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Pressure Measurement I. Fill in the blanks 1. Pressure refers to the force that acts (uniformly and perpendicularly) on a unit area. 2. The legal unit of pressure is (pascal), denoted by the symbol (Pa). 3. The physical meaning of 1 Pa is: (the distributed force resulting from a force of 1 N acting perpendicularly on an area of 1 m2). 4. The unit of “Pa” is too small; in engineering, a pressure unit that is 1×106 times that of “Pa” is commonly used, namely (megapascal), denoted by the symbol (MPa). 5. 1atm = (1.01325×105) Pa = (10332.3) mmH2O = (760) mmHg = (1.03323) kgf/cm2. 6. 1 kgf/cm2 = (9.80665×104) Pa = (10,000) mmH2O = (735.562) mmHg = (0.967841) atm. 7. Absolute pressure refers to the pressure (expressed with absolute vacuum as the zero point). 8. Gauge pressure refers to the pressure expressed with ambient pressure (atmospheric pressure) as the zero reference. 9. When the gauge pressure is positive, it is abbreviated as (pressure); when it is negative, it indicates (negative pressure or vacuum). 10. The liquid column manometer measures based on the principle of (hydrostatics). 11. The relationship between absolute pressure, gauge pressure, and atmospheric pressure is (P_abs = P_gauge + P_atm). 12. Classified by working principle, pressure measuring instruments can be divided into (liquid-column pressure gauges), (piston pressure gauges), (elastic pressure gauges), (electrical measurement type pressure gauges), etc. 13. Liquid column pressure gauges are generally used for measuring (low pressure), (negative pressure), and (pressure differences); they can also be employed in laboratories for the precise measurement of low pressures and for calibrating instruments. 14. In a U-tube manometer, the difference in liquid level heights on the two sides is (directly proportional) to the gauge pressure of the pressure being measured, and it is independent of the cross-sectional area of the inner bore of the U-tube. 15. The measurement accuracy of a U-tube manometer is affected by (reading precision) and (capillary action of the working fluid), and the value is generally read using the (apex of the meniscus) as the reference point. 16. When measuring negative pressure with a single-tube manometer, the object under measurement should be connected to the (glass tube). 17. When measuring pressure with a single-tube manometer, its absolute error is half that of a U-tube manometer. 18. The inclined tube of a diagonal tube micropressure gauge should not be tilted too sharply; generally, it should be at least (15°–20°). 19. Common elastic elements used in elastic pressure measuring instruments include (diaphragm type), (bellows type), (bimetallic strip type), etc. 20. Bellows pressure gauges use (bellows with springs) as the conversion element for pressure to displacement, with the aim of (reducing the hysteresis of the elastic element). 21. Common diaphragm pressure gauges include (single-diaphragm pressure gauges) and (multi-diaphragm pressure gauges). 22. A Bourdon tube pressure gauge is mainly composed of components such as the (Bourdon tube), (gear transmission mechanism), (indication device), and (enclosure). 23. The hairspring of a Bourdon tube pressure gauge is mainly used to (overcome the degradation of the gauge caused by gaps in the transmission mechanism). 24. For pressure gauges used to measure acetylene, the Bourdon tube shall not be a (copper) Bourdon tube. 25. Diaphragm pressure gauges are mainly used to measure the pressure of media with properties such as (high corrosivity), (high viscosity), or (tendency to crystallize). 26. Electrical pressure gauges are instruments that measure pressure by (converting pressure into various electrical quantities). 27. Common electrical-type pressure gauges include (resistive), (inductive), (capacitive), (Hall effect), (strain gauge), (string vibration), (piezoelectric), etc. 28. A Hall-type remote pressure gauge is an electrical-type pressure gauge based on the (Hall effect). 29. Capacitive pressure measuring instruments operate on the principle that (changes in pressure cause a change in the capacitance Cx of the sensor). 30. The capacitance of a parallel-plate capacitor is given by the formula C = εS/(3.6πd), where ε represents the dielectric constant of the material between the plates, S represents the overlapping area of the two plates, and d represents the distance between the two plates. 31. Capacitive pressure measuring instruments typically achieve the conversion of pressure to capacitance by changing the distance (d) between the plates. 32. A differential capacitive differential pressure transmitter mainly consists of a (converter) and a (measurement circuit). 33. The principle of operation of a string-type pressure measuring instrument is that the tension (pressure) on the string is in a corresponding relationship with the vibration frequency generated by the string. 34. The range selection of the instrument is determined based on the magnitude of the (measured pressure). 35. The accuracy of instruments is primarily determined by the allowable (maximum error) for production. 36. The commonly used pressure calibration instruments are (piston pressure gauge) and (pressure calibration pump). 37. The calibration of pressure gauges is generally divided into two main categories: (static calibration) and (dynamic calibration). The static calibration method further includes two approaches: (comparison with a standard gauge) and (calibration using weights). 38. The on-site installation of a pressure gauge generally includes tasks such as (selection of the pressure measurement point), (installation of the pressure conduit), and (installation of the gauge itself). 39. When measuring liquid pressure, the pressure measurement point should be located (at the lower part of the pipe); when measuring gas pressure, it should be located (at the upper part of the pipe). 40. When measuring oxygen pressure, (oil-impregnated gaskets) and (organic compound gaskets) must not be used ； Copper gaskets must not be used when measuring acetylene pressure. II. Short Answer Questions 1. What is pressure? Are pressure and stress the same thing? Pressure refers to a force that acts uniformly and perpendicularly on a unit area; in physics, it is known as stress. 2. What is the physical meaning of 1 standard atmosphere? 1 standard atmosphere is defined as the pressure exerted by a mercury column 760 mm high, acting vertically on a surface, at a temperature of 0°C and under standard gravitational acceleration. 3. How is the value of pressure transmitted? To ensure consistency in pressure measurement values, **the metrology department maintains China’s pressure benchmarks, which serve as the highest standards for pressure measurements within the country. These benchmarks are also compared with those used in national defense efforts in order to achieve consistency in values. Pressure values start with the unit values of pressure as established by **reference instruments, and through various standard instruments and calibration methods, these values are transmitted step by step to various types of pressure measuring instruments in use. Working instruments are generally calibrated through direct comparison. 4. What are the general methods for pressure measurement? There are the liquid pressure balance method, the mechanical force balance method, the elastic force balance method, as well as methods that utilize the relationship between other physical properties and pressure to measure it. 5. What are the requirements for the working fluid in a liquid-column pressure gauge? A liquid-column pressure gauge requires that the working fluid do not mix with or react chemically with the medium being measured, that its density versus temperature relationship is known, and that it does not vaporize or solidify within the range of changes in ambient temperature. 6. How to read a U-tube manometer? Why? A U-tube manometer must be read at both ends of the U-tube, with the measured pressure value being calculated based on the difference in liquid column heights at those two ends ； Since it is difficult to achieve complete uniformity in the inner diameter of the tubes during U-tube fabrication, during testing the distance that the liquid column descends in one tube differs from the distance that it rises in the other tube; therefore, readings must be taken at both ends of the U-tube. 7. Why can a single-tube liquid column manometer only display one reading? Strictly speaking, a single-tube manometer should also calculate pressure based on the height difference of the liquid columns at its two ends. The reason is that in a single-tube manometer, one of the tubes is replaced by a cup of larger diameter; as a result, when measuring pressure, the medium under test presses against this large-diameter cup, causing the liquid column inside the cup to drop by a very small amount that can be ignored. In such cases, it is sufficient to read the height of the liquid column in the smaller tube only. 8. Why does a single-tube manometer have a smaller absolute error than a U-tube manometer? Since a single-tube manometer reads a value only once per measurement, while a U-tube manometer needs to read two values per measurement, the absolute error of the single-tube manometer is smaller. 9. Why can’t the inclination angle of the inclined tube microbarometer be too steep? Because an excessive inclination can cause the liquid level inside the inclined tube to stretch or even get disrupted, resulting in inaccurate readings; therefore, its inclination angle should generally be no less than 10° to 20°. 10. What are the advantages and disadvantages of liquid column pressure gauges? Advantages: Simple structure, easy to use, low cost, and can achieve high precision under certain conditions. Disadvantages: fragile, not pressure-resistant, difficult to read, large in size, low measurement range, and not suitable for remote transmission and automatic recording. 11. What is the measurement principle of a flexible pressure gauge? Measurement is carried out based on the principle that the reaction force generated by the compression deformation of the elastic element balances the pressure being measured. 12. What are the characteristics of elastic pressure gauges? It features a simple structure, durability, clear indicators, low cost, high accuracy, a wide measurement range, and is easy to use and maintain. 13. How many stages of amplification are there in the transmission amplification of a standard Bourdon tube pressure gauge? Which levels? Two levels. Level 1 is radian amplification ； Level 2 is angular magnification. 14. What are the possible reasons for large oscillations of the pointer on a Bourdon tube pressure gauge? First, the actual pressure fluctuations of the medium under test are large ； Second, the installation location of the pressure gauge experiences high vibration. 15. What are the possible reasons why the pointer of a Bourdon tube pressure gauge does not return to zero? The pointer is bent, the spring torque is insufficient, the pointer is loose, there is friction in the transmission gears, the Bourdon tube is blocked, and there is excess pressure inside the watch. 16. On what principle does a Hall effect remote pressure gauge work? It operates on the principle of the Hall effect. 17. How to determine the range of a pressure gauge? The range of the gauge is determined by the magnitude of the pressure being measured. For elastic pressure gauges, when selecting the gauge range, it is also necessary to leave sufficient headroom based on the properties of the medium being measured. Generally speaking, when measuring stable pressure, the maximum operating pressure should not exceed 2/3 of the range ； When measuring pulsating pressure, the maximum operating pressure should not exceed 1/2 of the range ； When measuring high pressures, the maximum operating pressure should not exceed 3/5 of the range ； To ensure accuracy, the minimum operating pressure should not be lower than 1/3 of the range. 18. What are the various steps involved in calibrating a capacitive pressure transmitter? Zero adjustment, range adjustment, damping adjustment, linear adjustment. 19. How to put into use a pressure gauge that has just been installed on site? The drain valve should be closed first, after which the root valve should be opened slowly to prevent the instruments from being damaged by shock. Once the root valve is fully open, it should be turned back half a turn to facilitate future maintenance. 20. What are the special requirements for installing a pressure gauge when measuring steam pressure? When measuring steam pressure, an annular tube should be installed at the bottom of the pressure gauge; this tube allows the pressure to be transmitted through the steam condensate, thereby preventing hot steam from entering the gauge directly and damaging it. III. Essay Questions 1. The atmospheric pressure is generally 100 kPa in absolute terms; why doesn’t such a high pressure crush the human body? Since there are many spaces within the human body that are in communication with the atmosphere, the body is also subjected to atmospheric pressure. The pressure inside the body pushes outward, while the pressure outside pushes inward; these two pressures are equal in magnitude but opposite in direction, thus canceling each other out. As a result, the surface pressure on the human body is zero, and therefore the body is never compressed. 2. Is gauge pressure always greater than absolute pressure? Why? Not necessarily. The concepts of the two are different. Gauge pressure refers to the pressure expressed with ambient pressure as the zero point; gauge pressure can be positive or negative ； Absolute pressure, on the other hand, is the pressure expressed with a complete vacuum as the zero point, and it is always positive. 3. How does a inclined tube micromanometer further reduce errors? The inclined tube micromanometer modifies the single-tube pressure gauge by tilting the small tube at a certain angle. As a result, the height H of the liquid column generated when measuring pressure with this instrument is equal to Lsinα (where L is the length of the liquid column in the inclined tube and α is the tilt angle of the tube). This means that, for the same pressure, the length of the liquid column in the inclined tube is 1/sinα times greater than the height of the liquid column in a single-tube pressure gauge, thereby improving the accuracy of readings and reducing errors. 4. A pressure transmitter with a negative pressure side sealed at 100 kPa ABS, having a measurement range of 0–100 kPa ABS, is moved to the Qinghai-Tibet Plateau and placed in the atmosphere; will the measured output current be 20 mA? Why? No, it should be less than 20mA. Since the atmospheric pressure on the Tibetan Plateau is definitely less than 100 kPa ABS, this means that the pressure detected by the transmitter is below the range pressure of 100 kPa ABS; therefore, its output should be less than the output at the full scale point (20 mA). 5. Can a piston-type pressure gauge be used to calibrate both ordinary pressure gauges and oxygen pressure gauges? Why? No. For safety reasons, oxygen pressure gauges must be free of oil, as oxygen can easily explode when in contact with grease. Ordinary pressure gauges tend to introduce grease into piston-type pressure meters, so specialized calibration devices and tools are required for calibrating oxygen pressure gauges. 6. If the pressure value is around 12 MPa, can a pressure gauge with a range of 0–16 MPa be used for measurement? Why? No. Because when measuring high pressures, the maximum operating pressure should not exceed 3/5 of the instrument’s range; in this case, the operating pressure is 12 MPa, which exceeds 3/5 of the instrument’s range (9.6 MPa). Therefore, a pressure gauge with a range of 0–16 MPa cannot be used for measurement. 7. To measure the output current of a capacitive pressure transmitter in use, can the multimeter probes be connected in parallel directly to the two terminals of the transmitter? Why? It’s not possible, because the internal resistance of the ammeter’s current range is very low; connecting it in parallel to the two wires of the transmitter essentially shorts out the entire circuit. The correct way to make a measurement is to connect the ammeter in series within the instrument’s circuit. 8. How to choose a suitable pressure gauge? First, it is necessary to determine the range of the instrument based on the magnitude and nature of the pressure to be measured ； Secondly, it is necessary to determine the accuracy of the instrument based on the maximum error permitted by production ； Finally, the type and model of the instrument are determined based on factors such as process requirements, properties of the medium, and the on-site environment. 9. In pneumatic pressure transmitters, how do the distance between the nozzle and the baffle change in relation to the transmitter’s input and output? In a pneumatic pressure transmitter, as the input pressure increases, the distance between the nozzle and the baffle decreases, which leads to an increase in the back pressure of the amplifier and thus an increase in the transmitter’s output signal. The same is true in reverse. 10. Does a rupture in the diaphragm of a diaphragm pressure gauge or a leak in the isolation oil affect the measurements? Why? Yes. Since diaphragm pressure gauges are generally used for measuring the pressure of media that are highly corrosive, highly viscous, or prone to crystallization, if the diaphragm ruptures or the sealing fluid leaks, the medium being measured can enter the pressure gauge directly, leading to corrosion or crystallization that can block the instrument and cause damage to it. Therefore, diaphragm pressure gauges must be used only when the diaphragm is intact and the sealing fluid is present in sufficient quantity. 11. Does an uneven inner diameter of the glass tube in a liquid column manometer affect pressure measurement? Why? No, because a liquid-column pressure gauge calculates pressure using the height difference between the liquid columns at its two ends, P = (H1 + H2)ρ, and it is independent of the inner diameter of the glass tube. 12. For pressure gauges used to measure high pressures, what are the specific requirements for the gauge itself and its installation? For safety reasons, in addition to choosing instruments with ventilation holes in their casings for measuring high pressures, such instruments should be installed away from walls or areas where people walk, to prevent accidents. 13. Once a piston-type pressure gauge has been calibrated at the factory, can it be used anywhere without further calibration? Why? No, because the accuracy class of piston pressure gauges is generally calibrated under conditions of an ambient temperature of around 20°C and a standard gravitational acceleration; therefore, when the temperature and gravitational acceleration at the site of calibration deviate significantly from these values, necessary corrections must be made. 14. What are the requirements for the installation of pressure guide tubes when mounting a pressure gauge? ①The diameter and length of the pressure guide tube should be chosen appropriately; generally, the inner diameter is 6–10 mm and the length is 3–50 m ； ②The horizontally installed pressure tap pipes should maintain a slope of (1:10) to (1:20) ； ③When the medium under test is prone to condensation or freezing, insulation and heating pipes should be installed ； ④When measuring liquid pressure, a gas collector should be installed at the highest point of the pressure tap; when measuring gas pressure, a gas-liquid separator should be installed at the lowest point of the pressure tap. When the medium may produce precipitates, a sedimentator should be placed before the instrument. 15. What is the working principle of a compression vacuum gauge? At a certain temperature, a given volume of the gas under test is compressed so that its absolute pressure increases to a level that can be measured using a liquid column method; the pressure of the gas under test is then determined based on the compression ratio. IV. Calculation Problems 1. A gauge pressure indicates 150 kPa, and the local atmospheric pressure is 100 kPa. What value will be indicated by an absolute pressure gauge? P_abs = P_surface + P_gravity = 150 + 100 = 250 kPa. 2. What is the pressure generated by a 1-meter water column under a standard gravity acceleration of 4°C? P = Hρg; the density of water at 4°C and under standard gravity is 1010 kg/m3, so p = Hρg = 1 × 9806.65 = 9806.65 Pa. 3. A pressure gauge has an accuracy class of 0.5, with a measurement range of 0–500 kPa. What is its maximum allowable error? δ = (500 – 0) × 0.5% = 2.5 kPa; the maximum allowable error is ±2.5 kPa. 4. If a pressure gauge installed 5 meters below the boiler indicates a pressure of 500 kPa for the gas phase in the boiler, what is the actual pressure of the gas phase in the boiler? It is installed 5 m below the boiler, which means that the instrument suffers from an error equivalent to a water column height of 5 m; therefore, the actual pressure is P = P_measured – P Introduce = 500 – Hγ = 500 – 5×10000/1000 = 450 kPa. 5. For a pressure transmitter with a range of 0–200 kPa, what is the output current when the input pressure is 150 kPa? I＝［150/(200-0)］×(20-4)+4＝16mA 6. There is a standard spring tube pressure gauge with a range of 0–100 kgf/cm2 and an accuracy class of 1.5; the calibration results are as follows. Is this gauge qualified? Standard indicated value / (kgf/cm2): 0255075100; Calibrated indicated value / (kgf/cm2): Forward stroke – 0.12, 4.64, 9.87, 4.29, 9.8; Reverse stroke – 0.32, 5.85, 0.17, 5.81, 100. Note: 1 kgf/cm2 ≈ 105 Pa. According to the measurement data in the table, the maximum absolute error is +0.8 kgf/cm2, and the maximum error during reverse movement is +1.6 kgf/cm2. The allowable error as specified in this table is (100 – 0) × 1.5% = 1.5 kgf/cm2. For a qualified pressure gauge, the error requirements are that both the absolute error and the backflow error must not exceed the gauge’s allowable error limit. In this case, the backflow error of 1.6 kgf/cm2 is greater than the gauge’s allowable error of 1.5 kgf/cm2; therefore, this gauge is not qualified. 7. The pressure of the medium to be measured is 1.0 MPa, and the ambient temperature around the instrument is ta = 55°C. A Bourdon tube pressure gauge is used for measurement, with a required measurement accuracy of δa = 1%. Determine the measurement range Pd and the accuracy class δd of this pressure gauge (the temperature coefficient β is 0.0001). According to the regulations, the value to be measured should not exceed 2/3 of the instrument’s measurement range Pd; thus, 2/3Pd ≥ Pa, which means Pd ≥ 3/2 × 1.0 = 1.5 MPa. Therefore, the measurement range of the pressure gauge should be set at 0–1.6 MPa. The temperature-induced error is: ΔPF = Pdβ(ta – 25) = 1.5 × 0.0001 × (55 – 25) = 0.0045 MPa. The allowable error of the pressure gauge is: δd = Required accuracy – Temperature-induced error = 1% – 0.0045 = 0.0055 MPa. The accuracy of the instrument is calculated as (0.0055/1.6 – 0) × 100% = 0.34%. Hence, a pressure gauge with a measurement range of 0–1.6 MPa and an accuracy class of 0.25 should be selected. 8. A vacuum pressure gauge has a range of -100 to 500 kPa. During calibration, the maximum error occurs at 200 kPa; the calibration gauge indicates 194 kPa at the upper limit and 205 kPa at the lower limit. Does this gauge meet the accuracy requirement of class 1.0? Variation % = Δmax / (Upper range limit – Lower range limit) × 100% = (205 – 194) / [500 – (-100)] × 100% = 1.83% > 1.0%; therefore, the requirement for a 1.0-level accuracy is not met. 9. A 1151 absolute pressure transmitter with a measurement range of 0–80 kPa (absolute pressure) is being calibrated using a standard vacuum gauge with a scale range of 100–0 kPa. If the local atmospheric pressure is 98 kPa, what will be the reading indicated by the vacuum gauge when the transmitter outputs 12 mA? Assume that when the input pressure to the transmitter is P_abs, the output current is 12 mA; then P_abs/(80–0) × 16 + 4 = 12, so P_abs = 40 kPa. 10. A absolute pressure transmitter has a range of –100 to 500 kPa. Determine the input pressures at which the transmitter outputs 4 mA, 8 mA, 12 mA, 16 mA, and 20 mA respectively. What is the output when the transmitter is powered on but no pressure signal is applied? (The local atmospheric pressure is 100 kPa.) The measurement range of the instrument is from -100 to 500 kPa; therefore, its full scale is 500 – (-100) = 600 kPa. Assuming that the input pressure is P_abs, and the transmitter outputs the corresponding current value, then: (P_abs/600) × 16 + 4 = 4, which gives P_abs1 = 0 kPa; (P_abs2/600) × 16 + 4 = 8, so P_abs2 = 150 kPa; (P_abs3/600) × 16 + 4 = 12, hence P_abs3 = 300 kPa; (P_abs4/600) × 16 + 4 = 16, meaning P_abs4 = 450 kPa; (P_abs5/600) × 16 + 4 = 20, thus P_abs5 = 600 kPa. When there is no input pressure, the transmitter still experiences an atmospheric pressure of 1 kPa; therefore, the output current is I = (100/600) × 16 + 4 = 6.67 mA. V. Graphing problems: 1. Illustrate graphically the relationship between atmospheric pressure, gauge pressure, absolute pressure, and negative pressure. 2. Try to draw the circuit connection diagram for calibrating the 1151 pressure transmitter. 3. Draw a schematic diagram of the principle of a force-balanced pressure transmitter. 4. Please draw the wiring diagram for calibrating an absolute pressure transmitter. 5. If a Bourdon tube pressure gauge reads 0 when measuring the pressure inside a device in the atmosphere, will it still read 0 when moved to a vacuum to measure the pressure inside that same device? Please illustrate with a diagram.