Exercise 3-2 Pressure Loss EXERCISE OBJECTIVE Familiarize yourself with the pressure loss phenomenon. DISCUSSION OUTLINE The Discussion of this exercise covers the following point: Pressure loss Major losses. Minor losses. DISCUSSION Pressure loss This exercise introduces you to pressure losses, which are of the highest importance in an industrial process control system. When a fluid flows through a pipe or a system component, it necessarily suffers pressure losses. It is important to minimize these pressure losses to ensure that the process runs properly. Pressure losses are intrinsically related to flow, some aspects of the theory related to pressure losses will clear up when you will study flow measurement in the next unit. Pressure losses, also known as pressure differentials, pressure drops, and head losses are due to some resistance to flow in the system. Friction and turbulences are the main causes of resistance to flow in a system. The pressure loss or head loss in a system is a measure of the total pressure loss. This measure includes losses in static, hydrostatic, and dynamic pressure types. The total pressure loss in a system is the sum of two types of pressure losses: major losses and minor losses. Major losses are due to the friction of the fluid in straight pipes, while minor losses are due to components, such as valves, and to bends and tees in the piping. (3-9) where is the total pressure loss is a major pressure loss is a minor pressure loss Festo Didactic 86005-00 45
Ex. 3-2 Pressure Loss Discussion Major losses Despite the name, a major loss is not necessarily the most important in terms of magnitude. Major losses are due to friction of the fluid with the pipe wall and to the friction between the molecules of fluid. Major losses are proportional to the length of the pipe, to the square of the fluid velocity, and to a friction factor. They are also inversely proportional to the diameter of the pipe. The Darcy-Weisbach equation shows the relationship between the major losses and these various variables: (3-10) where is a major pressure loss is the Darcy friction factor is the length of the pipe is the diameter of the pipe is the mean velocity of fluid is the acceleration due to gravity The Darcy friction factor depends on the type of flow, either laminar or turbulent. Laminar and turbulent flows will be defined and discussed in the next unit. For now, let us just say that the difference between these two is identified by a single dimensionless number, the Reynolds number. For a laminar flow, the friction factor depends only on the Reynolds number; the roughness of the pipe can be ignored. For a turbulent flow however, the roughness of the pipe becomes important and must be considered in the friction factor. Figure 3-25 shows that even if a surface looks smooth, such as the inside wall of a pipe, small imperfections make the surface very rough at the microscopic level. This roughness is one of the causes of friction inside a pipe. Minor losses Figure 3-25. Microscopic view of a smooth surface. Valves, measuring instruments, joints, bends, tees, and other components of a system cause variations in the velocity of the fluid. Minor losses depend on the geometry of the components. The variation in the velocity of the fluid causes a loss of pressure after the components. For some components, the minor loss is more important than the pressure loss due to friction (major loss). Actually, a closed or nearly closed valve brings the fluid to rest and offers an infinite resistance to the flow. Hence, it frequently happens that minor losses are more important in terms of magnitude than major losses. 46 Festo Didactic 86005-00
Ex. 3-2 Pressure Loss Procedure Outline Minor losses are proportional to the square of the fluid velocity and to a loss coefficient. A minor loss is expressed mathematically as: (3-11) where is a minor pressure loss is the loss coefficient is the mean velocity of fluid is the acceleration due to gravity Sometimes it is convenient to express a minor loss in terms of a length of pipe that would produce an equivalent pressure loss. The equivalent length of pipe for a minor loss is inversely proportional to the Darcy friction factor and proportional to the loss coefficient and the pipe diameter as Equation (3-12) illustrates: (3-12) where is the equivalent length is the loss coefficient is the diameter of the pipe is the Darcy friction factor Both minor and major pressure losses depend on the velocity of the fluid. Therefore, if the fluid is not flowing in the pipe, there is no pressure loss. If a valve is closed in a system, the pressure at any point upstream of the valve increases to the maximum pressure the pump can develop at its outlet. When a valve is closed, the pressure is transmitted equally throughout the entire volume of fluid in the pipe, according to Pascal's Law. PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup and connections Pressure loss PROCEDURE Setup and connections 1. Connect the equipment as the piping and instrumentation diagram in Figure 3-26 shows and use Figure 3-27 to position the equipment correctly on the frame of the training system. Use the basic setup presented in the Familiarization with the Training System manual 1. Table 3-5 lists the equipment you must add to the basic setup to set up your system for this exercise. Table 3-5. Devices required for this exercise. Name Model Identification 1 This exercise does not require the column. Festo Didactic 86005-00 47
Ex. 3-2 Pressure Loss Procedure Differential-pressure transmitter (high-pressure range) 46920 PDI 1 Solenoid valve 46951 S Electrical unit 46970 Pneumatic unit 46971 Accessories 46993 Calibrator ---- Calibrator (4-20 ma) 24 V from the Electrical Unit Figure 3-26. P&ID. 48 Festo Didactic 86005-00
Ex. 3-2 Pressure Loss Procedure Figure 3-27. Setup. 2. Connect the control valve to the pneumatic unit. 3. Connect the pneumatic unit to a dry-air source with an output pressure of at least 700 kpa (100 psi). 4. Wire the emergency push-button so that you can cut power in case of an emergency. 5. Do not power up the instrumentation workstation before your instructor has validated your setup. 6. Connect the solenoid valve so that a voltage of 24 V dc actuates the solenoid when you turn the power on. 7. Install the differential-pressure transmitter so that the pressure differential between the inlet and the outlet of the control valve can be read. Festo Didactic 86005-00 49
Ex. 3-2 Pressure Loss Procedure a Be sure to use the differential pressure transmitter, Model 46920. This differential pressure transmitter has a high pressure range. 8. Connect the calibrator to the current to pressure converter of the control valve. 9. Before proceeding further, complete the following checklist to make sure you have set up the system properly. The points on this checklist are crucial elements for the proper completion of this exercise. This checklist is not exhaustive, be sure to follow the instructions in the Familiarization with the Training System manual as well. f The solenoid valve under the column is wired so that the valve opens when the system is turned on. The hand valves are in the positions shown in the P&ID. The control valve is fully open. The pneumatic connections are correct. The differential-pressure transmitter is installed correctly. 10. Ask your instructor to check and approve your setup. 11. Power up the electrical unit. 12. Use the calibrator to send a 4 ma signal to the current to pressure converter of the control valve. 13. Test your system for leaks. Use the drive to make the pump run at low speed in order to produce a small flow rate. Gradually increase the flow rate, up to 50% of the maximum flow rate the pumping unit can deliver. Repair all leaks. 14. Fill the pipes completely with water and bleed both sides of the differentialpressure transmitter. 15. Configure the differential-pressure transmitter so that it provides pressure readings in the desired units. 16. Adjust the zero of the differential-pressure transmitter to read a pressure differential of 0 kpa (0 psi) when there is no flow. 50 Festo Didactic 86005-00
Ex. 3-2 Pressure Loss Procedure Pressure loss 17. In this section, the differential-pressure transmitter is used to measure the pressure drop across the control valve in different circumstances. First, measure the pressure drop for various flow rates when the control valve is fully open. 18. Set the pump to 75% of its maximum speed and use the ball valve HV2 under the rotameter to adjust the flow rate to 4 L/min (1 gal/min). Record the pressure drop across the control valve in Table 3-6. Table 3-6. Pressure differential for different flow rates. Flow rate L/min (gal/min) 4 (1) P kpa (psi) 19. Use the ball valve HV2 to increase the flow rate by steps of 2 L/min (0.5 gal/min) until you reach 30 L/min (7.5 gal/min). For each flow rate, record the pressure drop across the control valve in Table 3-6. 20. Plot a graph of the pressure loss across the control valve as a function of the flow rate. 21. Fully open the ball valve (HV2). Festo Didactic 86005-00 51
Ex. 3-2 Pressure Loss Conclusion 22. Now, take pressure readings for different openings of the control valve. Use the calibrator to adjust the control valve opening. Use the opening percentages given in Table 3-7. Fill in the table with your data. Table 3-7. Pressure in the column for different openings of the control valve. Valve opening % Calibrator output ma p kpa (psi) Flow rate L/min (gal/min) 0 10 20 30 40 50 60 70 80 90 100 23. Plot a graph of the pressure drop across the control valve as a function of the valve opening. 24. Open HV4 to empty the column. Use the main switch to cut the power to the Instrumentation and Process Control Training System. CONCLUSION In this exercise, you learned the difference between a minor pressure loss and a major pressure loss. You measured the pressure loss across the control valve as a function of the flow rate and the pressure loss across the control valve as a function of the opening of the control valve. REVIEW QUESTIONS 1. What is a pressure loss? 2. What happens to the pressure loss ( ) if the length of a pipe is doubled? 52 Festo Didactic 86005-00
Ex. 3-2 Pressure Loss Review Questions 3. In which situation are major pressure losses more important than minor losses? 4. What is the primary cause of pressure loss across a control valve? 5. If the fluid flow rate doubles, what happens to the pressure drop across a control valve? Festo Didactic 86005-00 53