Calculation formula and example for differential pressure flow meters

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Calculation is an essential task for those working with differential pressure flowmeters. This post shares the common calculation formulas and examples related to differential pressure flowmeters; mastering these useful techniques can greatly enhance the efficiency of using such flowmeters. 1. The conversion relationship between differential pressure and flow rate in differential pressure flow meters: yunrun.com.cn/tech/1998.html. The differential pressure in differential pressure flow meters is proportional to the square of the flow rate; in other words, the flow rate is proportional to the square root of the differential pressure. This is expressed by the following formula: The scale unit of flow meters is expressed as a percentage of flow rate. When the lower limit of the differential pressure range is 0, the above formula applies. In this formula, △P represents any differential pressure ； Q is any flow rate ； △Pmax is the upper limit of the differential pressure ； Qmax is the upper limit of flow rate ； Let n be any percentage value representing flow rate. A certain differential pressure transmitter has a range of 0–40 kPa, corresponding to a flow rate of 0–160 m3/h, with an output signal of 4–20 mA. What is the flow rate when the output current of the differential pressure transmitter is 8 mA? What is the differential pressure? Solution: ① When the output of the differential pressure flow meter is 8 mA, the flow rate is 80 m3/h. ②It is known that when the differential pressure transmitter outputs 8 mA, the flow rate is 80 m3/h, which corresponds to 50% of the full scale. The differential pressure value at this point is 10 kPa, with an output current of 8 mA. 2. Conversion between volumetric flow rates under standard conditions and operating conditions The conversion formula for volumetric flow rates under standard conditions and operating conditions is as follows: In the formula, qv represents the volumetric flow rate under operating conditions, with the unit of m3/h ； qn is the volumetric flow rate under standard conditions, in units of m3/h ； P is the absolute pressure under operating conditions, in Pa ； Pn is the absolute pressure under standard conditions, in units of Pa ； T is the thermodynamic temperature in the operating state, in units of K ； Tn is the thermodynamic temperature under standard conditions, in units of K ； Z is the gas compression coefficient under operating conditions ； Zn is the gas compressibility coefficient at standard conditions ； A certain air flow meter is designed for a range of 0–2000 m3/h (at 20°C and 101.325 kPa). The pressure under operating conditions is 0.5 MPa, and the temperature is 60°C. Determine the volumetric flow rate under these operating conditions. Solution: Substitute the data into the formula to calculate the volumetric flow rate under operating conditions. The volumetric flow rate range of this flow meter when it is in operation is 0–460 m3/h. 3. Calculation for adjusting the range of a standard orifice plate: On-site, it is sometimes the case that the flow rate to be measured exceeds the maximum range of the orifice plate, or the flow rate is so low that it can only be displayed at less than 30% of the maximum range ； Emergency situations can be addressed by expanding or narrowing the differential pressure range. The basis for changing the range is a formula; since the maximum differential pressure and maximum flow rate of the flow meter are known, these two parameters can be used to carry out the calculations for changing the range. There is a orifice plate flow meter; its originally designed differential pressure range is 0-60 kPa, and its flow rate range is 0-10,000 kg/h. As the production scale has expanded and the process flow rate has exceeded the maximum capacity of the orifice plate, it is planned to increase the range to 0–15000 kg/h. Solution: The corresponding maximum pressure difference is calculated using the formula. The pressure difference values obtained through this simple calculation will have certain errors; they are not suitable for trade settlements, but they are acceptable for use in ordinary production environments, as the uncertainty does not pose a problem. However, the pressure loss will increase. When changing the range of a orifice plate, it is necessary to take into account the effects of many parameter changes; ideally, an iterative calculation method should be used. How big is the difference between iterative calculation and simple calculation? The following is a comparative example: A certain steam flow meter originally had a maximum flow rate of 70,000 kg/h and a maximum differential pressure of 100 kPa. Since the actual flow rate was too low, it was planned to increase the maximum flow rate to 35,000 kg/h. The result of iterative calculations using a computer showed that a maximum differential pressure of 24.837 kPa corresponded to this flow rate. Solution: Using a simple formula, the maximum differential pressure corresponding to 35,000 kg/h was calculated to be 25 kPa. If the result of the iterative calculations is taken as the standard value, the error resulting from the simple calculation is… When comparing the two methods, the error incurred by the simple calculation method is 0.656%, which is acceptable in many production environments, especially in emergency situations, as replacing the orifice plate requires ordering new parts and shutting down the equipment. To reduce errors, certain parameters can also be indirectly corrected in the flow integrator or DCS (such as the discharge coefficient, expansion coefficient, fluid density, etc.). To change the range of a standard orifice plate manually, first perform calculations; then set the range of the differential pressure transmitter based on those calculations and carry out calibration ； By setting new parameters for the flow integrator and DCS, it can be put into use. Flow integrator: yunrun.com.cn/product/999.html. There are limitations on modifying the range of orifice plates on one’s own; the newly set range cannot exceed the 3:1 adjustable range of standard orifice plates. When possible, it is better to use an iterative calculation method or redesign the orifice plate.