The relationship between differential pressure and flow rate
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In q=k×√△p, is the value of k fixed? On the Internet, when searching on Baidu, there are formulas like q multiplied by q equals k·△p – what does this mean? Does this refer to taking the square root in the table header or on the control panel?
I can’t see it clearly when I open this picture, sir.
Orifice plate flow meters can be widely used in industries such as petroleum, chemicals, natural gas, metallurgy, power generation, and pharmaceuticals for the continuous measurement of the volumetric or mass flow rate of various liquids, gases, natural gases, and steam. However, many people do not know how the flow rate is calculated using orifice plate flow meters. Today, I will discuss with you the calculation formula for orifice plate flow meters. In simple terms, the differential pressure value must be squared before it can be used to determine the flow rate. In practical applications, the calculations are quite complex, and it is rare for people to carry out these calculations manually; instead, software is used for such purposes. Let me give you a practical example to illustrate this.
I. Overview of Flow Rate Compensation: The measurement principle of differential pressure flow meters is based on the conversion between the mechanical energy of fluids. Fluid flowing in a horizontal pipe possesses dynamic pressure energy and static pressure energy (with potential energy being equal to zero); under certain conditions, these two forms of energy can be converted into one another, yet the total amount of energy remains constant. Taking the volumetric flow rate formula as an example: ? ???????????????? Qv = CεΑ/sqr(2ΔP/(1-β＾4)/ρ1)? Where: C is the discharge coefficient ； ? ε: Coefficient of thermal expansion; ? Α: Cross-sectional area of the orifice in the throttle device, in M＾2; ? ΔP: Differential pressure generated by the throttle device, in Pa; ? β: Diameter ratio; ? ρ1: Density of the fluid being measured at point I-I, in kg/m3; ? Qv: Volumetric flow rate, in m3/h. To meet the compensation requirements, temperature and pressure compensation must be applied. According to the calculation procedures, the process parameters at 50 degrees are used as a basis to determine the flow rate under any other temperature and pressure conditions. What’s important actually is the conversion of density. The calculation formula is as follows: Q = 0.004714187 *d²*ε*√(ΔP/ρ) Nm3/h at 0°C and 101.325 kPa, which represents the volumetric flow rate under standard atmospheric conditions at 0 degrees, as required to be displayed on the screen. ? Using the density formula: ? ρ = P * T50 / (P50 * T) * ρ50, where ρ, P, and T represent the values at any temperature and pressure; ρ50, P50, and T50 represent the process reference point at a gauge pressure of 0.04 MPa at 50 degrees. By combining these two formulas, it is possible to develop the program accordingly. ? ? II. Program Analysis ? 1. Instantaneous quantities – Temperature measurements: Must be converted to absolute Celsius temperature ； That is +273.15? Pressure: It must be converted to absolute pressure for calculation. Is it gauge pressure + atmospheric pressure? The compensation calculation is based on a specific formula, and the data is stored in the PLC’s registers. At the same time, monitor it on the intouch screen. ? ? 2. Accumulation: Accumulation is carried out by triggering on one of the rising edges of each 2-second scan; that is, the compensated flow rate value (Nm3/h) is divided by 1800 to convert it into a flow rate value per 2 seconds, and these values are then accumulated. The display screen has a reset function.
I. Overview of Flow Rate Compensation: The measurement principle of differential pressure flow meters is based on the conversion between the mechanical energy of fluids. Fluid flowing in a horizontal pipe possesses dynamic pressure energy and static pressure energy (with potential energy being equal to zero); under certain conditions, these two forms of energy can be converted into one another, yet the total amount of energy remains constant. Taking the volumetric flow rate formula as an example: ? ???????????????? Qv = CεΑ/sqr(2ΔP/(1-β＾4)/ρ1)? Where: C is the discharge coefficient ； ? ε: Coefficient of thermal expansion; ? Α: Cross-sectional area of the orifice in the throttle device, in M＾2; ? ΔP: Differential pressure generated by the throttle device, in Pa; ? β: Diameter ratio; ? ρ1: Density of the fluid being measured at point I-I, in kg/m3; ? Qv: Volumetric flow rate, in m3/h. To meet the compensation requirements, temperature and pressure compensation must be applied. According to the calculation procedures, the process parameters at 50 degrees are used as a basis to determine the flow rate under any other temperature and pressure conditions. What’s important actually is the conversion of density. The calculation formula is as follows: Q = 0.004714187 *d²*ε*√(ΔP/ρ) Nm3/h at 0°C and 101.325 kPa, which represents the volumetric flow rate under standard atmospheric conditions at 0 degrees, as required to be displayed on the screen. ? Using the density formula: ? ρ = P * T50 / (P50 * T) * ρ50, where ρ, P, and T represent the values at any temperature and pressure; ρ50, P50, and T50 represent the process reference point at a gauge pressure of 0.04 MPa at 50 degrees. By combining these two formulas, it is possible to develop the program accordingly. ? ? II. Program Analysis ? 1. Instantaneous quantities – Temperature measurements: Must be converted to absolute Celsius temperature ； That is +273.15? Pressure: It must be converted to absolute pressure for calculation. Is it gauge pressure + atmospheric pressure? The compensation calculation is based on a specific formula, and the data is stored in the PLC’s registers. At the same time, monitor it on the intouch screen. ? ? 2. Accumulation: Accumulation is carried out by triggering on one of the rising edges of each 2-second scan; that is, the compensated flow rate value (Nm3/h) is divided by 1800 to convert it into a flow rate value per 2 seconds, and these values are then accumulated. The display screen has a reset function.
In simple terms, your formula involves using a fixed coefficient multiplied by the square root of the current differential pressure. For example, if the coefficient is 123 and the current differential pressure is 4 kPa, then the flow rate formula is 123 X 2 = 246. Taking the square root is okay, but only one end should be taken; both ends cannot be used.
The K values in these two formulas are not the same; it can be considered that K1 equals the square root of K2； The square root of the differential pressure needs to be calculated only once; you can choose either the gauge or the central control unit.
Just look at a calculation sheet for an orifice plate and you’ll understand; the coefficients and formulas are all there