carried away when it exits through section 2, as well as the energy lost by the fluid as it flows through the system due to overcoming resistance. If the 0-plane is taken as the reference horizontal plane, the vertical distances of the two cross-sections from this reference level are z1 and z2 respectively. The flow velocities at these two cross-sections are u1 and u2, while the pressures are p1 and p2. The density of the fluid at these cross-sections is … The work done on unit mass of fluid by the pump is We, and the total energy loss as the fluid flows from cross-section 1- to cross-section 2- is Σhf. Then, according to the law of conservation of energy, in equation (1-7), gz1, … represent respectively the potential energy, kinetic energy, and static pressure energy of the fluid at section 1-, in J/kg ； gz2, etc., represent the potential energy, kinetic energy, and static pressure energy of the fluid at section 2-, in J/kg ； Equation (1-7) is known as the Bernoulli equation for real fluids; it is based on a unit mass of fluid, with all units in J/kg. It reflects the laws of conversion and conservation of various energies during fluid flow, and holds great significance in fluid transportation. A fluid that is inviscid, incompressible, and experiences no flow resistance while flowing is generally referred to as an ideal fluid. When no external work is supplied to the flow system (i.e., We = 0), equation (1-8) becomes Bernoulli’s equation for an ideal fluid. This shows that, in the steady flow of an ideal fluid, the total mechanical energy at each cross-section is equal; this total mechanical energy remains constant. However, the various forms of mechanical energy are not necessarily equal to one another, and they can be converted into one another. By dividing each term in the Bernoulli equation based on unit mass of fluid by g, we obtain That is, in equation (1-9), z, and p respectively denote the potential head, dynamic head, and static head – the mechanical energy possessed by unit weight (1 N) of fluid, m ； He——effective head, the work done on unit weight of fluid between section 1- and section 2-, in meters ； Hf——head loss, the energy loss per unit weight of fluid flowing from section 1- to section 2-, in m. The above equation is the Bernoulli equation based on the unit weight of the fluid; each term in it represents the energy per unit weight of the fluid, with the unit being J/N (m). The physical meaning of m is: the mechanical energy per unit weight of fluid, which is the height to which it can be lifted from a reference horizontal plane. Applicable to stable, continuous incompressible systems. During the flow, the flow rate between the two cross-sections remains constant, satisfying the continuity equation. 【Example 1-2】 As shown in the attached diagram, there is a normal-pressure counter-current absorption tower used to absorb ammonia from a gas mixture using water; the water is pumped from a reservoir to the top of the tower by a centrifugal pump and then sprayed out through nozzles. The pump inlet pipe is a seamless steel tube with dimensions of φ108×4 mm, and the flow rate of the fluid in this pipe is 40 m3/h. The outlet pipe is a seamless steel tube with dimensions of φ89×3.5 mm. The water depth in the tank is 2 m, and the vertical distance from the bottom of the tank to the inlet of the nozzle at the top of the tower is 20 m. The total pressure loss in the pipeline is 40 J/kg, and the pressure at the inlet of the nozzle is 120 kPa (gauge pressure). Find out what the effective power required by the pump is in kW The water surface of the tank is taken as section 1-, the inlet of the nozzle as section 2-, and section 1- is taken as the reference horizontal plane. Apply Bernoulli’s equation between section 1- and section 2-, that is, where z1 = 0 ； z2 = 20 – 2 = 18m ； u1≈0 ； d1 = 108－2×4 =100mm ； d2 = 89 - 2×3.5 = 82mm ； ∑hf = 40J/kg ； p1 = 0 (gauge pressure), p2 = 120 kPa (gauge pressure) ； By applying Bernoulli’s equation, we obtain a value of 338.75 J/kg. The mass flow rate qm is given by A2u2/ρ, and its value is 0.785×(0.082)2×2.11×1000 = 11.14 kg/s. The effective power Pe is equal to We•qm, which equals 338.75×11.14 = 3774 W, or 3.77 kW. Suggestions for further learning: The application of Bernoulli’s equation can be taught through examples related to fluid transport in both classroom and practical training settings. Students should be encouraged to discuss other engineering applications of Bernoulli’s equation, thereby deepening their understanding of it and enabling them to use it more skillfully. III. Flow patterns of fluids In chemical production, processes such as fluid transport, heat transfer, mass transfer, and operations are all closely related to the flow state of fluids; therefore, it is necessary to understand the flow patterns of fluids as well as their velocity distribution within circular pipes. (1) Classification of flow types: When a fluid flows, two distinctly different flow patterns can occur depending on the flow conditions, namely laminar flow and turbulent flow. See Table 1-4. Table 1-4 Reynolds experiment and two flow regimes. Flow regime, experimental phenomena, characteristics of particle motion, velocity distribution, examples: Laminar flow. The experimental setup is shown in Figure 1-13; assuming that the liquid level in the water tank remains constant, when the flow velocity of the water inside the pipe is low, the colored water moves along the axis of the pipe as a clear straight line, as shown in Figure 1-14a. The fluid particles move in a straight line along the pipe axis, resulting in laminar flow, which is also known as steady flow. In laminar flow, the velocity distribution curve is parabolic in shape. As shown in Figure 1-15. The velocity is zero at the wall of the tube, and it is maximum at the center of the tube. The average flow velocity u = 0.5 umax applies to low-speed flow of fluids in pipes, flow of highly viscous liquids, and flow of fluids in capillaries and porous media. In the transitional state, the control valve is opened wider; as the flow velocity gradually increases to a certain value, it can be observed that the colored lines begin to take on a wavy shape, yet they still maintain a relatively clear outline, as shown in Figure 1-14b. The transitional state is not an independent flow pattern; it lies between laminar flow and turbulent flow. It can be regarded as incomplete turbulence, or unstable laminar flow, or an alternation of the two, depending on external conditions and being controlled by disturbances in fluid flow. In the turbulent flow, by further opening the valve, it can be observed that the colored stream mixes with the main water flow. Once the flow rate of water reaches a certain value, the colored water mixes completely with the regular water as soon as it enters the glass tube, as shown in Figure 1-14c. In addition to moving primarily along the axis, fluid particles also exhibit intense random motion in all directions; this is known as turbulence. In turbulent flow, the velocity distribution curve does not follow a strictly parabolic shape. The velocity distribution near the center of the pipe is relatively uniform, as shown in Figure 1-16; the average flow velocity is u = 0.82 umax. In engineering applications, the flow of fluid inside pipes is mostly turbulent. Figure 1-13 Schematic diagram of the Reynolds experiment setup. Figure 1-14 Comparison of Reynolds experiment results. Figure 1-15 Velocity distribution in a circular pipe under laminar flow. Figure 1-16 Velocity distribution in a circular pipe under turbulent flow. (II) Determination of fluid flow patterns 1. Reynolds number. In order to determine the flow pattern of a fluid, Reynolds conducted numerous experiments by changing various experimental parameters such as the fluid used, the type and diameter of the pipe, and the flow velocity, and then summarized the results of these experiments. The flow pattern of a fluid is primarily determined by factors such as the fluid’s density ρ, viscosity μ, flow velocity u, and inner diameter d of the pipe. These physical quantities can be combined to form a numerical value known as the Reynolds number (Re), which is used to determine the flow pattern. (1-10) Reynolds number, unitless. The Re value reflects the degree of turbulence in the fluid; the higher the Re, the greater the turbulence in the fluid flow. As long as units from the same unit system are used in the calculations, the results will be the same. 2. Criterion: Under normal circumstances, when fluid flows inside a pipe, the flow is turbulent at Re4000 ； While Re in the range of 2000–4000 represents a transitional state. It could be laminar or turbulent. In the transition region, the flow pattern changes due to external influences; factors such as changes in pipe shape or slight external vibrations can easily lead to turbulence. In general engineering calculations, a Re value of >2000 can be used to consider the flow as turbulent. 【Example 1-3】 At 20°C, the density of the oil is 830 kg/m3 and its viscosity is 3 cp. It flows in a circular straight pipe with a flow rate of 10 m3/h; the pipe specifications are φ89×3.5 mm. Determine the flow regime. Solution: Given ρ = 830 kg/m3, μ = 3cP = 3×10-3 Pa•s, and d = 89 – 2×3.5 = 82 mm = 0.082 m. Then, Re = … m/s. Since Re > 4000, this flow regime is turbulent. Find out how to determine the Reynolds number for non-circular pipes and how to identify the flow pattern (III) Laminar inner layer in turbulent flow: When the fluid inside a pipe flows turbulently, the flow velocity at the pipe wall is also zero. The thin layer of fluid near the pipe wall has a very low velocity and remains in a laminar state; this thin layer is known as the laminar inner layer. The thickness of the laminar inner layer decreases as the Reynolds number Re increases, but it does not disappear. The presence of a laminar inner layer has a significant impact on both heat transfer and mass transfer processes. In turbulent flow, it moves from the laminar inner layer toward the center of the pipe, with the velocity increasing gradually. There exists a flow regime that is neither laminar nor turbulent; this region is known as the transition layer or buffer layer. Moving further toward the center of the pipe is where the main turbulent region lies. It can be seen that when the fluid flows turbulently inside a pipe, its cross-section is radially divided into three regions: a laminar inner layer, a transition layer, and a turbulent core. IV. Flow resistance of fluids in pipes The resistance encountered by fluids as they flow through pipes is divided into straight-line pipe resistance and local resistance. The frictional resistance of a straight pipe is the resistance that arises due to the internal friction of the fluid as it flows through a straight pipe of a certain diameter. Local resistance is the resistance caused by local areas in a fluid flow through pipelines, such as fittings, valves, and sudden expansions and contractions in the cross-section. The total resistance is equal to the sum of the straight-line pipe resistance and the local resistance. (1) Viscosity of fluids – Observe more. (1) Which has better fluidity, gases or liquids? At the same temperature, which has better fluidity, water or oil? (2) Observe the flow of the river water – why is the flow velocity of the water in the center of the river higher than that at the riverbanks? 1. Viscosity: When a fluid flows, there is an attractive force between the fluid particles. The flow velocities at different points on the cross-section are not equal; in other words, relative motion exists within the fluid. When a particle moves forward at a certain speed, the particles adjacent to it exert a restraining force on it, hindering its movement. This mutual restraining force between fluid particles is known as internal friction. When a fluid flows, energy is required to overcome this internal friction force. The property of fluids that causes internal friction as they flow is known as the viscosity of the fluid. Fluids with high viscosity have poor flowability, while those with low viscosity have good flowability. Viscosity is an inherent property of fluids; fluids possess viscosity whether they are at rest or in motion. As shown in Figure 1-17, there are two parallel plates placed one above the other; these plates have a large area and are positioned very close to each other, with some liquid filling the space between them. If the lower plate is fixed and a constant external force F is applied to the upper plate, the upper plate moves at a constant speed u in the x-direction. At this point, the liquid between the two plates divides into countless parallel thin layers that move. The thin layer of liquid adhering to the bottom surface of the upper plate also moves at a speed of u along with the upper plate; the speeds of the layers of liquid below decrease successively, and the speed of the layer of liquid adhering to the lower surface is zero. The internal friction force between adjacent layers of the fluid is F. Experiments have shown that F is proportional to the rate of change of velocity Δu/Δy in the y-direction between the upper and lower plates, as well as proportional to the contact area A. When a fluid flows inside a circular tube, the relationship between u and y is linear; therefore, the rate of change mentioned above should be expressed as du/dy, which is known as the velocity gradient. If the internal friction per unit area of the flow layer is called shear stress, then equation (1-11) represents Newton’s law of viscosity, namely that the shear stress between fluid layers is proportional to the velocity gradient. In the formula, the proportionality constant is known as dynamic viscosity or absolute viscosity, commonly referred to simply as viscosity. Check whether the flow of paint and slurry obeys Newton’s law of viscosity Try to understand the patterns of such fluids. 2. Viscosity: Viscosity is a physical quantity that indicates the degree of viscosity of a fluid; it is one of the important physical properties of fluids. The greater the viscosity of a fluid, the higher its value. Its value is determined experimentally. The viscosity of a fluid varies depending on the type and state of the fluid; the viscosity of liquids decreases as temperature rises, while the viscosity of gases increases as temperature rises. When pressure changes, the viscosity of a liquid remains essentially constant, while the viscosity of a gas increases only slightly with rising pressure, and this increase can be ignored in most engineering calculations. The viscosities of certain common fluids can be found in relevant handbooks and the appendix to this book. The legal unit of measurement for viscosity is Pa•s ； However, in engineering manuals, the unit of viscosity is commonly expressed in the physical unit system as poise (P) or centipoise (cP). The relationship between them is 1 Pa•s = 10 P = 1000 cP. The viscosity of a fluid can also be expressed as the ratio of viscosity to density, known as dynamic viscosity, denoted by μ (1-12). The standard unit of measurement for dynamic viscosity is m2/s ； In the physical unit system, the unit of dynamic viscosity is cm2/s, known as St. (II) Friction loss in straight pipes 1. Fanning’s formula The friction loss in straight pipes is also known as frictional loss along the pipe length. The resistance of a straight pipe is usually calculated using the Fanning formula, which is given by equation (1-13). In this equation, hf represents the resistance of the straight pipe, in J/kg ； ——Coefficient of friction, also known as friction factor, is dimensionless ； l —— length of the straight pipe, m ； d —— inner diameter of the straight pipe, m ； u — the flow velocity of the fluid inside the pipe, in m/s. The friction factor in the Fanning formula is an important parameter for determining the pressure loss in straight pipes. The value is related to Re, which reflects the degree of fluid turbulence, and to ε, which represents the roughness of the pipe inner wall. 2. Wall roughness: Pipes used in industrial production can be roughly divided into smooth pipes and rough pipes, depending on the properties of their material and the way they are processed. Glass tubes, copper tubes, and plastic tubes are generally classified as smooth tubes, while steel tubes and cast iron tubes are classified as rough tubes. In fact, even for pipes made of the same material, the roughness of their walls can vary significantly due to differences in usage duration and the extent of corrosion and scaling. ①Absolute roughness refers to the average height of the protruding parts on the pipe wall, denoted by ε, as shown in Figure 1-18. Table 1-5 lists the absolute roughness values for certain industrial pipes. Figure 1-18: Effect of pipe wall roughness on fluid flow. Table 1-5: Absolute roughness of certain industrial pipes. Pipe category | Absolute roughness ε/mm: Seamless brass, copper, and aluminum pipes; New seamless steel pipes or galvanized iron pipes; New cast iron pipes; Seamless steel pipes with mild corrosion; Seamless steel pipes with severe corrosion; Old cast iron pipes; Clean glass pipes; Well-smoothed cement pipes: 0.01–0.05, 0.1–0.2, 0.3, 0.2–0.3, over 0.5; over 0.85. 0.0015–0.01, 0.33. ② Relative roughness: Relative roughness refers to the ratio of absolute roughness to the inner diameter of the pipe, that is, ε/d. The degree to which wall roughness affects the friction coefficient is related to the pipe diameter; therefore, when calculating flow resistance, the relative roughness must be taken into account. 3. Coefficient of friction (1) Coefficient of friction in laminar flow: When the fluid flows in a laminar manner, the uneven surfaces on the pipe wall are covered by regular layers of fluid; therefore, the coefficient of friction is independent of ε/d and depends only on the Reynolds number (1-14). Substituting this value into the Fanning formula yields equation (1-15). This equation is known as the Hagen-Poiseuille equation, and it is used to calculate the resistance encountered when fluid flows laminarly inside a circular straight pipe. (2) Friction coefficient in turbulence: Due to the complex movement of fluid particles in turbulent flow, it is not yet possible to derive a formula for the friction coefficient in turbulence using purely theoretical analysis methods; instead, empirical formulas are obtained through experimental measurements. Various empirical formulas have certain ranges of applicability; relevant materials can be consulted. For ease of calculation, the relationship curve between the friction coefficient and Re as well as ε/d is usually plotted on a double logarithmic scale, as shown in Figure 1-19; this graph is known as the Moody diagram. In this way, it is convenient to look up the λ values for various conditions in the graph based on the Re and ε/d values. Depending on the value of the Reynolds number, four distinct regions can be identified in the graph: Region a, the laminar flow region, is when Re is 4000 and the value lies below the dashed line in the graph; in this case, =f(Re, ε/d). For a certain ε/d, it decreases as the Re value increases. The fully turbulent region is the area above the dashed line in the diagram; it is independent of the Re value and depends only on ε/d. -The Re curve is almost horizontal; it remains a constant when the ε/d ratio of the pipe is fixed. In this region, the drag loss is proportional to u2, hence it is also known as the drag square region. As can be seen from the graph, the larger the ε/d value, the lower the Re value at which the drag square region is reached. 【Example 1-4】 Water at 20°C flows through a steel pipe at a velocity of 1 m/s. The specifications of the pipe are φ60×3.5 mm. Determine the friction loss when the water passes through a 100 m long straight pipe Solution: From the appendix of this book, the values for water at 20°C are ρ = 998.2 kg/m³, μ = 1.005×10⁻³ Pa•s, d = 60 – 3.5×2 = 53 mm, L = 100 m, and u = 1 m/s. The absolute roughness of the steel pipe wall is taken as ε = 0.2 mm. Using the values of Re and ε/d, the friction coefficient λ can be determined from Figure 1-19; it is λ = 0.03. Figure 1-19 shows the relationship between λ, Re, and ε/d. (III) Local resistance: Local resistance is the resistance generated by various local features in the pipeline, such as fittings, valves, as well as sudden expansions and contractions in the cross-sectional area, as the fluid flows through these areas. When fluid flows through sections such as the inlet and outlet of a pipeline, elbows, valves, sudden expansions, sudden contractions, or flow meters, there are inevitable sudden changes in the flow velocity and direction of the fluid. The flow is disrupted and subjected to shocks, resulting in the formation of vortices and increased turbulence, which leads to a significant rise in flow resistance, as shown in Figure 1-20. There are generally two methods for calculating local resistance: the drag coefficient method and the equivalent length method. Figure 1-20 Flow disturbances under different conditions 1. Equivalent length method The equivalent length method is a technique for converting the calculation of local resistance as fluid passes through a local obstacle into the calculation of resistance loss in a straight pipe. The so-called equivalent length is the length of a straight pipe with the same diameter that results in the same energy loss as a certain local obstruction; it is denoted by le, with units of meters. It can be calculated using equation (1-16), where u represents the average flow velocity of the fluid inside the pipe, in m/s. le——equivalent length, in m; when the local flow cross-section changes, u should be taken as the fluid velocity at the smaller cross-section. The Le value is determined experimentally; under turbulent conditions, the equivalent lengths of certain pipe fittings and valves can also be found in Figure 1-21. 2. Coefficient of resistance method: Local resistance is expressed as a multiple of kinetic energy; in equation (1-17), ζ represents the coefficient of local resistance, which has no units and its value is determined experimentally. The common local resistance coefficients are shown in Table 1-6. (IV) Total resistance: The total resistance of a piping system is equal to the sum of the resistances of all straight pipes and all local resistances. 1. Equivalent length method: When calculating local resistance using the equivalent length method, the formula for total resistance is given by equation (1-18). In this formula, Σle represents the sum of the equivalent lengths of all the fittings and valves in the pipeline, in meters. 2. Resistance coefficient method: When using the resistance coefficient method to calculate local resistance, the formula for total resistance is given by equation (1-19), where Σζ represents the sum of all the local resistance coefficients in the pipeline. It should be noted that when a pipeline is composed of several pipe sections with different diameters, the total energy loss of the pipeline should be calculated for each section separately and then summed together. In addition to being expressed in terms of energy, the total resistance can also be represented by the head loss Hf (the flow resistance for 1 N of fluid, in meters) and the pressure drop Δpf (the flow resistance when 1 m3 of fluid flows, in meters). The relationship between them is hf = Hfg (1-20) and Δpf = ρhf = ρHf g (1-21). [Example 1-5] Water at 20°C flows through a pipe at a rate of 16 m3/h; the pipe specifications are φ57×3.5 mm. The pipeline is equipped with two standard 90° elbows and one gate valve (1/2 size), with a straight pipe section length of 30 m. Calculate the total resistance loss as the fluid flows through this pipeline. From the calculations, it is found that at 20°C, the density of water is 998.2 kg/m3, and its viscosity is 1.005 mPa•s. The inner diameter of the pipe is d = 57 – 2×3.5 = 50 mm = 0.05 m. The flow velocity of water inside the pipe is in m/s. The Reynolds number for the fluid flowing in the pipe is calculated as follows. Using a table, the absolute roughness of the pipe wall is found to be ε = 0.2 mm; thus, ε/d = 0.2/50 = 0.004. By referring to a chart based on the Re value and the ε/d value, λ = 0.0285 is obtained. ⑴Calculated using the drag coefficient method; from the table: for a 90° standard elbow, ζ=0.75 ； Gate valve (1/2 open), ζ=4.5. Therefore, for J/kg ⑵, the equivalent length method is used for calculation; from the tables, it is found that for a 90° standard elbow, l/d = 30 ； Globe valve (1/2 open), l/d=200. J/kg. As can be seen from the above calculations, the results obtained using the two methods for calculating local resistance differ little, and this is acceptable in engineering calculations. Figure 1-21: Diagram showing the equivalent lengths of pipe fittings and valves in a straight line. Table 1-6: Resistance coefficients for common local obstacles. Recommendations: Analyze the reasons for flow resistance, determine the necessity of calculating it, and select an actual water transmission pipeline to perform the resistance calculations.

Section 3: Selection of Pipes and Pipeline Installation. Determining the diameter of the conveying pipes and arranging and installing them properly are of great significance for ensuring the smooth operation of production, as well as reducing equipment and operational costs. I. Selection of pipes The formula for calculating the inner diameter of a pipe is given in equation (1-22), where d represents the inner diameter of the pipe, in meters ； u — appropriate flow rate, in m/s; a reasonable flow rate is selected through economic analysis. The flow rate is generally determined by the production tasks, so the key is to select an appropriate flow speed. If the flow rate is chosen to be too high, although the pipe diameter can be reduced, the resistance of the fluid flowing through the pipe increases, leading to higher energy consumption and thus increased operating costs. Conversely, if the flow rate is chosen to be too low, the operating costs can be reduced accordingly, but an increase in the pipe diameter leads to higher costs for the piping equipment. Therefore, the appropriate flow rate must be determined through economic considerations based on the specific circumstances. The typical flow rate ranges for certain fluids in pipelines are listed in Table 1-7. Table 1-7 Common flow velocity ranges for certain fluids in pipes. Fluid category and conditions, Flow velocity range/m/s: Water and low-viscosity liquids (0.1~1.0 MPa), Industrial water supply (below 0.8 MPa), Boiler water supply (below 0.8 MPa), Saturated steam, General gases (at atmospheric pressure), Centrifugal pump discharge pipes (water-type liquids), Natural flow velocity of liquids (condensate, etc.), Gas flow velocity under vacuum conditions: 1.5~3.0, 1.5~3.0, >3.0, 20~40, 10~20, 2.5~3.0, 0.5

Section 4: Fluid Transfer Machinery. Generally speaking, fluid transfer machinery can be divided into machinery for transferring liquids (commonly known as pumps) and machinery for transferring gases (such as fans, compressors, vacuum pumps, etc.). Based on their working principles, they can be further divided into centrifugal, reciprocating, rotary, and fluid-acting types. Among them, the centrifugal type is the most common. I. Structural types of centrifugal pumps Centrifugal pumps feature a simple structure, stable performance, easy maintenance, straightforward operation, and strong adaptability, which makes them widely used in chemical production. 1. Structure of the centrifugal pump: Figure 1-22 shows a horizontal single-stage, single-suction centrifugal pump installed in a pipeline. Figure (a) shows its basic structure, while (b) is a schematic diagram of it in a pipeline. (a) Schematic diagram of the structure (b) Schematic diagram in the pipeline Figure 1-22 Structure of a single-stage, single-suction centrifugal pump l – Pump body ； 2-Impeller ； 3-Sealing ring ； 4-axis sleeve ； 5- Pump cover ； 6-Pump shaft ； 7-Bracket ； 8-Coupling ； 9-Bearing ； 10 - Shaft sealing device ； 11-Inlet ； 12-Snail-shaped pump casing ； 13-blade ； 14-Inlet tube ； 15-Bottom valve ； 16-Filter ； 17-Regulating valve ； 18-Discharge pipe (1) Impeller: The function of the impeller is to transfer the mechanical energy from the prime mover directly to the liquid, thereby increasing the liquid’s static pressure energy and kinetic energy (with a primary increase in static pressure energy). An impeller generally has 6 to 12 backward-curving blades. Impellers come in three types: open, semi-closed, and closed, as shown in Figure 1-23. Figure 1-23: Impeller of a centrifugal pump. Figure 1-24: Liquid suction method in a centrifugal pump. An open impeller has no covers on either side of the blades; it is simple to manufacture and easy to clean. It is suitable for transporting materials containing a large amount of suspended solids, but its efficiency is low and it cannot handle liquids at high pressures ； The semi-closed impeller has no cover on the suction side but one on the other side; it is suitable for transporting materials that tend to settle or contain particles, and its efficiency is relatively low ； A closed impeller has front and rear cover plates on both sides of the blades; it offers high efficiency and is suitable for transporting clean liquids free from impurities. Most centrifugal pump impellers are of this type. The balance holes on the rear cover are used to eliminate axial thrust. The liquid pressure around the impeller is already high; a portion of it seeps behind the rear cover of the impeller. Meanwhile, the liquid inlet on the front side of the impeller is at low pressure, which generates an axial thrust that pushes the impeller toward the pump inlet side. This can easily cause wear at the contact point between the impeller and the pump casing, and in severe cases, it can also lead to vibration. The balance hole allows a portion of the high-pressure liquid to leak into the low-pressure area, reducing the pressure difference before and after the impeller. But this also leads to a decrease in pump efficiency. Impellers come in two types of liquid suction methods: single-suction and double-suction. As shown in Figure 1-24. (2) Pump casing: Its function is to enclose the impeller within a certain space, so that the impeller can draw in and discharge liquid. The pump casing is often designed in a volute shape, which is why it is also called a volute. As the cross-sectional area of the flow channel gradually increases, the high-speed fluid ejected from around the impeller sees its velocity decrease, allowing part of its kinetic energy to be effectively converted into static pressure energy. The pump casing not only collects the liquid thrown out by the impeller but also serves as an energy conversion device. To improve the energy conversion efficiency of the liquid inside the pump, guide vanes are installed on the outer periphery of the impeller. The guide wheel is a bladed ring fixed around the periphery of the impeller. The bending direction of these blades is opposite to that of the impeller blades, and their bending angle is precisely matched to the direction in which the fluid flows out of the impeller. This helps to guide the fluid to change direction smoothly within the pump casing channels, thereby minimizing energy loss and improving the efficiency of converting kinetic energy into static pressure energy. (3) The shaft seal device serves to prevent the liquid inside the pump casing from leaking out along the shaft, or to prevent outside air from entering the pump casing. The common shaft sealing devices are packing seals and mechanical seals. The filler is generally oil-impregnated or graphite-coated asbestos rope. Mechanical seals achieve sealing primarily through the relative motion of the rotating ring mounted on the shaft and the stationary ring fixed to the pump casing at their end faces. 2. Types of centrifugal pumps There are a wide variety of centrifugal pumps, and corresponding classification methods also exist in abundance. For example, based on the properties of the liquid, they can be classified into water pumps, corrosion-resistant pumps, oil pumps, pumpes for handling impurities, shielded pumps, submersible pumps, and cryogenic pumps, among others. Various types of centrifugal pumps are grouped into separate series based on their structural characteristics, with one or several Chinese pinyin letters used as series codes. Within each series, different specifications are distinguished by additional letters and numbers. The following provides a brief overview of the types of centrifugal pumps commonly used in chemical plants, as shown in Table 1-8. Table 1-8 Types of Centrifugal Pumps Type Structural Features Applications Water pump IS type: Single-stage, single-suction design. Both the pump body and the pump cover are made of cast iron. It is characterized by a pump body and pump cover with a back-access design, which offers the advantage of easy maintenance as there is no need to disassemble the pump body, pipelines, or motor. It is the most widely used type of centrifugal pump, designed for transporting clean water as well as other liquids with physical and chemical properties similar to those of water. Type D multi-stage pumps can achieve high head pressures, as shown in Figure 1-25; they are suitable for situations where a high head pressure is required but the flow rate is not very high. Type S double-suction centrifugal pumps have two inlets, which allows for a higher flow rate of liquid, as shown in Figure 1-26; they are appropriate for situations where a high flow rate of liquid is needed but a high head pressure is not required. Corrosion-resistant pumps (Type F): Their characteristic is that the components in contact with the liquid are made of corrosion-resistant materials, and high sealing standards are required; mechanical seal devices are often used. Types FH (gray cast iron), FG (high-silicon cast iron), FB (chromium-nickel alloy steel), FM (chromium-nickel-molybdenum-titanium alloy steel), and Fs (polytrifluorochloroethylene plastic) are used for transporting corrosive liquids such as acids and alkalis. Oil pumps (Type Y) have excellent sealing properties. The shaft sealing device and bearings of hot oil pumps are equipped with cooling water jackets. Pumps used for transporting petroleum products; impurity pumps (type P) have wide impeller channels and a small number of blades, and often use semi-open or open impellers. Some pump casings are lined with wear-resistant cast steel plates. Not prone to clogging, easy to disassemble, wear-resistant. PW type (sewage pump), PS type (sand pump), PN (slurry pump) – used for transporting suspensions and viscous slurries. Shielded pumps: leak-free pumps, with the impeller and motor integrated into a single unit that is sealed within the same pump casing, eliminating the need for a shaft seal. The disadvantage is lower efficiency, around 26–50%. They are often used to transport flammable, explosive, highly toxic, and radioactive liquids. Submersible pumps (Type EY) are typically installed within liquid storage tanks; they require minimal specifications regarding shaft sealing, which helps save space and improves the operating environment. Its drawback is low efficiency. Suitable for transporting various corrosive liquids and liquids with high freezing points in chemical processing. Figure 1-25: Schematic diagram of a multi-stage pump. Figure 1-26: Schematic diagram of a double-suction pump. II. Working principle of centrifugal pumps: The impeller of a centrifugal pump is installed inside the pump casing and secured to the pump shaft, which is driven directly by the motor. The liquid enters the pump through the bottom valve and the suction pipe. It is discharged through the extrusion tube. Before starting the pump, the pump casing is filled with the liquid to be transported ； Once started, the impeller rotates at high speed driven by the shaft, and the liquid between the blades must also rotate along with it. Under the effect of centrifugal force, the liquid is thrown from the center of the impeller toward the outer edge, gaining energy as it exits the outer edge of the impeller at high speed and enters the volute pump casing. In the volute, the liquid slows down as the flow channel widens, converting some of its kinetic energy into static pressure energy; it then flows into the discharge pipe at a higher pressure and is sent to the desired location. As the liquid flows from the center of the impeller toward the outer edge, a vacuum is created at the center of the impeller. Since the pressure above the liquid level in the tank is greater than the pressure at the pump inlet, the liquid is continuously forced into the impeller. It can be seen that as long as the impeller keeps rotating, the liquid will continue to be drawn in and discharged. Fun fact: Gas entrapment phenomenon. If the pump casing is filled with gas before startup, when the gas at the center of the impeller is expelled after startup, a sufficient vacuum cannot be created there; as a result, the liquid in the chambers cannot be drawn in. This phenomenon is known as gas entrapment. To prevent vapor locking, the space inside the pump casing must be filled with liquid before starting the centrifugal pump. This step is called priming the pump. To prevent the liquid filled in the pump casing from flowing into the sump due to gravity, a check valve (foot valve) is installed at the inlet of the pump’s suction line ； If the pump is located below the liquid level in the tank, there is no need to fill the pump before starting it; simply opening the outlet valve will allow the liquid to flow into the pump automatically. III. Main performance parameters and characteristic curves of centrifugal pumps 1. Main performance parameters of centrifugal pumps The performance parameters of centrifugal pumps are physical quantities used to describe their characteristics. See Table 1-9. Table 1-9 Main performance parameters of centrifugal pumps Performance parameter Unit Definition Influencing factors Flow rate Q m3/h, m3/s The volume of liquid delivered by the centrifugal pump into the pipeline system per unit time. Pump’s structural dimensions (such as the diameter of the impeller and the width of the blades) and the speed of rotation of the impeller. The actual flow rate of a centrifugal pump is also related to the characteristics of the piping system. Head H m: The mechanical energy provided by a centrifugal pump to each unit weight of liquid. The head of a centrifugal pump depends on the pump’s design (such as the diameter of the impeller and the curvature of its blades), the speed at which the impeller rotates, and the flow rate of the pump. At a specified rotational speed, there is a definite relationship between the pressure head and flow rate. Its value is determined experimentally. Shaft power, expressed in PW or kW, refers to the power required by the pump shaft; it increases by 100% as the size of the equipment, the viscosity of the fluid, and the flow rate increase. Efficiency is a dimensionless value that represents the ratio of the effective power of a centrifugal pump to its shaft power, and it indicates the extent of energy loss in the pump. The efficiency of a centrifugal pump depends on the pump’s size, type, level of precision in manufacturing, as well as the properties and flow rate of the liquid being pumped. Generally, small pumps have an efficiency of 50% to 70%, while larger pumps can achieve an efficiency of around 90%; these values are determined through experimental measurements. 【Example 1-7】The experimental setup shown in Figure 1-27 is used to determine the performance of a centrifugal pump. The suction pipe and discharge pipe of the pump have the same diameter, and the vertical distance between the two pressure taps is 0.5 m. The pump’s speed is 2900 r/min. Using clean water at 20°C as the medium, the following values were measured: the flow rate was 54 m3/h, the gauge pressure at the pump outlet was 255 kPa, the vacuum reading at the inlet was 26.7 kPa, and the power meter indicated that the power consumed was 6.2 kW. The pump is driven directly by an electric motor, whose efficiency is 93%. Determine the head, shaft power, and efficiency of this pump under these operating conditions. Solution: (1) The head of the pump: Applying Bernoulli’s equation at the sections where the vacuum gauge and the pressure gauge are located, denoted as 1-1’ and 2-2’ respectively, we have …, where m is in kPa (gauge pressure). Since the pipelines between these two measurement points are very short, the flow resistance in them can be ignored; thus, … (2) The shaft power of the pump: The power measured by the power meter represents the power consumed by the motor. As the pump is driven directly by the motor, the transmission efficiency can be considered to be 100%, so the output power of the motor is equal to the shaft power of the pump. Since the motor itself consumes a portion of the power, its efficiency is 93%. Therefore, the output power of the motor is given by: Motor output power = Power consumed by the motor / Motor efficiency = 6.2 / 0.93 = 5.77 kW. The shaft power of the pump is P = 5.77 kW. (3) Efficiency of the pump. 2. Characteristic curve of centrifugal pumps: Both theoretical and experimental studies show that the key performance parameters of centrifugal pumps, such as head, power, and efficiency, are related to flow rate. To help users better understand and utilize the performance of centrifugal pumps, the relationship between them and flow rate is often represented graphically, which is known as the characteristic curve of the centrifugal pump. The characteristic curve of a centrifugal pump is generally provided by the manufacturer of the pump and is shown in the pump’s product manual; the measurement conditions are usually clean water at 20°C, with a fixed rotational speed as well. The typical performance curve of a centrifugal pump is shown in Figure 1-28. (1) The H-Q curve represents the relationship between the pump’s head and flow rate. The head of a centrifugal pump decreases as the flow rate increases (with exceptions at very low flow rates). (2) The P-Q curve represents the relationship between the pump’s shaft power and flow rate. The shaft power of a centrifugal pump increases as the flow rate increases, and it is at its minimum when the flow rate is zero. Therefore, when starting a centrifugal pump, the outlet valve of the pump should be closed to reduce the starting current of the motor and protect it. (3) The -Q curve represents the relationship between the pump’s efficiency and flow rate. When Q=0, η=0 ； As the flow rate increases, efficiency rises as well until it reaches a maximum value ； Then, as the flow rate increases further, the efficiency decreases. This indicates that a centrifugal pump has a maximum efficiency point at a certain speed, known as the design point. The pump operates most economically at the flow rate and head corresponding to its highest efficiency; therefore, the Q, H, and N values associated with this point of highest efficiency become the optimal operating parameters. The performance parameters indicated on the nameplate of a centrifugal pump refer to the operating conditions of that pump when it is running at its maximum efficiency point. Due to the requirements of the delivery conditions, it is often not possible for a centrifugal pump to operate at its optimal conditions; therefore, only a working range can be specified, known as the pump’s high-efficiency zone, which is usually around 92% of the maximum efficiency. When selecting a centrifugal pump, it should be operated within this range as much as possible. Activity suggestion: Through hands-on practice, organize students to discuss the factors affecting the characteristics of centrifugal pumps. IV. Selection of Centrifugal Pumps The selection of centrifugal pumps can generally be carried out according to the following principles: 1. Determine the type of centrifugal pump The type of centrifugal pump should be determined based on the properties of the liquid to be transported and the operating conditions. Factors such as the temperature, pressure, viscosity, corrosiveness of the liquid, the presence of solid particles, and whether it is flammable or explosive are all important considerations in selecting the appropriate type of centrifugal pump. 2. Determine the flow rate and head of the conveying system. The flow rate of the liquid to be conveyed is generally specified by the production requirements; if the flow rate varies, it should be based on the maximum flow rate. Based on the pipeline conditions and Bernoulli’s equation, determine the head pressure required at maximum flow rate. 3. Determine the model of the centrifugal pump: Select an appropriate model of centrifugal pump based on the flow rate Q and head H required by the pipeline. When making the selection, changes in operating conditions should be taken into account, and a certain margin should be reserved. When selecting, the flow rate to head ratio of the chosen pump should be slightly higher than what is required for the task. If selection is made using series characteristic curves, the (Q, H) point must lie below the pump’s Q–H curve and within the high-efficiency region. If several models of pumps meet the specific requirements of the pipeline, the one with higher efficiency should be chosen, while also taking into account the price of the pump. 4. Check of shaft power: When the density of the liquid is greater than that of water, it is necessary to check the shaft power. 5. List the pump’s performance at the design point for reference during use. V. Installation of Centrifugal Pumps 1. Cavitation in Centrifugal Pumps (1) Cavitation in Centrifugal Pumps The suction of liquid by a centrifugal pump is achieved through the pressure difference between the liquid surface and the inlet. The higher the suction line, the greater the suction height, and the lower the pressure at the suction inlet will be. When the pressure at the inlet is lower than the saturated vapor pressure of the liquid being transported under operating conditions, the liquid will vaporize to form bubbles. Once this bubble-containing liquid enters the pump, it moves into the high-pressure area due to the action of the rotating impeller. Under this high pressure, the bubbles condense back into liquid. The space left behind by these bubbles creates a local vacuum, which causes the surrounding liquid to quickly fill in that space under high pressure. The frequency of such high-speed impacts is very high, reaching several thousand times per second, and the impact pressure can be several hundred atmospheres or even higher. Such high-intensity, high-frequency impacts can cause fatigue in the impeller in mild cases; in more severe cases, they can destroy the impeller and the pump casing, or even turn the impeller into a honeycomb structure. This phenomenon of erosion of the impeller caused by the vaporization and re-condensation of the liquid being pumped inside the pump is known as cavitation in centrifugal pumps. (2) Hazards of cavitation: When cavitation occurs, it generates noise and causes vibrations; the flow rate, head, and efficiency all decline rapidly, and in severe cases, liquid suction becomes impossible. According to engineering standards, cavitation occurs when the pump’s head drops by 3%. 2. Installation height of centrifugal pumps. The fundamental way to prevent cavitation in engineering is to limit the installation height of the pump. The maximum installation height that prevents cavitation in a centrifugal pump is known as the allowable installation height of the centrifugal pump, or also referred to as the allowable suction height. It refers to the maximum vertical distance that can exist between the pump’s suction inlet 1-1’ and the liquid level in the suction tank 0-0’, denoted by the symbol Hg, as shown in Figure 1-29. Assuming that the pump operates at the highest allowable position, and using the liquid level as the reference plane, applying Bernoulli’s equation between the two sections – the liquid level in the storage tank at 0-0’ and the pump’s suction inlet at 1-1’ – yields equation (1-23). In this equation, Hg represents the allowable installation height, in meters ； p0 —— Inlet liquid level pressure, Pa ； p1——Minimum allowable pressure at the inlet, Pa ； u1——flow velocity at the inlet, m/s ； ——Density of the liquid being transported, kg/m3 ； ——Resistance of the fluid flowing through the suction pipe, in m. Think about it: what are the factors that affect the installation height of a centrifugal pump? 3. Calculation of the installation height for centrifugal pumps: In industrial production, the allowable head method is commonly used to calculate the permissible installation height of centrifugal pumps. The cavitation resistance parameter of centrifugal pumps is also expressed by the allowable cavitation head. The allowable cavitation head is the minimum value by which the sum of the dynamic head and static head at the pump inlet is higher than the saturated vapor pressure head of the liquid being transported, under the condition that cavitation does not occur. It is denoted by , that is, (1-24). Substituting this expression into (1-23) yields equation (1-25). In this equation, —— is the allowable cavitation head, in meters, which can be obtained from the pump’s performance table ； ——Saturated vapor pressure of the liquid at the operating temperature, in Pa. It increases as the flow rate increases; therefore, when determining the allowable installation height, the value corresponding to the maximum flow rate should be used. When the allowable installation height is negative, the suction inlet of the centrifugal pump is below the liquid level in the tank. For safety reasons, the actual installation height of the pump is usually lower than the permitted installation height by (0.5–1) m. 【Example 1-8】 A centrifugal pump of model IS65-40-200, with a rotational speed of 2900 rpm, a flow rate of 25 m3/h, a head of 50 m, and an (NPSH)r value of 2.0 m, is used to pump water at 50°C from an open reservoir. Given that the total resistance loss in the suction pipeline is 2 m of water column, and the local atmospheric pressure is 100 kPa, determine the installation height of the pump. Solution: According to the appendix, the saturated vapor pressure of water at 50°C is 12.34 kPa, and the density of water is 998.1 kg/m3. Given that P = 100 kPa and h = 2.0 m, the installation height of the pump should not exceed 5.04 m. VI. Comparison of various types of pumps The comparison of different types of pumps is shown in Table 1-10. Table 1-10 Comparison of Various Pumps
Type: Centrifugal Pump, Reciprocating Pump, Rotary Pump, Vortex Pump, Fluid-Action Pump
Flow Rate:
1. Uniform
2. High volume
3. Flow rate varies depending on the pipeline conditions
1. Non-uniform
2. Low volume
3. Constant flow rate, hardly affected by pressure head changes
1. Relatively uniform
2. Low volume
3. Constant flow rate, same as that of reciprocating pumps
1. Uniform
2. Low volume
3. Flow rate varies depending on pipeline conditions
1. Low volume
2. Intermittent discharge

Head:
1. Generally not high
2. Only a certain head for a specific flow rate
1. High
2. Different heads possible for a specific flow rate, determined by the piping system
1. High
2. Different heads possible for a specific flow rate, determined by the piping system
1. High
2. Only a certain head for a specific flow rate
The head should not be too high, as higher heads result in lower efficiency.

Efficiency:
1. Up to about 70%
2. Highest at the design point; efficiency decreases as deviation from this point increases
1. Around 80%
2. Remains high even at different heads
1. 60%–90%
2. Higher leakage reduces efficiency at high heads
25%–50%
Generally only 15%–20%

Structure:
1. Simple, inexpensive, and easy to install
2. Rotates at high speed; can be directly connected to a motor
3. Small volume for the same flow rate
4. High requirements for shaft sealing to prevent air leakage
1. Many parts, complex structure
2. Severe vibration; cannot operate at high speeds; difficult to install
3. Large size, occupies more space
4. Requires suction and discharge valves
5. More complex structure when transporting corrosive liquids
1. No valves
2. Can be directly connected to a motor
3. Fewer parts, but high precision in manufacturing is required
1. Simple and compact structure with a high suction height
2. Rotates at high speed; can be directly connected to a motor
3. Very small clearance required between the impeller and pump casing
4. High requirements for shaft sealing to prevent air leakage
1. No moving parts
2. Simple

Operation:
1. Air entrapment occurs; liquid must be filled before starting, and no air leakage is allowed during operation
2. Easy to maintain and operate
3. Flow rate can be easily adjusted using valves
4. Not damaged due to pipeline blockages
1. Many parts, prone to failure; difficult to repair
2. Flow rate can only be adjusted using bypass valves
3. Maintains high efficiency even when head and flow rate change
1. Repair is more complex than for centrifugal pumps but easier than for reciprocating pumps
2. Flow rate can only be adjusted using bypass valves
1. Power increases as flow rate decreases; the outlet valve should be opened when starting
2. Flow rate can only be adjusted using bypass valves
1. Some operate intermittently
2. Difficult to adjust flow rate

Application Range:
Suitable for transporting corrosive or suspension-type fluids; not suitable for highly viscous fluids. Generally, high flow rate with low head.
For clean liquids requiring high head and low flow rate.
High head and low flow rate; especially suitable for transporting viscous liquids such as oils.
Particularly suitable for liquids with low flow rate but high head; not suitable for dirty liquids.
Intermittent transportation of corrosive liquids.

VII. Operation of Centrifugal Pumps
1. Flow Rate Adjustment
When the speed of the pump’s impeller remains constant, the liquid flow rate and head provided by a pump under specific operating conditions can be represented by a point on the H–Q characteristic curve. As for the specific location of this point, it depends on the piping conditions before and after the pump. When discussing the operation of a pump, it is necessary to take into account the specific conditions of the piping system. The operating characteristics of a pump are determined by both the properties of the pump itself and those of the piping system. (1) Pipeline characteristic curve: The formula for calculating the external pressure head is derived from Bernoulli’s equation (1-26). The greater the value of Q, the greater the external pressure head He required by the flow system. The relationship between the flow rate through a specific pipeline and the external pressure head required for it is known as the characteristic of that pipeline. The head loss in the above equation is given by (1-27). If the difference in dynamic head between the upstream and downstream sections is ignored, then (1-28) applies. If is considered a constant, then (1-29) holds. The above equation is known as the characteristic equation of the pipeline, as it expresses the relationship between the external pressure head required for the pipeline and the flow rate through it. The curve corresponding in H~Q coordinates is called the pipeline characteristic curve, as shown in Figure 1-30. The pipeline characteristic curve reflects the relationship between flow rate and head for a specific pipeline under given operating conditions. The shape of this curve depends only on the piping layout and operating conditions, and not on the characteristics of the pump. (2) Operating point of the centrifugal pump: By plotting the H～Q curve of the pump and the H～Q curve of the pipeline in the same coordinate system, the intersection point M of the two curves is known as the operating point of the pump. As shown in Figure 1-31. ①The operating point of the pump is determined by both the characteristics of the pump and those of the piping system; it can be obtained by simultaneously solving the equations describing the pump’s characteristics and those describing the piping system’s characteristics ； ②For a pump installed in a pipeline, its flow rate is equal to the flow rate of the pipeline ； At this flow rate, the head provided by the pump is the external pressure head required by the pipeline. Therefore, the pump head corresponding to the pump’s operating point is provided by the pump as well as being required by the pipeline ； ③When a pump is specified to be installed in a particular pipeline, there can only be one stable operating point M. (3) Flow rate adjustment of centrifugal pumps: Due to changes in production requirements, the flow rate required in the pipeline sometimes needs to be altered, which essentially means changing the operating point of the pump. Since the operating point of the pump is determined by both the characteristics of the piping system and those of the pump itself, changing either the characteristics of the pump or those of the piping system can alter the operating point, thereby enabling flow rate regulation. ①Changing the opening degree of the outlet valve: As can be seen from equation (1-29), changing the opening degree of the valves in the piping system can alter the value of K, which in turn changes the position of the piping characteristic curve and thus the operating point, as shown in Figure 1-32. In production, the main method of adjustment is to change the opening degree of the pump outlet valve. Since it is simple and convenient to adjust using valves, and the flow rate can be varied continuously, this method is primarily used in industrial production. Quick info: Other methods for adjusting the flow rate of centrifugal pumps 1. Changing the impeller speed – An increase in the impeller speed leads to an increase in both flow rate and head pressure. This method of regulating flow is reasonable and economical, but it was once considered inconvenient to operate and unable to achieve continuous regulation. However, with the development of modern industrial technology, the use of continuously variable transmission devices in industry has overcome the aforementioned drawbacks. It is this type of regulation method that enables the pump to operate in the efficient range, which is particularly important for energy savings in large pumps. 2. Turning the impeller diameter: This method of adjustment is inconvenient to implement, and its range of adjustment is also limited. 【Example 1-9】 Determine whether the pump meets the transportation requirements. Transfer 95% nitric acid from a tank at atmospheric pressure to equipment at atmospheric pressure; the transfer rate required is 36 m3/h, and the lift height of the liquid is 7 m. The delivery pipeline is composed of tempered glass tubes with an inner diameter of 80 mm, and its total length is 160 m (including the equivalent length of all local resistances). A certain model of acid-resistant pump is currently used, whose performance is listed in the attached table for this item. Question: (1) Is this pump suitable? (2) What are the actual flow rate, head, efficiency, and power consumption? Q(L/s) 0 3 6 9 12 15 H(m) 19.5 19 17.9 16.5 14.4 12 (%) 0 17 30 42 46 44 Given: The viscosity of the acid at the transport temperature is 1.1510‑3 Pas ； The density is 1545 kg/m3. The friction coefficient can be taken as 0.015. Solution: (1) For this problem, the head required by the pipeline is determined by applying Bernoulli’s equation between the liquid level 1-1’ in the tank and the liquid level 2-2’ of the equipment at atmospheric pressure. Here, the flow velocity within the pipe is given by; the head loss in the pipe is given by; the head required by the pipeline is given by; and the flow rate required by the pipeline, expressed in L/s, is given by. As can be seen from the attached table, this pump can provide a head of 14.4 m when the flow rate is 12 L/s. When the flow rate is 10 L/s, which is the value required by the pipeline, the head provided by the pump will be even higher, at 13.06 m. Therefore, this pump is available for fulfilling the given transportation task. As can be seen from the attached table, the maximum efficiency of this pump is 46% ； At a flow rate of 10 L/s, the efficiency of this pump is approximately 43%. Therefore, the pump is operating in its high-efficiency range. (2) The actual flow rate, power consumption, and efficiency depend on the operating point of the pump, which is determined by both the characteristics of the piping system and those of the pump. From Bernoulli’s equation, the characteristic equation for the pipeline is obtained: (where the flow rate is in L/s). Using this equation, it is possible to calculate the head pressure required for various flow rates, as shown in the table below: Q (L/s): 0, 3, 6, 9, 12, 15; H (m): 7, 7.545, 9.181, 11.91, 15.72, 20.63. Based on these values, it is possible to draw the characteristic curve of the pipeline as well as the characteristic curve of the pump, as shown in the figures attached to this problem. The intersection point of the two curves is the working point, corresponding to a piston stroke of 14.8 m ； The flow rate is 11.4 L/s ； The shaft power at an efficiency of 45% can be calculated as follows: 2. Startup and shutdown procedures for centrifugal pumps (1) Preparations before startup ① It is necessary to thoroughly understand the physicochemical properties of the material to be transported, including whether it is corrosive, whether there are any suspended particles, its viscosity, freezing point, vaporization temperature, and saturated vapor pressure. ②Learn in detail about the operating conditions of the material being transported: transmission temperature, pressure, flow rate, transmission height, suction height, range of load variations, etc. ③Taking into account these two factors, and referring to the performance curve of centrifugal pumps, the most suitable centrifugal pump for actual production use can be selected. ④For some high-demand centrifugal pumps, it is necessary to consider installing filters in the inlet pipe and check valves behind the outlet valve during design. Additionally, two sets of monitoring devices should be installed in the control room and on-site to handle any unexpected incidents. ⑤After installation, a trial run must be conducted; only pumps whose performance parameters meet the requirements during this trial run can be put into production. (2) Pump startup procedure: ① Before starting the pump, open the pump’s inlet valve and the seal fluid valve first, and check to ensure that the pump chamber is filled with liquid. ②Once it is confirmed that the pump chamber is filled with liquid and the sealant is flowing properly, notify the receiving station to start the centrifugal pump. ③Slowly open the pump’s outlet valve, and adjust it to the desired flow rate using the flow and pressure indicators. (3) Shutdown procedure: ① After contacting the receiving station, slowly close the outlet valve of the centrifugal pump. ②Press the motor button to stop the motor from running. ③Close the centrifugal pump inlet valve and the seal fluid valve. (4) Pump switching: During production, it is common to need to switch between two pumps. First, start the standby pump and gradually open its outlet valve; then slowly close the outlet valve of the pump that is currently in operation. Throughout this process, it is necessary to maintain communication with the control room in order to keep the flow rate output by the centrifugal pump stable, thereby preventing the system from stopping due to fluctuations in flow rate. 3. Daily operation and maintenance (1) Inspections during operation ① Check the liquid level in the tank from which the liquid is drawn to prevent the material from running out. ②Check whether the pump’s outlet pressure or flow rate indicator is stable. ③Check whether the flow rate of the end-face seal fluid is normal. ④Check the pump body for leaks. ⑤Check the pump body and bearing system for any abnormal noises or vibrations. ⑥Check whether the lubricating oil in the pump shaft is fully present and in good condition. (2) Maintenance of centrifugal pumps ① Check the filter located before the pump’s inlet valve to see if the filter screen is damaged; if it is damaged, it should be replaced promptly to prevent particles such as weld slag from entering the pump ； Clean the filter regularly. ②The pump casing and impeller are disassembled, cleaned, and reassembled. Adjust the clearance between the impeller and the pump casing. If the impeller is damaged or corroded, the cause should be analyzed and appropriate action taken promptly. ③Clean the shaft seal and shaft sleeve system. Replace the lubricant to maintain a good lubrication condition. ④Replace the packing of the packing seal in a timely manner and adjust it to an appropriate tightness ； In cases where mechanical seals are used, the rotating ring and seal fluid should be replaced promptly. ⑤Check the motor. After long-term parking, the motor should be dried before driving it again. ⑥Check whether the indications of the primary and secondary instruments at the site and those controlled remotely are correct and functioning properly, and repair or replace any faulty instruments or components. ⑦Inspect the valve bodies of the pump’s inlet and outlet valves to check for any internal leakage caused by wear; if such leakage is present, the valves should be replaced promptly. 4. Accident handling: See Tables 1-11 and 1-12. Table 1-11: Failures of Centrifugal Pump Equipment and Corresponding Remedies
Equipment Failure | Cause Analysis | Remedies
Damaged impeller | 1. Cavitation occurs during operation of the centrifugal pump, causing intense impact of liquid on the blades and shaft, leading to vibration of the entire pump and damage to the impeller. | 1. Adjust the dimensions of the suction pipeline to ensure proper installation height and sufficient effective net positive suction head at the pump inlet. | 2. Implement strict maintenance procedures to ensure thorough cleaning after repairs; install a filter in front of the inlet valve if necessary.
Burnt motor | 1. Excessive gap between the pump casing and the impeller, along with the presence of foreign objects. | 1. Adjust the gap and remove foreign objects. | 2. Adjust the tightness of the packing and perform a spin test before starting the pump. | 3. Install fuses in the motor’s wiring to protect it.
Detached inlet/outlet valve seats | 1. Quality issues in valve manufacturing. | 1. Replace the valves with new ones.
Burnt stuffing box or mechanical seal rotating ring | 1. Excessive tightness in the stuffing box, resulting in heat generation due to friction and subsequent damage to the packing, causing leaks. | 1. Replace the packing and adjust its tightness to an appropriate level. | 2. Replace the rotating ring and adjust the contact surfaces to ensure proper alignment. | 3. Adjust the sealant properly.
Vibration of the shaft | 1. Misalignment during installation or inadequate leveling. | 1. Reinstall the pump and ensure proper alignment and leveling. | 2. Improve lubrication by adding more grease or replacing it with fresh grease.

Table 1-12: Operational Accidents of Centrifugal Pumps and Preventive Measures
Operational Accident | Cause Analysis | Preventive Measures
No flow after startup | 1. The pump chamber is not filled with liquid before starting the pump. | 1. Stop the pump, exhaust air and refill it with liquid before restarting. | 2. Close the outlet valve and restart the pump. | 3. Replace the pressure gauge. | 4. Reconnect the motor’s phase wires to ensure correct rotation. | 5. Adjust the gap between the impeller and the pump casing to the required level.
Empty storage tank | Failure to check the liquid level promptly after starting the pump, resulting in an empty storage tank and air entering the pump chamber, thereby preventing flow. | Stop the pump, refill it with liquid and expel air; restart the pump once the chamber is filled with liquid.
Axial seal leakage | 1. The packing is not tightened enough or has lost its elasticity. | 1. Adjust the tightness of the packing or replace it with new packing. | 2. Replace the rotating ring and reinstall it, ensuring proper alignment.
Burnt packing and rotating ring | 1. Excessive tightness of the packing, along with failure to perform a spin test before starting the pump. | 1. Replace the packing, perform a spin test, and adjust its tightness. | 2. Adjust the sealant properly.
Full high-level tank | Inadequate communication between operators, resulting in failure to inform the next shift before starting the pump. | 1. Improve communication between shifts when starting and stopping the pump. | 2. Replace the overflow pipe with one of appropriate diameter. | 3. Open the outlet valve slowly, without rushing it too much.

Skill Training 2: Operation of Centrifugal Pumps
● Training Objectives:
1. Understand the structure and characteristics of centrifugal pumps and learn how to operate them. 2. Determine the curve relationships between the effective head H, shaft power N, and overall efficiency η of the centrifugal pump at a constant rotational speed, and the effective flow rate Q. ●Training Preparation 1. Understand the structure, characteristics, and basic principles of centrifugal pumps. 2. Understand the characteristic curve of a centrifugal pump under constant speed conditions. 3. Understand the working principle and usage methods of flow regulation in centrifugal pumps. 4. The process is shown in Figure 1-33. ●Training steps (key points): 1. Fill the water pump with water ； After filling with water, close the pump’s outlet valve and the filling valve. 2. Start the centrifugal pump; after it has started, open the outlet valve to its maximum position to begin the experiment with the centrifugal pump. 3. Flow regulation: (1) Manual regulation: Adjust the flow rate through the pump outlet valve ； (2) Automatic adjustment: The opening degree of the electric control valve is adjusted through a flow automatic control instrument, thereby enabling manual or automatic control of the flow rate: ① Manual adjustment by the instrument ； ②The instrument adjusts automatically. Fig. 1-33: Schematic diagram of the centrifugal pump unit. 4. Manual adjustment experimental method: Adjust the opening degree of the outlet gate valve until it is fully open. Once the flow rate stabilizes, add weights to the motorized balance so that the balance arm aligns with the reticle, and then read the weight p of the weights. Read the motor speed n, flow rate Q, water temperature t, vacuum gauge reading p1, and outlet pressure gauge reading p2 on the dashboard and record them ； Reduce the flow rate by closing the valve slightly, repeat the above process to measure the various data corresponding to the other flow rate; it is generally advisable to repeat this 8–9 times. Procedure for automatic adjustment: Turn off the manual flow control valve, open the valve located in front of the electric control valve, turn on the power switch for the electric control valve, and supply power to it ； Use of the flow automatic regulator: ① Manual adjustment of the instrument: In manual mode, press the up button (∧) to increase the output to its maximum level, thereby opening the control valve fully. Then, once the flow rate stabilizes, hang the hook of the torque sensor on the motor’s lever arm, and rotate the disk below to align the balance arm with the target. Once the data becomes stable, press the “Data Collection” button in the software to collect the data. After collecting the data, lower the hook of the torque sensor. Use the down arrow key (∨) to reduce the flow rate; press the “Data Collection” button at each different flow rate to collect data ； ②Automatic valve adjustment: On the software interface, click the “Manual Adjustment in Progress” button to enter automatic adjustment mode (“Automatic Adjustment in Progress”). Then click the “Set Output” button, enter 100, and open the control valve to its maximum position. Once the flow rate stabilizes, hang the hook of the torque sensor on the motor’s balance arm, and rotate the disk below to align the balance arm with the target. Once the data becomes stable, press the “Data Collection” button in the software to collect the data. After collecting the data, remove the hook from the torque sensor. Change the output size of the settings, vary the traffic levels, and collect data at different traffic levels. 5. Turn off the power to all devices that were previously turned on. ●Thought and Analysis 1. Why is it necessary to fill the pump with water before starting a centrifugal pump? If it still won’t start after priming the pump, what do you think could be the reason? 2. Why is the pump’s outlet valve used to regulate flow? What are the advantages and disadvantages of this method? 3. After the pump starts, if the outlet valve cannot be opened, will the pressure gauge reading gradually increase? Why? 4. Is it reasonable to install a valve on the inlet pipeline of a properly operating centrifugal pump? Why? 5. Analyze the following: When using a water pump to transport brine with a density of 1200 kg/m³ (ignoring the effect of viscosity), do you think the pressure exerted by the pump will change at the same flow rate? Does the shaft power change? Skill Training 3: Centrifugal Pump Operation Simulation Training ●Training Objectives 1. Understand the structure and characteristics of centrifugal pumps, and learn how to operate them. 2. Master the analysis, identification, and troubleshooting of faults in centrifugal pump operation. ●Training Preparation 1. Understand the structure, characteristics, and basic principles of centrifugal pumps. 2. Master the basic operations of computer control systems. ●Training steps (key points): 1. Introduction to the process flow: Centrifugal pumps are one of the common devices used for transporting liquids in chemical production processes. Their working principle involves drawing in liquid due to the pressure difference between the inside and outside of the pump; the high-speed rotation of the impeller gives the liquid kinetic energy, which is then converted into pressure energy through diffuser tubes or vanes, thereby enabling the transportation of liquids. The pressurized liquid at approximately 40°C from a certain device enters the pressurized tank V101 via the control valve LV101; the liquid level in the tank is controlled by the level controller LIC101, which adjusts the feed rate to V101 ； The pressure inside the tank is controlled via proportional control by PIC101; PV101A and PV101B regulate the amount of nitrogen entering and leaving V101 respectively, thereby maintaining the tank pressure at 5.0 atm (gauge). The liquid in the tank is pumped out by pumps P101A/B; the flow rate at the pump outlets is regulated by flow controller FIC101 and then sent to other equipment. 2. The process flow (refer to the process simulation interface) is shown in Figure 1-34. Figures 1-34: Process flow diagram 3. Training program (see Table 1-13) Table 1-13: Training program for centrifugal pumps Number Project name Teaching objectives and key points 1 Procedures for cold-starting the system Master the standard startup procedures for the plant 2 Procedures for normal operation of the system Master the standard operating procedures for the plant 3 Procedures for normal shutdown of the system Master the standard shutdown procedures for the plant 4 Failure of pump P101A Master fault handling procedures 5 Jamming of valve FIC101 Master fault handling procedures 6 Blockage in the inlet pipeline of pump P101A Analyze the cause as soon as possible to restore feeding 7 Cavitation in pump P101A Master fault handling procedures 8 Air entrapment in pump P101A Master fault handling procedures 4. Operations (1) Preparation work ① Rotating the pump ； ②Verify inhalation conditions ； ③Adjust the packing or mechanical seal. (2) Preparations before starting the pump ① Fill the pump ； ②Exhaust (3) Start the centrifugal pump ①Start the centrifugal pump ； ②Fluid transport ； ③Adjusting operating parameters (4) Load adjustment: It is possible to change the on/off status of pumps and buttons, as well as the opening degree of manual control valves, along with the opening degrees of level control valves, flow control valves, and stage pressure control valves; observe the resulting effects. (5) Parking procedures ① Stop feeding to V101 tank ； ②Stop the pump ； ③Leakage from pump P101A ●Thoughts and analysis 1. When switching between pump P101A and pump P101B, how should their outlet valves VD04 and VD08 be adjusted, and why is this necessary? 2. After a centrifugal pump has been operating normally for some time, its flow rate begins to decrease. What could be the possible reasons for this? 3. How should high or low outlet pressure of a centrifugal pump be adjusted? 4. How should high or low inlet pressure of a centrifugal pump be adjusted? ●Extended training (see Table 1-14) Table 1-14: Handling of centrifugal pump accidents Accident Phenomenon Handling method Pump P101A is damaged 1. The outlet pressure of pump P101A drops sharply ； 2. The flow rate of FIC101 decreased sharply; switch to the backup pump P101B: (A) Fully open the inlet valve VD05 of pump P101B to fill the pump, and fully open the drain valve VD07 to discharge the non-condensable gases from P101B; once the indicator light turns green, close VD07 ； (B) After the filling pump and exhaust are completed, start P101B ； (C) Once the outlet pressure of pump P101B rises to 1.5–2 times the inlet pressure, open the outlet valve VD08 of P101B, while slowly closing the outlet valve VD04 of P101A, in order to minimize flow fluctuations ； (D) Once the inlet and outlet pressure indicators of P101B show normal values, stop P101A according to the shutdown sequence, close the inlet valve VD01 of pump P101A, and notify the maintenance staff. P101A pump cavitation 1. Fluctuations in the inlet and outlet pressures of the P101A pump ； 2. Fluctuations in the outlet flow rate of pump P101A (it fails to reach the normal value most of the time). Switch to the standby pumps P101B and P101A according to the pump switching procedure; pump gas trapping occurs. 1. The inlet and outlet pressures of pump P101A drop sharply ； 2. The flow rate of FIC101 has decreased sharply. Switch to the standby pump P101B according to the pump switching procedure. Reading material: Seamless switching in DCS operation. The production processes in large, modern chemical plants are mostly controlled by computers. A control loop generally consists of a primary sensing element, a transmitter, a computer, and an actuator (usually a control valve). The automatic regulation control mode (referred to as automatic mode) involves the transmitter converting the signals measured by the primary sensing element into electrical signals, which are then fed into a computer. The computer continuously compares the measured values (known as actual values) with the set values. It performs calculations based on the direction of deviation from the set values (whether they are too high or too low), the direction of change (whether they are moving further away from or closer to the set values), and the speed of change. Based on these considerations, the computer sends signals to the actuator to adjust its state, thereby achieving automatic regulation of the controlled variable. Its essence is to change the state of the actuator in order to counteract the disturbances caused by preceding and following processes on the control variable. The corresponding other operating state is the manual control state (abbreviated as manual mode). The manual mode means that the operator directly sends a signal to the actuator via the computer to determine its state; if the actuator is to change state, the operator must re-enter a signal on the computer. In computer operations, it is common to switch from manual mode to automatic mode (referred to as switching to automatic operation) in order to reduce the workload on operators; the computer then takes over the automatic adjustment of control variables, thereby ensuring the stable operation of the system. Before switching to automatic mode, it is necessary to gradually adjust the control variable in manual mode; switch to automatic mode only when the control variable is close to the set value. It is important not to switch to automatic mode when there is a large difference between the control variable and the set value in manual mode, as this will cause the computer to make large adjustments to the actuator once in automatic mode. At this point, the control variable approaches the set value by damping the oscillations; during this process, large fluctuations in the control variable can severely affect the safe and stable operation of the system, or even cause the system to shut down sequentially. Additionally, when operating in automatic mode and a significant adjustment of the load is required, this can generally be achieved by changing the set value. However, adjustments to the set value must be made gradually; the speed should not be too fast and the magnitude should not be too large, otherwise it will also cause significant fluctuations in the system.

Section 5: Gas Conveyance Machinery. Gas conveyance machinery is widely used in chemical production. The structure and principle of gas transfer machinery are generally similar to those of liquid transfer machinery, and it also includes types such as centrifugal, rotary, reciprocating, and fluid-action types. However, gases are compressible and have a density that is much lower than that of liquids (about 1/1000 of the liquid density), which gives gas transportation certain characteristics different from those of liquid transportation. Generally, gas compression machinery can be divided into four categories based on the final pressure or compression ratio (the ratio of outlet pressure to inlet pressure), as shown in Table 1-15. Table 1-15 Classification of Gas Compression Machinery Type Final Pressure/kPa (gauge) Compression Ratio Application Fan <15 1–1.15 Used for ventilation Blower 15–300 1.15–4 Used for air delivery Compressor >300 >4 Generates high pressure Vacuum Pump Local atmospheric pressure Determined by vacuum level Used for pressure reduction I. Centrifugal Fans The most commonly used fans in industry are centrifugal fans and axial flow fans. Axial flow fans generate very low air pressure and are generally used only for ventilation. For gas transportation, centrifugal fans are commonly used. (1) Working principle and structure of centrifugal fans. The working principle of centrifugal fans is the same as that of centrifugal pumps: there is a high-speed rotating impeller in the volute, and the centrifugal force generated by the rotation of this impeller increases the pressure of the gas, thereby enabling its expulsion. The structure of a centrifugal ventilator is also similar to that of a single-stage centrifugal pump. Figures 1-35 show a centrifugal fan. Its casing is also spiral-shaped, and the gas passage within the casing, which gradually widens, as well as the cross-section of its outlet, can be either square or circular; generally, medium and low-pressure fans use square cross-sections, while high-pressure fans tend to use circular ones. The fan impeller has a large number of blades that are relatively short; some of these blades are straight, while others are curved backward or forward. Figures 1-36 show a flat-blade impeller used in a low-pressure ventilator. The blades of medium and high-pressure fans are curved; therefore, the appearance and structure of high-pressure fans are more similar to those of single-stage centrifugal pumps. Based on the size of the impeller produced, centrifugal fans can be classified as follows: Low-pressure centrifugal fans: The outlet air pressure is below 0.9807×103 Pa (gauge pressure) ； Medium-pressure centrifugal ventilator: outlet air pressure is 0.9807×103～2.942×103 Pa (gauge pressure) ； High-pressure centrifugal ventilator: Outlet air pressure is 2.942×103～14.7×103 Pa (gauge pressure). (II) Main performance parameters of centrifugal fans The main performance parameters of centrifugal fans include air volume, air pressure, shaft power, and efficiency, as shown in Table 1-16. Table 1-16 Main performance parameters of centrifugal ventilators. Performance parameter, Unit, Definition: Air volume Q, m3/h, m3/s – The volume flow rate of gas passing through the inlet; Wind pressure HT, N/m2 – The energy acquired by unit volume of gas as it passes through the fan. , where (p2 – p1) is called the still wind pressure Hp ； ρu22/2 is called the dynamic wind pressure HK, where 1 denotes the fan inlet and 2 denotes the outlet. Shaft power P, total pressure efficiency in kW – no unit. (III) Selection of centrifugal fans: The selection process for centrifugal fans is similar to that for centrifugal pumps. The steps involved are as follows: (1) Calculate the air pressure required under the operating conditions of the delivery system, and convert it into the air pressure HT under experimental conditions. Characteristic curve of the centrifugal ventilator; the experimental medium is air at a pressure of 1.0133×105 Pa and a temperature of 20°C, under which the density of air ρ = 1.2 kg/m3. Since wind pressure is related to density, when the actual operating conditions differ from those in the aforementioned experiments, the wind pressure H’T under the operating conditions must be converted to the wind pressure HT under experimental conditions using the following formula; the fan should then be selected based on the value of HT. (1-30) In the equation, ρ is the density of the gas under operating conditions, in kg/m3 ； HT — wind pressure of the gas under operating conditions, N/m2. (2) Determine the type of fan based on the properties of the gas to be transported (such as clean air, flammable, explosive, or corrosive gases, as well as dust-containing gases) and the wind pressure range. If clean air or gases with properties similar to air are being transported, a standard type of centrifugal fan can be used. (3) Based on the actual air volume Q (measured at the fan inlet) and the air pressure HT under experimental conditions, select an appropriate model number from the characteristic curves or performance tables provided in the fan samples or product catalogs. The principles for making this selection are the same as those for centrifugal pumps, so no further explanation is needed. (4) Calculate the shaft power. The shaft power of a fan is related to the density of the gas being transported. The shaft power values listed in the fan’s performance table correspond to experimental conditions where the density of air is 1.2 kg/m3. If the density of the gas being transported differs from this value, an adjustment can be made using the following formula: Equation (1-31). In this equation, P’ represents the shaft power when the gas density is ρ’, in kW ； P —— Shaft power at a gas density of 1.2 kg/m3, in kW. II. Centrifugal Compressors 1. Working principle, main structure, and models of centrifugal compressors. Centrifugal compressors, also known as turbine compressors, have a structure and working principle similar to those of centrifugal ventilators and blowers. However, since a single-stage compressor cannot generate very high air pressure, centrifugal compressors are multi-stage; they have a large number of impeller stages, usually more than 10. The impeller rotates at a high speed, generally above 5000 r/min. Therefore, a very high outlet pressure can be generated. Due to the significant changes in gas volume and the considerable rise in temperature, centrifugal compressors are often divided into several sections, with each section comprising multiple stages; the diameter of the impellers decreases from one section to another, and the width of the impellers also reduces at each stage. Intermediate coolers are installed between sections to cool the gas, preventing its final temperature from becoming too high. As shown in Figure 1-37. The main advantages of centrifugal compressors are: small size and light weight, smooth operation, high and uniform exhaust volume, low floor space required, reliable operation, good adjustability, low demand for spare parts, easy maintenance, and completely oil-free compression, making them highly suitable for handling gases that should not come into contact with oil. Main disadvantages: Efficiency decreases when the actual flow rate deviates from the design value, high manufacturing precision is required, and it is difficult to process. In recent years, in chemical production, the use of centrifugal compressors has become increasingly widespread, except in cases where an extremely high final pressure is required. There are many methods for compiling the model codes of domestic centrifugal compressors. There is a method similar to that used for naming centrifugal blower models; for example, the DA35-61 centrifugal compressor features single-sided suction, a flow rate of 350 m3/min, 6 stages of impellers, and it was the first product designed using this approach. Another method for assigning model codes is to use the first pinyin letter of the name of the gas being compressed. For example, LTl85—13—1 is a centrifugal compressor for petroleum cracking gas. The flow rate is 185 m3/min, it has 13 impellers, and it is the first product designed of this type. When a centrifugal compressor is used as a chiller, its model code indicates its cooling capacity. There are other methods for assigning model codes; refer to the user manual for details. Fig. 1-37 Typical structure diagram of a centrifugal compressor 1- Suction chamber ； 2-Impeller ； 3-Diffuser ； 4--Curve ； 5-Refluxer ； 6- Ventriculus ； 7,8-Axial End Sealing ； 9-Diaphragm Sealing ； 10-Round Seal Replacement ； 11- Balance disk 2. Performance curve and regulation of centrifugal compressors: The performance curve of a centrifugal compressor is similar to that of a centrifugal pump, and it is determined through experiments. Figures 1-38 show the typical performance curve of a centrifugal compressor, which is quite similar to the characteristic curve of a centrifugal pump. However, its minimum flow rate Q is not zero, but equals a certain fixed value. Centrifugal compressors also have a design point at which the efficiency η is highest when the actual flow rate equals the design flow rate ； The greater the deviation between the flow rate and the design flow rate, the lower the efficiency ； Generally, the greater the flow rate, the smaller the compression ratio ε; that is, with a constant intake pressure, a higher flow rate results in a lower outlet pressure. When the actual flow rate is lower than the minimum flow rate indicated by the performance curve, the centrifugal compressor enters an unstable operating condition known as surge. At the onset of surge, due to the sudden drop in the outlet pressure of the compressor, gas cannot be delivered, and the gas with higher pressure in the outlet pipe flows back into the compressor. After gas backflow occurs, the amount of gas inside the compressor increases; once this volume exceeds the minimum flow rate, the compressor resumes normal operation in accordance with the pattern indicated by its performance curve, pushing the backflowed gas out again. Once the compressor resumes air supply, the amount of air inside the machine decreases; when this amount falls below the minimum level, the pressure drops suddenly again. The gas with higher pressure at the compressor outlet flows back into the compressor, causing the aforementioned phenomenon to repeat itself. In this way, the backflow and discharge of gas occur repeatedly. During this process, the compressor and exhaust system generate low-frequency, high-amplitude pressure fluctuations, which increase the stress on the impeller, amplify noise, cause the entire machine to vibrate violently, and prevent it from functioning. Due to the possibility of surge occurring in centrifugal compressors, their flow operation range is subject to quite strict limitations; it cannot be lower than the minimum flow rate within the stable operating range. Generally, the minimum flow rate is 70% to 85% of the design flow rate. The minimum flow rate of the compressor decreases as the speed of the impeller decreases, and it also decreases as the inlet pressure of the gas decreases. The methods for adjusting a centrifugal compressor include: ① Adjusting the opening degree of the outlet valve. The method is simple, but it increases the compression ratio and consumes more additional power, which is not economical. ②Adjust the opening degree of the inlet valve. The method is simple; essentially, it maintains a low compression ratio to reduce the outlet pressure. It requires less additional power compared to the aforementioned methods, which results in a lower minimum flow rate and an expanded stable operating range. This is a commonly used adjustment method. ③Change the speed of the impeller. The most economical method. It is convenient to use when equipped with a speed control device or powered by a steam engine. 3. Operation of centrifugal compressors (1) Preparations before startup ① Check whether the electrical switches, audio-visual signals, interlock devices, shaft position indicators, anti-surge devices, safety valves, and alarm systems are sensitive, accurate, and reliable. ②Check the fuel tank for water accumulation and impurities; the fuel level should be no lower than 2/3 of the tank’s height ； Are the oil pump and filter functioning properly? ； Are the valves in the fuel system operating smoothly and effectively? ③Check whether the cooling water system is unobstructed and free of leaks. ④Check the intake system for any blockages or accumulation of liquid, and ensure that the valves, safety valves, and check valves in the exhaust system operate smoothly and reliably. (2) Operation ① Before starting the host, turn on the oil pump first to ensure that all lubrication points are adequately supplied with oil; check whether the oil pressure and volume are normal ； Check whether the axis gauge is at zero and whether the inlet and outlet valves are open. ②After startup, the system was operated with no load for over 15 minutes without any abnormalities detected; then the vent valve was gradually closed to increase pressure, while the air supply valve was opened to release air outward. ③Pay regular attention to gas pressure, bearing temperature, vapor pressure or current level, gas flow rate, main engine speed, etc., and make adjustments promptly when issues are detected. ④Regularly check the operating sound and vibration of the compressor, and address any abnormalities promptly. ⑤Frequently check and adjust the exhaust temperature and pressure in each section to prevent them from being too high or too low. ⑥Strictly prevent the compressor from running out of pressure or reversing, to avoid damaging the equipment. (3) Parking: When parking, close the intake and exhaust valves simultaneously. First, shut down the main engine, as well as the oil pump and cooling water. If the temperatures of the cylinders and rotor are high, the rotor should be rotated 180º every 15 minutes until the temperature drops to 30°C, in order to prevent the rotor from bending. (4) An emergency stop should be initiated in the following situations: ① In case of power loss, fuel loss, or steam loss ； ②The oil pressure drops rapidly, exceeding the specified limit and causing the interlock device to stop functioning ； ③When the bearing temperature continues to rise despite exceeding the alarm value ； ④When the motor is smoking and producing sparks ； ⑤When the axis gauge indicates a value above the limit and the protection device is not functioning ； ⑥When the compressor experiences severe vibration or abnormal noises. Skill Training 4: Simulation Training for Centrifugal Compressor Operation ●Training Objectives 1. Understand the structure and characteristics of centrifugal compressors, and learn how to operate them. 2. Master the methods of flow regulation for centrifugal compressors. 3. Master the analysis, identification, and troubleshooting of faults in centrifugal pump operation. ●Training Preparation 1. Understand the structure, characteristics, and basic principles of centrifugal compressors. 2. Process flow description: As shown in Figures 1-39, low-pressure methane with a pressure of 1.2–1.6 atm (absolute) and a temperature of around 30°C enters the methane storage tank FA311 via valve VD01; the pressure inside the tank is maintained at 300 mmH2O. Methane exits from storage tank FA311 and enters compressor GB301; after being compressed by the compressor, it is discharged as medium-pressure methane with a pressure of 4.03 atm (absolute) and a temperature of 160°C, and then enters the fuel system via manual control valve VD06. To prevent surging in the compressor, this process includes a return line from the compressor outlet to tank FA311, that is, a pipeline that runs from the compressor outlet, through heat exchanger EA305 and valve PV304B, to the tank. The returned methane is cooled by cooler EA305. Additionally, tank FA311 is equipped with an overpressure protection controller PIC303; when the pressure in FA311 becomes too high, low-pressure methane can be released through PIC303 to the flare system, thereby reducing the pressure in the tank. The compressor GB301 is driven coaxially by the steam turbine GT301; the steam supplied to the turbine is medium-pressure steam at 15 at (absolute pressure) coming from the steam network, while the exhaust steam is low-pressure steam at 3 at (absolute pressure) that enters the low-pressure steam network. The process **has two sets of automatic control systems: PIC303 serves as the overpressure protection controller for FA311; it automatically opens the flare valve when the pressure in tank FA311 becomes too high. PRC304 is a pressure range control system; when the output of this regulator is within the 50%–100% range, the output signal is sent to the speed control system of the steam turbine GT301, namely PV304A, in order to control the amount of medium-pressure steam supplied, thereby adjusting the compressor’s rotation speed between 3350 and 4704 rpm. At this time, valve PV304B is fully closed. When the output of this regulator is within the 0% to 50% range, the opening degree of the PV304B valve varies within the 100% to 0% range. During the initial acceleration phase, the turbine’s speed is increased manually using the controller HC311; once the speed exceeds 3450 rpm, it can be switched to being controlled by PIC304 via a switch. Figure 1-39 Simulation process flow diagram of centrifugal compressors ● Training steps (key points) 1. Startup Ⅰ Preparatory work before startup (1) Starting utility systems ； (2) Drive with the oil circuit active ； (3) Turn the shaft ； (4) Warm-up ； (5) Start up of cooling water. Ⅱ Tank FA311 is filled with low-pressure methane. (1) Open the PIC303 control valve to send the gas to the flare, with an opening degree of 50% ； (2) Open the FA311 inlet valve; set VD11 at 50% opening, and slightly open VD01 ； (3) Open valve PV304B and slowly pressurize the system; adjust the safety valves VD03 and VD01 at the top of FA311 to maintain the system pressure at 300~500 mmH2O ； (4) Adjust the opening of the PIC303 valve to maintain the pressure at 0.1 atm. Ⅲ Startup of single-stage turbine compressor (1) Manual speed increase ； (2) Tripping test (the execution of this operation is determined based on specific circumstances) ； (3) Increase speed manually again ； (4) Start the speed control system ； (5) Adjust the operating parameters to normal values. 2. Compressor anti-surge operation: (1) After starting the speed control system, the PV304A valve must be opened slowly. During this process, the bypass valve of the outlet safety valve can be opened appropriately to adjust the outlet pressure and prevent surge from occurring ； (2) When methane enters the fuel system, the PIC303 valve should be closed ； (3) When the compressor speed reaches full speed, the outlet safety bypass valve should be closed. 3. Parking Operations I: Normal Parking Process (1) Shut down the speed control system ； (2) Manual speed reduction ； (3) Stop FA311 feed II – Emergency shutdown (1) Press the emergency shutdown button ； (2) Confirm that the PV304B valve and PIC303 are in the open position ； (3) Close the turbine steam inlet valve and outlet valve ； (4) Methane gas is discharged from the PIC303 flare ； (5) The rest is the same as normal parking. 4. Accident scenarios (see Table 1-17) Table 1-17 Accident handling Accident name Main symptoms Handling method Excessively high inlet pressure Rising pressure in tank FA311 Manually open the vent valve PV303 appropriately Excessively high outlet pressure Rising pressure at the compressor outlet Open the valve VD06 leading to the fuel system Broken inlet pipe Falling pressure in storage tank FA311 Open the inlet valves VD01 and VD11 of FA311 Broken outlet pipe Falling pressure at the compressor outlet Emergency shutdown Excessively high inlet temperature Rising readings on TI301 and TI302 Emergency shutdown ●Thoughts and analysis 1. What is surge? How to prevent surge? 2. In manual speed control mode, why is the anti-surge valve PV304B on the anti-surge line kept fully open to prevent surge? 3. Using Bernoulli’s equation, explain how a compressor does work and facilitates the conversion between kinetic energy, pressure, and temperature. 4. Based on this unit, understand the concepts of cranking, manual speed increase, and automatic speed increase. 5. What are the advantages of centrifugal compressors? Chapter Summary, Review & Reflections 1. What are absolute pressure, gauge pressure, and vacuum? What are the things to keep in mind when performing pressure calculations? 2. What is the viscosity of a fluid? How to measure it? 3. What are steady-flow systems and unsteady-flow systems? Give an example to illustrate. 4. What issues should be considered when applying Bernoulli’s equation? How to select the reference plane and cross-section? 5. It is known that water flows in a horizontal pipe from A to B. Which is larger, ① or, at the A and B sections? Why? ②Which one is larger, the volumetric flow rate qVA or qVB? Why? ③Which is larger, uA or uB? Why? 6. What are the types of fluid flow? How to tell? What is the laminar inner layer? What factors determine the thickness of the laminar inner layer? 7. What causes flow resistance? What are the components that make up flow resistance? 8. For a fluid flowing in laminar flow within a circle or a straight pipe, if the pipe diameter is reduced by half, how do the flow velocity, Reynolds number, and pressure drop change? 9. What are the ways to reduce flow resistance? 10. Why is it necessary to choose an appropriate flow rate for fluids in pipes? How to choose? 11. Describe the principles for the layout and installation of pipelines. 12. Main structural components of centrifugal pumps, working principle. 13. What is cavitation? What damage does cavitation cause? How can cavitation be prevented? 14. Methods for regulating the flow rate of centrifugal pumps, the basic principle and advantages of using an outlet valve to control flow rate. 15. What is surge in a centrifugal compressor? How to prevent surge? 16. After a centrifugal pump has been operating normally for some time, its flow rate begins to decrease. What could be the possible reasons for this? Calculation problem 1: Given that the densities of sulfuric acid and water are 1830 kg/m3 and 998 kg/m3 respectively, determine the density of a sulfuric acid-water solution that is 60% by mass sulfuric acid. 2. When the atmospheric pressure is 760 mmHg, what is the absolute pressure at a depth of 20 m underwater in pa? 3. In a steady-flow system, water continuously flows from the large tube into the small tube. The inner diameter of the thick tube is d1=10 cm, and the inner diameter of the thin tube is d2=5 cm. When the flow rate is 4×10⁻³ m³/s, what are the flow velocities of water in the thick tube and the thin tube? 4. Water is drawn from the river using a steel pipe with an inner diameter of 100 mm, and then pumped into the reservoir. Water enters from the bottom of the pool; the water level in the pool is 30 m above the river surface. The flow velocity of the water inside the pipe is 1.5 m/s, and the pressure loss in the pipeline is 1.72 m. If the shaft power of the pump is 5 kW, what is the efficiency of the pump? 5. Water flows from the water tower to various users through pipes with an inner diameter of 200 mm. The water level inside the water tower is 25 m above the end of the discharge pipe, and the water level in the tower is kept constant. Given that the total energy loss in the pipeline is 24.5 mH2O, what is the volumetric flow rate of water in the pipeline in m3/h? 6. A liquid with a viscosity of 8×10-3 Pa·s and a density of 850 kg/m3 flows through a steel pipe with an inner diameter of 14 mm. The flow velocity of the liquid is 1 m/s. Calculate the Reynolds number Re and determine what type of flow regime this represents. 7. Water flows inside a horizontal steel pipe with dimensions of φ38×1.5 mm; the temperature is 293 K, the flow velocity is 2.5 m/s, and the length of the pipe is 100 m. Given the absolute wall roughness ε=0.3 mm, determine the friction loss in the straight pipe. Question 9, Figure 8: As shown, this is a schematic diagram of the chilled brine circulation system. The density of the saltwater is 1100 kg/m3, and the flow rate is 36 m3/hr. The total resistance loss from A to B is 98.1 J/kg, and from B to A it is 49 J/kg, with the pipe diameter remaining constant. Find: (1) The effective power Ne of the pump ； (2) If the pressure gauge reading at point A is 2.5 kg/cm2, what is the pressure gauge reading at point B in kg/cm2? 9. A centrifugal pump transports fluid with a density of 850 kg/m³ at a flow rate of 71 m³/h. For the solution, the pressure gauge on the discharge pipeline reads 3.2 atm, while the vacuum gauge on the suction pipeline reads 220 mmHg; the vertical distance between these two gauges is 0.4 m. The diameters of the pump’s inlet and outlet pipes are equal. The flow resistance in the pipeline between the two pressure taps can be ignored. If the pump’s efficiency is 60%, determine the shaft power of this pump. 10. Water is drawn from the river using a steel pipe with an inner diameter of 100 mm and sent to the reservoir. The water level in the pool is 30 m above the river level, and the length of the pipeline (including the equivalent length of the fittings) is 60 m. The flow velocity of water in the pipe is 1.5 m/s. The warehouse currently has centrifugal pumps of the following four specifications; please select a suitable pump from them. The friction coefficient of the pipeline is known to be 0.028. Pump I II III IV Flow rate Q, L/s: 17 16 15 12 Head H, mH2O: 42 38 35 32. 11. A butane solution at a temperature of 30°C is stored in a tank in a workshop; the pressure at the liquid surface of the tank is 3.2 atm (absolute), and the lowest point of the liquid level is 2.4 m below the centerline of the pump inlet pipe. It is known that at 30°C, the saturated vapor pressure of butane is 3.1 atm, its relative density is 0.58, the head loss in the pump’s suction line is 1.6 m, and the pump’s net positive suction head is 3.2 m. Can the installation height of this pump ensure normal operation? The main symbol in this chapter: A —— cross-sectional area of flow, m2 ； d, D —— diameter, m ； h —— height, m ； hf —— straight pipe resistance, J/kg ； —— Local resistance, J/kg ； —— Total energy loss, J/kg ； He—— The effective head provided by the conveying equipment to the fluid, in meters ； ——Head loss, m ； l —— length of the straight pipe, m ； —— Equivalent length of local components such as fittings and valves, in meters ； m —— mass of the fluid, kg ； M —— kilomolar mass of the fluid, kg/kmol ； Mm —— average molar mass of the mixed fluid, kg/kmol ； Pe —— the effective power of the conveying machinery, W ； p —— pressure of the fluid, Pa ； R —— universal gas constant, 8.314 kJ/kmol•K ； Re——Reynolds number, unitless ； t —— Celsius temperature,℃ ； T — Absolute temperature, K ； u —— flow velocity of the fluid, m/s ； umax — maximum flow velocity at the flow cross-section, m/s ； qv——volumetric flow rate, m3/s ； qm——mass flow rate, kg/s ； We—— additional work, J/kg ； z —— height, distance, in m. ρ —— Density of the fluid, kg/m3 ； wi —— the mass fraction of each component in the mixture ； ν—— dynamic viscosity, m2/s ； μ — dynamic viscosity, Pa•s ； ε —— absolute roughness, m ； ——Local drag coefficient, unitless λ – Friction coefficient, unitless ； η—— Efficiency ； Hg – The allowable installation height of the centrifugal pump, in m.
HK – The dynamic pressure of the centrifugal fan, in m.
Hp – The static pressure of the centrifugal fan, in m.
HT – The total pressure of the centrifugal fan, in m.
n – The rotational speed of the centrifugal pump impeller, in r/min.
Δh – The allowable net positive suction head of the centrifugal pump, in m.
Pv – The saturated vapor pressure of the liquid, in Pa.
Q – The flow rate of the pump or fan, in m3/s

Section 5: Gas Conveyance Machinery. Gas conveyance machinery is widely used in chemical production. The structure and principle of gas transfer machinery are generally similar to those of liquid transfer machinery, and it also includes types such as centrifugal, rotary, reciprocating, and fluid-action types. However, gases are compressible and have a density that is much lower than that of liquids (about 1/1000 of the liquid density), which gives gas transportation certain characteristics different from those of liquid transportation. Generally, gas compression machinery can be divided into four categories based on the final pressure or compression ratio (the ratio of outlet pressure to inlet pressure), as shown in Table 1-15. Table 1-15 Classification of Gas Compression Machinery Type Final Pressure/kPa (gauge) Compression Ratio Application Fan <15 1–1.15 Used for ventilation Blower 15–300 1.15–4 Used for air delivery Compressor >300 >4 Generates high pressure Vacuum Pump Local atmospheric pressure Determined by vacuum level Used for pressure reduction I. Centrifugal Fans The most commonly used fans in industry are centrifugal fans and axial flow fans. Axial flow fans generate very low air pressure and are generally used only for ventilation. For gas transportation, centrifugal fans are commonly used. (1) Working principle and structure of centrifugal fans. The working principle of centrifugal fans is the same as that of centrifugal pumps: there is a high-speed rotating impeller in the volute, and the centrifugal force generated by the rotation of this impeller increases the pressure of the gas, thereby enabling its expulsion. The structure of a centrifugal ventilator is also similar to that of a single-stage centrifugal pump. Figures 1-35 show a centrifugal fan. Its casing is also spiral-shaped, and the gas passage within the casing, which gradually widens, as well as the cross-section of its outlet, can be either square or circular; generally, medium and low-pressure fans use square cross-sections, while high-pressure fans tend to use circular ones. The fan impeller has a large number of blades that are relatively short; some of these blades are straight, while others are curved backward or forward. Figures 1-36 show a flat-blade impeller used in a low-pressure ventilator. The blades of medium and high-pressure fans are curved; therefore, the appearance and structure of high-pressure fans are more similar to those of single-stage centrifugal pumps. Based on the size of the impeller produced, centrifugal fans can be classified as follows: Low-pressure centrifugal fans: The outlet air pressure is below 0.9807×103 Pa (gauge pressure) ； Medium-pressure centrifugal ventilator: outlet air pressure is 0.9807×103～2.942×103 Pa (gauge pressure) ； High-pressure centrifugal ventilator: Outlet air pressure is 2.942×103～14.7×103 Pa (gauge pressure). (II) Main performance parameters of centrifugal fans The main performance parameters of centrifugal fans include air volume, air pressure, shaft power, and efficiency, as shown in Table 1-16. Table 1-16 Main performance parameters of centrifugal ventilators. Performance parameter, Unit, Definition: Air volume Q, m3/h, m3/s – The volume flow rate of gas passing through the inlet; Wind pressure HT, N/m2 – The energy acquired by unit volume of gas as it passes through the fan. , where (p2 – p1) is called the still wind pressure Hp ； ρu22/2 is called the dynamic wind pressure HK, where 1 denotes the fan inlet and 2 denotes the outlet. Shaft power P, total pressure efficiency in kW – no unit. (III) Selection of centrifugal fans: The selection process for centrifugal fans is similar to that for centrifugal pumps. The steps involved are as follows: (1) Calculate the air pressure required under the operating conditions of the delivery system, and convert it into the air pressure HT under experimental conditions. Characteristic curve of the centrifugal ventilator; the experimental medium is air at a pressure of 1.0133×105 Pa and a temperature of 20°C, under which the density of air ρ = 1.2 kg/m3. Since wind pressure is related to density, when the actual operating conditions differ from those in the aforementioned experiments, the wind pressure H’T under the operating conditions must be converted to the wind pressure HT under experimental conditions using the following formula; the fan should then be selected based on the value of HT. (1-30) In the equation, ρ is the density of the gas under operating conditions, in kg/m3 ； HT — wind pressure of the gas under operating conditions, N/m2. (2) Determine the type of fan based on the properties of the gas to be transported (such as clean air, flammable, explosive, or corrosive gases, as well as dust-containing gases) and the wind pressure range. If clean air or gases with properties similar to air are being transported, a standard type of centrifugal fan can be used. (3) Based on the actual air volume Q (measured at the fan inlet) and the air pressure HT under experimental conditions, select an appropriate model number from the characteristic curves or performance tables provided in the fan samples or product catalogs. The principles for making this selection are the same as those for centrifugal pumps, so no further explanation is needed. (4) Calculate the shaft power. The shaft power of a fan is related to the density of the gas being transported. The shaft power values listed in the fan’s performance table correspond to experimental conditions where the density of air is 1.2 kg/m3. If the density of the gas being transported differs from this value, an adjustment can be made using the following formula: Equation (1-31). In this equation, P’ represents the shaft power when the gas density is ρ’, in kW ； P —— Shaft power at a gas density of 1.2 kg/m3, in kW. II. Centrifugal Compressors 1. Working principle, main structure, and models of centrifugal compressors. Centrifugal compressors, also known as turbine compressors, have a structure and working principle similar to those of centrifugal ventilators and blowers. However, since a single-stage compressor cannot generate very high air pressure, centrifugal compressors are multi-stage; they have a large number of impeller stages, usually more than 10. The impeller rotates at a high speed, generally above 5000 r/min. Therefore, a very high outlet pressure can be generated. Due to the significant changes in gas volume and the considerable rise in temperature, centrifugal compressors are often divided into several sections, with each section comprising multiple stages; the diameter of the impellers decreases from one section to another, and the width of the impellers also reduces at each stage. Intermediate coolers are installed between sections to cool the gas, preventing its final temperature from becoming too high. As shown in Figure 1-37. The main advantages of centrifugal compressors are: small size and light weight, smooth operation, high and uniform exhaust volume, low floor space required, reliable operation, good adjustability, low demand for spare parts, easy maintenance, and completely oil-free compression, making them highly suitable for handling gases that should not come into contact with oil. Main disadvantages: Efficiency decreases when the actual flow rate deviates from the design value, high manufacturing precision is required, and it is difficult to process. In recent years, in chemical production, the use of centrifugal compressors has become increasingly widespread, except in cases where an extremely high final pressure is required. There are many methods for compiling the model codes of domestic centrifugal compressors. There is a method similar to that used for naming centrifugal blower models; for example, the DA35-61 centrifugal compressor features single-sided suction, a flow rate of 350 m3/min, 6 stages of impellers, and it was the first product designed using this approach. Another method for assigning model codes is to use the first pinyin letter of the name of the gas being compressed. For example, LTl85—13—1 is a centrifugal compressor for petroleum cracking gas. The flow rate is 185 m3/min, it has 13 impellers, and it is the first product designed of this type. When a centrifugal compressor is used as a chiller, its model code indicates its cooling capacity. There are other methods for assigning model codes; refer to the user manual for details. Fig. 1-37 Typical structure diagram of a centrifugal compressor 1- Suction chamber ； 2-Impeller ； 3-Diffuser ； 4--Curve ； 5-Refluxer ； 6- Ventriculus ； 7,8-Axial End Sealing ； 9-Diaphragm Sealing ； 10-Round Seal Replacement ； 11- Balance disk 2. Performance curve and regulation of centrifugal compressors: The performance curve of a centrifugal compressor is similar to that of a centrifugal pump, and it is determined through experiments. Figures 1-38 show the typical performance curve of a centrifugal compressor, which is quite similar to the characteristic curve of a centrifugal pump. However, its minimum flow rate Q is not zero, but equals a certain fixed value. Centrifugal compressors also have a design point at which the efficiency η is highest when the actual flow rate equals the design flow rate ； The greater the deviation between the flow rate and the design flow rate, the lower the efficiency ； Generally, the greater the flow rate, the smaller the compression ratio ε; that is, with a constant intake pressure, a higher flow rate results in a lower outlet pressure. When the actual flow rate is lower than the minimum flow rate indicated by the performance curve, the centrifugal compressor enters an unstable operating condition known as surge. At the onset of surge, due to the sudden drop in the outlet pressure of the compressor, gas cannot be delivered, and the gas with higher pressure in the outlet pipe flows back into the compressor. After gas backflow occurs, the amount of gas inside the compressor increases; once this volume exceeds the minimum flow rate, the compressor resumes normal operation in accordance with the pattern indicated by its performance curve, pushing the backflowed gas out again. Once the compressor resumes air supply, the amount of air inside the machine decreases; when this amount falls below the minimum level, the pressure drops suddenly again. The gas with higher pressure at the compressor outlet flows back into the compressor, causing the aforementioned phenomenon to repeat itself. In this way, the backflow and discharge of gas occur repeatedly. During this process, the compressor and exhaust system generate low-frequency, high-amplitude pressure fluctuations, which increase the stress on the impeller, amplify noise, cause the entire machine to vibrate violently, and prevent it from functioning. Due to the possibility of surge occurring in centrifugal compressors, their flow operation range is subject to quite strict limitations; it cannot be lower than the minimum flow rate within the stable operating range. Generally, the minimum flow rate is 70% to 85% of the design flow rate. The minimum flow rate of the compressor decreases as the speed of the impeller decreases, and it also decreases as the inlet pressure of the gas decreases. The methods for adjusting a centrifugal compressor include: ① Adjusting the opening degree of the outlet valve. The method is simple, but it increases the compression ratio and consumes more additional power, which is not economical. ②Adjust the opening degree of the inlet valve. The method is simple; essentially, it maintains a low compression ratio to reduce the outlet pressure. It requires less additional power compared to the aforementioned methods, which results in a lower minimum flow rate and an expanded stable operating range. This is a commonly used adjustment method. ③Change the speed of the impeller. The most economical method. It is convenient to use when equipped with a speed control device or powered by a steam engine. 3. Operation of centrifugal compressors (1) Preparations before startup ① Check whether the electrical switches, audio-visual signals, interlock devices, shaft position indicators, anti-surge devices, safety valves, and alarm systems are sensitive, accurate, and reliable. ②Check the fuel tank for water accumulation and impurities; the fuel level should be no lower than 2/3 of the tank’s height ； Are the oil pump and filter functioning properly? ； Are the valves in the fuel system operating smoothly and effectively? ③Check whether the cooling water system is unobstructed and free of leaks. ④Check the intake system for any blockages or accumulation of liquid, and ensure that the valves, safety valves, and check valves in the exhaust system operate smoothly and reliably. (2) Operation ① Before starting the host, turn on the oil pump first to ensure that all lubrication points are adequately supplied with oil; check whether the oil pressure and volume are normal ； Check whether the axis gauge is at zero and whether the inlet and outlet valves are open. ②After startup, the system was operated with no load for over 15 minutes without any abnormalities detected; then the vent valve was gradually closed to increase pressure, while the air supply valve was opened to release air outward. ③Pay regular attention to gas pressure, bearing temperature, vapor pressure or current level, gas flow rate, main engine speed, etc., and make adjustments promptly when issues are detected. ④Regularly check the operating sound and vibration of the compressor, and address any abnormalities promptly. ⑤Frequently check and adjust the exhaust temperature and pressure in each section to prevent them from being too high or too low. ⑥Strictly prevent the compressor from running out of pressure or reversing, to avoid damaging the equipment. (3) Parking: When parking, close the intake and exhaust valves simultaneously. First, shut down the main engine, as well as the oil pump and cooling water. If the temperatures of the cylinders and rotor are high, the rotor should be rotated 180º every 15 minutes until the temperature drops to 30°C, in order to prevent the rotor from bending. (4) An emergency stop should be initiated in the following situations: ① In case of power loss, fuel loss, or steam loss ； ②The oil pressure drops rapidly, exceeding the specified limit and causing the interlock device to stop functioning ； ③When the bearing temperature continues to rise despite exceeding the alarm value ； ④When the motor is smoking and producing sparks ； ⑤When the axis gauge indicates a value above the limit and the protection device is not functioning ； ⑥When the compressor experiences severe vibration or abnormal noises. Skill Training 4: Simulation Training for Centrifugal Compressor Operation ●Training Objectives 1. Understand the structure and characteristics of centrifugal compressors, and learn how to operate them. 2. Master the methods of flow regulation for centrifugal compressors. 3. Master the analysis, identification, and troubleshooting of faults in centrifugal pump operation. ●Training Preparation 1. Understand the structure, characteristics, and basic principles of centrifugal compressors. 2. Process flow description: As shown in Figures 1-39, low-pressure methane with a pressure of 1.2–1.6 atm (absolute) and a temperature of around 30°C enters the methane storage tank FA311 via valve VD01; the pressure inside the tank is maintained at 300 mmH2O. Methane exits from storage tank FA311 and enters compressor GB301; after being compressed by the compressor, it is discharged as medium-pressure methane with a pressure of 4.03 atm (absolute) and a temperature of 160°C, and then enters the fuel system via manual control valve VD06. To prevent surging in the compressor, this process includes a return line from the compressor outlet to tank FA311, that is, a pipeline that runs from the compressor outlet, through heat exchanger EA305 and valve PV304B, to the tank. The returned methane is cooled by cooler EA305. Additionally, tank FA311 is equipped with an overpressure protection controller PIC303; when the pressure in FA311 becomes too high, low-pressure methane can be released through PIC303 to the flare system, thereby reducing the pressure in the tank. The compressor GB301 is driven coaxially by the steam turbine GT301; the steam supplied to the turbine is medium-pressure steam at 15 at (absolute pressure) coming from the steam network, while the exhaust steam is low-pressure steam at 3 at (absolute pressure) that enters the low-pressure steam network. The process **has two sets of automatic control systems: PIC303 serves as the overpressure protection controller for FA311; it automatically opens the flare valve when the pressure in tank FA311 becomes too high. PRC304 is a pressure range control system; when the output of this regulator is within the 50%–100% range, the output signal is sent to the speed control system of the steam turbine GT301, namely PV304A, in order to control the amount of medium-pressure steam supplied, thereby adjusting the compressor’s rotation speed between 3350 and 4704 rpm. At this time, valve PV304B is fully closed. When the output of this regulator is within the 0% to 50% range, the opening degree of the PV304B valve varies within the 100% to 0% range. During the initial acceleration phase, the turbine’s speed is increased manually using the controller HC311; once the speed exceeds 3450 rpm, it can be switched to being controlled by PIC304 via a switch. Figure 1-39 Simulation process flow diagram of centrifugal compressors ● Training steps (key points) 1. Startup Ⅰ Preparatory work before startup (1) Starting utility systems ； (2) Drive with the oil circuit active ； (3) Turn the shaft ； (4) Warm-up ； (5) Start up of cooling water. Ⅱ Tank FA311 is filled with low-pressure methane. (1) Open the PIC303 control valve to send the gas to the flare, with an opening degree of 50% ； (2) Open the FA311 inlet valve; set VD11 at 50% opening, and slightly open VD01 ； (3) Open valve PV304B and slowly pressurize the system; adjust the safety valves VD03 and VD01 at the top of FA311 to maintain the system pressure at 300~500 mmH2O ； (4) Adjust the opening of the PIC303 valve to maintain the pressure at 0.1 atm. Ⅲ Startup of single-stage turbine compressor (1) Manual speed increase ； (2) Tripping test (the execution of this operation is determined based on specific circumstances) ； (3) Increase speed manually again ； (4) Start the speed control system ； (5) Adjust the operating parameters to normal values. 2. Compressor anti-surge operation: (1) After starting the speed control system, the PV304A valve must be opened slowly. During this process, the bypass valve of the outlet safety valve can be opened appropriately to adjust the outlet pressure and prevent surge from occurring ； (2) When methane enters the fuel system, the PIC303 valve should be closed ； (3) When the compressor speed reaches full speed, the outlet safety bypass valve should be closed. 3. Parking Operations I: Normal Parking Process (1) Shut down the speed control system ； (2) Manual speed reduction ； (3) Stop FA311 feed II – Emergency shutdown (1) Press the emergency shutdown button ； (2) Confirm that the PV304B valve and PIC303 are in the open position ； (3) Close the turbine steam inlet valve and outlet valve ； (4) Methane gas is discharged from the PIC303 flare ； (5) The rest is the same as normal parking. 4. Accident scenarios (see Table 1-17) Table 1-17 Accident handling Accident name Main symptoms Handling method Excessively high inlet pressure Rising pressure in tank FA311 Manually open the vent valve PV303 appropriately Excessively high outlet pressure Rising pressure at the compressor outlet Open the valve VD06 leading to the fuel system Broken inlet pipe Falling pressure in storage tank FA311 Open the inlet valves VD01 and VD11 of FA311 Broken outlet pipe Falling pressure at the compressor outlet Emergency shutdown Excessively high inlet temperature Rising readings on TI301 and TI302 Emergency shutdown ●Thoughts and analysis 1. What is surge? How to prevent surge? 2. In manual speed control mode, why is the anti-surge valve PV304B on the anti-surge line kept fully open to prevent surge? 3. Using Bernoulli’s equation, explain how a compressor does work and facilitates the conversion between kinetic energy, pressure, and temperature. 4. Based on this unit, understand the concepts of cranking, manual speed increase, and automatic speed increase. 5. What are the advantages of centrifugal compressors? Chapter Summary, Review & Reflections 1. What are absolute pressure, gauge pressure, and vacuum? What are the things to keep in mind when performing pressure calculations? 2. What is the viscosity of a fluid? How to measure it? 3. What are steady-flow systems and unsteady-flow systems? Give an example to illustrate. 4. What issues should be considered when applying Bernoulli’s equation? How to select the reference plane and cross-section? 5. It is known that water flows in a horizontal pipe from A to B. Which is larger, ① or, at the A and B sections? Why? ②Which one is larger, the volumetric flow rate qVA or qVB? Why? ③Which is larger, uA or uB? Why? 6. What are the types of fluid flow? How to tell? What is the laminar inner layer? What factors determine the thickness of the laminar inner layer? 7. What causes flow resistance? What are the components that make up flow resistance? 8. For a fluid flowing in laminar flow within a circle or a straight pipe, if the pipe diameter is reduced by half, how do the flow velocity, Reynolds number, and pressure drop change? 9. What are the ways to reduce flow resistance? 10. Why is it necessary to choose an appropriate flow rate for fluids in pipes? How to choose? 11. Describe the principles for the layout and installation of pipelines. 12. Main structural components of centrifugal pumps, working principle. 13. What is cavitation? What damage does cavitation cause? How can cavitation be prevented? 14. Methods for regulating the flow rate of centrifugal pumps, the basic principle and advantages of using an outlet valve to control flow rate. 15. What is surge in a centrifugal compressor? How to prevent surge? 16. After a centrifugal pump has been operating normally for some time, its flow rate begins to decrease. What could be the possible reasons for this? Calculation problem 1: Given that the densities of sulfuric acid and water are 1830 kg/m3 and 998 kg/m3 respectively, determine the density of a sulfuric acid-water solution that is 60% by mass sulfuric acid. 2. When the atmospheric pressure is 760 mmHg, what is the absolute pressure at a depth of 20 m underwater in pa? 3. In a steady-flow system, water continuously flows from the large tube into the small tube. The inner diameter of the thick tube is d1=10 cm, and the inner diameter of the thin tube is d2=5 cm. When the flow rate is 4×10⁻³ m³/s, what are the flow velocities of water in the thick tube and the thin tube? 4. Water is drawn from the river using a steel pipe with an inner diameter of 100 mm, and then pumped into the reservoir. Water enters from the bottom of the pool; the water level in the pool is 30 m above the river surface. The flow velocity of the water inside the pipe is 1.5 m/s, and the pressure loss in the pipeline is 1.72 m. If the shaft power of the pump is 5 kW, what is the efficiency of the pump? 5. Water flows from the water tower to various users through pipes with an inner diameter of 200 mm. The water level inside the water tower is 25 m above the end of the discharge pipe, and the water level in the tower is kept constant. Given that the total energy loss in the pipeline is 24.5 mH2O, what is the volumetric flow rate of water in the pipeline in m3/h? 6. A liquid with a viscosity of 8×10-3 Pa·s and a density of 850 kg/m3 flows through a steel pipe with an inner diameter of 14 mm. The flow velocity of the liquid is 1 m/s. Calculate the Reynolds number Re and determine what type of flow regime this represents. 7. Water flows inside a horizontal steel pipe with dimensions of φ38×1.5 mm; the temperature is 293 K, the flow velocity is 2.5 m/s, and the length of the pipe is 100 m. Given the absolute wall roughness ε=0.3 mm, determine the friction loss in the straight pipe. Question 9, Figure 8: As shown, this is a schematic diagram of the chilled brine circulation system. The density of the saltwater is 1100 kg/m3, and the flow rate is 36 m3/hr. The total resistance loss from A to B is 98.1 J/kg, and from B to A it is 49 J/kg, with the pipe diameter remaining constant. Find: (1) The effective power Ne of the pump ； (2) If the pressure gauge reading at point A is 2.5 kg/cm2, what is the pressure gauge reading at point B in kg/cm2? 9. A centrifugal pump transports fluid with a density of 850 kg/m³ at a flow rate of 71 m³/h. For the solution, the pressure gauge on the discharge pipeline reads 3.2 atm, while the vacuum gauge on the suction pipeline reads 220 mmHg; the vertical distance between these two gauges is 0.4 m. The diameters of the pump’s inlet and outlet pipes are equal. The flow resistance in the pipeline between the two pressure taps can be ignored. If the pump’s efficiency is 60%, determine the shaft power of this pump. 10. Water is drawn from the river using a steel pipe with an inner diameter of 100 mm and sent to the reservoir. The water level in the pool is 30 m above the river level, and the length of the pipeline (including the equivalent length of the fittings) is 60 m. The flow velocity of water in the pipe is 1.5 m/s. The warehouse currently has centrifugal pumps of the following four specifications; please select a suitable pump from them. The friction coefficient of the pipeline is known to be 0.028. Pump I II III IV Flow rate Q, L/s: 17 16 15 12 Head H, mH2O: 42 38 35 32. 11. A butane solution at a temperature of 30°C is stored in a tank in a workshop; the pressure at the liquid surface of the tank is 3.2 atm (absolute), and the lowest point of the liquid level is 2.4 m below the centerline of the pump inlet pipe. It is known that at 30°C, the saturated vapor pressure of butane is 3.1 atm, its relative density is 0.58, the head loss in the pump’s suction line is 1.6 m, and the pump’s net positive suction head is 3.2 m. Can the installation height of this pump ensure normal operation? The main symbol in this chapter: A —— cross-sectional area of flow, m2 ； d, D —— diameter, m ； h —— height, m ； hf —— straight pipe resistance, J/kg ； —— Local resistance, J/kg ； —— Total energy loss, J/kg ； He—— The effective head provided by the conveying equipment to the fluid, in meters ； ——Head loss, m ； l —— length of the straight pipe, m ； —— Equivalent length of local components such as fittings and valves, in meters ； m —— mass of the fluid, kg ； M —— kilomolar mass of the fluid, kg/kmol ； Mm —— average molar mass of the mixed fluid, kg/kmol ； Pe —— the effective power of the conveying machinery, W ； p —— pressure of the fluid, Pa ； R —— universal gas constant, 8.314 kJ/kmol•K ； Re——Reynolds number, unitless ； t —— Celsius temperature,℃ ； T — Absolute temperature, K ； u —— flow velocity of the fluid, m/s ； umax — maximum flow velocity at the flow cross-section, m/s ； qv——volumetric flow rate, m3/s ； qm——mass flow rate, kg/s ； We—— additional work, J/kg ； z —— height, distance, in m. ρ —— Density of the fluid, kg/m3 ； wi —— the mass fraction of each component in the mixture ； ν—— dynamic viscosity, m2/s ； μ — dynamic viscosity, Pa•s ； ε —— absolute roughness, m ； ——Local drag coefficient, unitless λ – Friction coefficient, unitless ； η—— Efficiency ； Hg – The allowable installation height of the centrifugal pump, in m.
HK – The dynamic pressure of the centrifugal fan, in m.
Hp – The static pressure of the centrifugal fan, in m.
HT – The total pressure of the centrifugal fan, in m.
n – The rotational speed of the centrifugal pump impeller, in r/min.
Δh – The allowable net positive suction head of the centrifugal pump, in m.
Pv – The saturated vapor pressure of the liquid, in Pa.
Q – The flow rate of the pump or fan, in m3/s

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