Exercise 3-2 Orifice Plates EXERCISE OBJECTIVE In this exercise, you will study how differential pressure flowmeters operate. You will describe the relationship between the flow rate and the pressure drop produced by an orifice plate, as well as the behavior of a liquid as it flows through an orifice plate. You will also measure the permanent pressure loss caused by an orifice plate. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Orifice plates Measuring principle Industrial applications Advantages and limitations Description of the supplied orifice plate Permanent pressure loss DISCUSSION Orifice plates An orifice plate (Figure 3-12) is a type of differential pressure flowmeter that can be used with liquids and gases. This primary flow element consists of a thin metal plate with a sharp-edged upstream aperture (orifice) usually machined in the middle of this plate. An orifice plate is normally inserted between two flanges at a location where the flow rate must be determined. Figure 3-12. Common design for an orifice plate. The orifice plate is typically used with a secondary device such as a DP transmitter to provide flow rate measurement. The DP transmitter measures the pressure differential between the two pressure taps, computes the corresponding flow rate, and displays the value locally and/or converts it into a signal that can be interpreted by a PID controller, PLC, or DCS. Measuring principle Like all differential pressure flowmeters, the orifice plate operates by restricting the area through which the liquid flows in order to produce a pressure drop. The pressure drop (P) is measured between a high-pressure tap (H), located Festo Didactic 87996-00 117
Ex. 3-2 Orifice Plates Discussion upstream of the restriction, and a low-pressure tap (L), located after the restrictions. Figure 3-13 shows the main steps of flow measurement using an orifice plate. High-pressure tap Low-pressure tap flow Figure 3-13. Flow measurement using an orifice plate (side view). 1. A pressure measurement is taken at the high-pressure tap, near the sharp-edged upstream aperture of the orifice. a There are several locations where taps for pressure measurement can be drilled. Considerations such as pipe diameter and flow stability may restrict the location of these taps. 2. The orifice forces the fluid to converge to flow through it, causing an increase in velocity and a corresponding decrease in static pressure. a The orifice plate of the training system is beveled on its downstream side to reduce frictional losses by minimizing the contact between the orifice and the moving liquid. 3. The fluid velocity reaches a maximum at a point slightly downstream from the orifice called the vena contracta. At this point, the pressure is at its minimum. A second pressure measurement is taken at or close to this location (low-pressure tap). The pressure differential is picked up by the DP transmitter and used to calculate the flow rate. 4. Beyond the vena contracta, the fluid spreads out and slows down causing the pressure to increase. The pressure recovers; but never up to its initial value measured at the high pressure tap. There is a permanent pressure loss mainly attributable to friction between the fluid and the aperture of the orifice plate. The volumetric flow rate Q is related to the pressure differential measured between the high and low pressure taps. If we assume that the measured liquid is incompressible and that the flow is turbulent, the volumetric flow rate can be determined with the following formula: (3-11) where is the volumetric flow rate is the discharge coefficient found in manufacturer s table is the area of the aperture facing upstream is the pressure differential between the high and low pressure taps is the fluid density is the aperture diameter-to-pipe internal diameter ratio (d/d) 118 Festo Didactic 87996-00
Ex. 3-2 Orifice Plates Discussion This relationship shows that the flow rate is proportional to the square root of the measured pressure differential, or (3-12) The discharge coefficient C takes into account the size of the restriction and the frictional losses through it. The magnitude of this coefficient is related to the Reynolds number of the flow. a If the mass flow rate must be determined, Equation (3-2) is used. Industrial applications Orifice plates are compatible with a wide variety of liquids, vapors, and gases used in the industry. Slurries and dirty liquids can be handled as well, but they require particular attention to avoid blocking the plate or the impulse lines. Orifice plates with slightly different designs exist for potentially problematic applications. For example, eccentric and segmental orifice plates (shown in Figure 3-14) are used when the fluid contains extraneous matter to a degree that the concentric orifice would become plugged. concentric eccentric segmental Figure 3-14. Eccentric and segmental designs. Advantages and limitations Orifice plates are versatile and used extensively in the industry. The main advantages are listed below: Inexpensive (the primary element itself, not necessarily its use) Easy to install Wide range of applications (provided the plate material and geometry are compatible with the fluid) However, some limitations should be considered: For large flows, pressure losses through an orifice plate can result in significant costs in power requirements. Slurries and dirty liquids can accumulate near the orifice plate. They are subject to erosion (causing inaccuracies). Small nicks and burrs on the sharp-edged side of the aperture can result in surprisingly large errors in measurement. Festo Didactic 87996-00 119
Ex. 3-2 Orifice Plates Discussion Description of the supplied orifice plate Figure 3-15 shows the orifice plate assembly provided with the training system. The orifice plate itself is a thin circular metal plate containing a small hole (orifice) in the middle. The orifice plate has a beta ratio ( ) of 0.45 and is mounted between a pair of flanges inserted directly into the flow stream. The liquid from the inlet port is directed toward the orifice plate through the upstream pipe. As the liquid flows through the restricted area of the orifice, a pressure drop occurs across the orifice plate. This pressure drop can be measured by means of two flange taps, located just upstream and downstream of the orifice plate. Orifice plate Low-pressure (L) port Outlet port High-pressure (H) tap Inlet port Downstream pipe Flanges Upstream pipe Figure 3-15. Orifice plate, Model 6552. 120 Festo Didactic 87996-00
Ex. 3-2 Orifice Plates Procedure Outline Permanent pressure loss The permanent pressure loss of differential pressure flowmeters, such as orifice plates, venturi tubes, or pitot tubes, is usually defined as the ratio of the pressure differential between the inlet and outlet of the instrument and the differential pressure between the high-pressure and low-pressure ports of the flowmeter: (3-13) where is the percentage of permanent pressure loss of the differential pressure flowmeter is the pressure differential between the inlet and outlet of the flowmeter is the pressure differential between the high-pressure and lowpressure ports of the flowmeter PROCEDURE OUTLINE The Procedure is divided into the following sections: Preparation question Set up and connections Measuring the pressure drop-versus-flow curve of the orifice plate Linearizing the orifice plate curve Permanent pressure loss of the orifice plate End of the exercise PROCEDURE Preparation question 1. What is the aperture diameter (d) of the orifice plate, Model 6552, if the pipe inside diameter is 1.54 cm (0.608 in)? Set up and connections 2. Set up the system shown in Figure 3-16. Note that the orifice plate can operate either vertically or horizontally. a Connect the pressure measuring devices to the high- and low-pressure ports. Festo Didactic 87996-00 121
Ex. 3-2 Orifice Plates Procedure H L Figure 3-16. Measuring flow rate with an orifice plate. 3. Power up the DP transmitter. 4. Make sure the reservoir of the pumping unit is filled with about 12 L (3.2 gal) of water. Make sure the baffle plate is properly installed at the bottom of the reservoir. 5. On the pumping unit, adjust pump valves HV1 to HV3 as follows: Open HV1 completely. Close HV2 completely. Set HV3 for directing the full reservoir flow to the pump inlet. 6. Turn on the pumping unit. Transmitter calibration This exercise can also be accomplished using the optional industrial differential-pressure transmitter (Model 46929). Should you choose this piece of equipment, refer to Appendix I for instructions on how to install and use the transmitter for pressure measurements. In steps 7 through 12, you will be adjusting the ZERO and SPAN knobs of the DP transmitter so that its output current varies between 4 ma and 20 ma when the flow rate through the orifice plate is varied between 0 L/min and 10 L/min (0 gal/min and 2.5 gal/min). 7. Connect a multimeter to the 4-20 ma output of the DP transmitter. 122 Festo Didactic 87996-00
Ex. 3-2 Orifice Plates Procedure 8. Make the following settings on the DP transmitter: ZERO adjustment knob: MAX. SPAN adjustment knob: MAX. LOW PASS FILTER switch: I (ON) 9. With the pump speed at 0%, turn the ZERO adjustment knob of the DP transmitter counterclockwise and stop turning it as soon as the multimeter reads 4.00 ma. 10. Adjust the pump speed until you read a flow rate of 10 L/min (2.5 gal/min) on the rotameter. This will be the maximum flow rate through the orifice plate. 11. Adjust the SPAN knob of the DP transmitter until the multimeter reads 20.0 ma. 12. Due to interaction between the ZERO and SPAN adjustments, repeat steps 9 through 11 until the DP transmitter output actually varies between 4.00 ma and 20.0 ma when the controller output is varied between 0% and 100%. Measuring the pressure drop-versus-flow curve of the orifice plate 13. Adjust the pump speed to obtain a flow rate of 10 L/min (2.5 gal/min). 14. Measure and record the difference between the readings of pressure gauges PI1 and PI2. This is the pressure drop produced by the orifice plate at maximum flow rate. a The DP transmitter should generate 100% output, i.e., 20 ma. 15. Adjust the pump speed until you read a flow rate of 2 L/min (0.5 gal/min) on the rotameter. In Table 3-2, record the analog output value generated by the DP transmitter for that flow rate. 16. Vary the pump speed to increase the flow rate by steps of 1 L/min (or 0.25 gal/min) until you reach 10 L/min (2.5 gal/min) on the rotameter. After each new flow setting, measure the analog output value generated by the DP transmitter and record it in Table 3-2. Festo Didactic 87996-00 123
Ex. 3-2 Orifice Plates Procedure Table 3-2. Orifice plate data. Rotameter flow L/min (gal/min) DP transmitter output ma Pressure drop PHL kpa (psi) kpa 1/2 (psi 1/2 ) 2 (0.50) 3 (0.75) 4 (1.00) 5 (1.25) 6 (1.50) 7 (1.75) 8 (2.00) 9 (2.25) 10 (2.50) 17. Stop the pump. 18. Based on the pressure drop you obtained in step 14 for an output of 20 ma, calculate the pressure drop PHL produced by the orifice plate for each flow rate listed in Table 3-2. Record your results in this table. 19. Using Table 3-2, plot the relationship between the flow rate and the pressure drop PHL. 20. From the curve obtained, is the relationship between the flow rate and the pressure drop produced by the orifice plate linear? Explain. Linearizing the orifice plate curve 21. Calculate the square root of the pressure drop for each flow rate listed in Table 3-2. Record your results in this table. 124 Festo Didactic 87996-00
Ex. 3-2 Orifice Plates Procedure 22. Using Table 3-2, plot the relationship between the flow rate and the square root of the pressure drop, P 1/2. 23. From the curve obtained, does a linear relationship exist between the flow rate and the square root of the pressure drop produced by the orifice plate? Explain. Permanent pressure loss of the orifice plate 24. Set up the system shown in Figure 3-17. It is the same set up as Figure 3-16 except that the pressure measuring devices are connected to the inlet and outlet pressure ports of the orifice plate instead of the H and P pressure taps. Inlet Outlet Figure 3-17. Measuring flow rate with an orifice plate. 25. Adjust the pump speed to obtain a flow rate of 10 L/min (2.5 gal/min). 26. Calibrate the DP transmitter so that the analog output generates 4 ma at 0 L/min (0 gal/min), and 20 ma at 10 L/min (2.5 gal/min). Adjust the pump speed and use the rotameter to obtain your two reference flow rate values. Festo Didactic 87996-00 125
Ex. 3-2 Orifice Plates Procedure 27. Measure and record the difference between the readings of pressure gauges PI1 and PI2. This is the permanent pressure drop loss produced by the orifice plate at maximum flow rate. a The DP transmitter should generate 100% output, i.e., 20 ma. 28. Adjust the pump speed until you read a flow rate of 2 L/min (0.5 gal/min) on the rotameter. In Table 3-3, record the analog output value generated by the DP transmitter for that flow rate. 29. By varying the pump speed, increase the flow rate by steps of 1 L/min (or 0.25 gal/min) until you reach 10 L/min (2.5 gal/min) on the rotameter. After each new flow setting, measure the analog output value generated by the DP transmitter and record it in Table 3-3. Table 3-3. Orifice plate permanent pressure loss. Rotameter flow L/min (gal/min) DP transmitter output ma Pressure loss PIO kpa (psi) Loss % 2 (0.50) 3 (0.75) 4 (1.00) 5 (1.25) 6 (1.50) 7 (1.75) 8 (2.00) 9 (2.25) 10 (2.50) 30. Stop the pump and turn off the pumping unit. 31. Based on the permanent pressure loss you obtained in step 27 for an output of 20 ma, calculate the permanent pressure loss PIO produced by the orifice plate for each flow rate listed in Table 3-3. Record your results in this table. 126 Festo Didactic 87996-00
Ex. 3-2 Orifice Plates Conclusion 32. Using Table 3-3, plot the relationship between the flow rate and the permanent pressure loss PIO. 33. From the curve obtained, does this relationship resemble the one between flow rate and pressure drop PHL (step 19)? Explain. 34. Calculate the percentage of permanent pressure loss for the orifice plate at different flow rates. Use Equation (3-13) and record your results in Table 3-3. 35. Is the percentage of permanent pressure loss relatively constant over the range of interest? Explain. End of the exercise 36. Disconnect the circuit. Return the components and hoses to their storage location. 37. Wipe off any water from the floor and the training system. CONCLUSION In this exercise, you learned that differential pressure flowmeters operate on Bernoulli's principle, which states that when the velocity of a liquid increases, the pressure of the liquid decreases. Conversely, when the velocity of the liquid decreases, the pressure of the liquid increases. You realized that a non-linear relationship exists between the flow rate and the pressure drop observed at the pressure taps of an orifice plate. In fact, the flow rate proves to be proportional to the square root of the pressure drop. Finally, you realized that the percentage of permanent pressure loss remains relatively constant for different flow rates. REVIEW QUESTIONS 1. What are the advantages and limitations of orifice plates? Festo Didactic 87996-00 127
Ex. 3-2 Orifice Plates Review Questions 2. What is meant by the permanent pressure loss caused by an orifice plate? 3. Briefly describe the behavior of the liquid as it flows through the orifice plate. 4. What is the vena contracta? 5. Is the relationship between the flow rate and the pressure drop produced by an orifice plate linear? Why? 128 Festo Didactic 87996-00