6.4 Recommended Velocity of Flow in Pipe and Tubing Many factors affect the selection of a satisfactory velocity of flow in fluid systems. When we discussed the continuity equation in Section 6.2, we learned that the velocity of flow increases as the area of the flow path decreases. Therefore, smaller tubes will cause higher velocities and larger tubes will provide lower velocities. Later we will explain that energy losses and the corresponding pressure drop increase dramatically as the flow velocity increases. For this reason it is desirable to keep the velocities low.
Because larger pipes and tubes are more costly, however, some limits are necessary. Figure 6.3 provides very rough guidance for specifying pipe sizes as a function of volume flow rate for typical pumped fluid distribution systems. In general, the flow velocity is kept lower in suction lines providing flow into a pump to ensure proper filling of the suction inlet passages. The lower velocity also helps to limit energy losses in the suction line, keeping the pressure at the pump inlet relatively high to ensure that pure liquid enters the pump. Lower pressures may cause a damaging condition called cavitation to occur, resulting in excessive noise, significantly degraded performance, and rapid erosion of pump and impeller surfaces.
Cavitation is discussed more fully in Chapter 13. Note that specifying one size larger or one size smaller than indicated by the lines in Fig. 6.3 will not affect the performance of the system very much. In general, you should favor the larger pipe size to achieve a lower velocity unless there are difficulties with space, cost, or compatibility with a given pump connection.
The resulting flow velocities from the recommended pipe sizes in Fig. 6.3 are generally lower for the smaller pipes and higher for the larger pipes, as shown for the following data. 13.39, other elements may be added to the discharge line as required. A pressure relief valve will protect the pump and other equipment in case of a blockage of the flow or accidental shut-off of a valve.
A check valve prevents flow back through the pump when it is not running and it should be placed between the shut-off valve and the pump. If an enlarger is used from the pump discharge port it should be placed between the check valve and the pump. A tap into the discharge line for a gauge with its shut-off valve is highly recommended.
Combined with the pressure gauge in the suction line, the operator can determine the total head on the pump and compare that to design requirements. A sample cock will allow a small flow of the fluid to be drawn off for testing without disrupting operation. Figure 13.1 and Fig ure 7.1 in Chapter 7 show illustrations of actual installations. In many industrial piping installations, other process elements related to manufacturing are frequently included in the discharge line of the system. Examples are heat exchangers, filters, strainers, fluid power actuators, spray heads, and lubrication systems for machinery. Each of these elements provides additional resistance to the system.
In oil, gas, chemical, and food processing, and machinery lubrication systems, pressures, flow rates, fluid temperatures, and viscosities may be monitored and adjusted continuously. As a result, most systems of these types require flow control valves that adjust the flow rate in response to changing system needs. See also Section 13.15 for more discussion of control valves.
Reference 12 is a standard for use of thermal mass dispersion flowmeters. A third style of mass flow measurement device is called the gas laminar flowmeter, described in Internet resource 19. A temperature probe is included in the unit from which the viscosity and specific weight of the fluid can be determined. When a fluid is maintained in laminar flow, the energy loss and the pressure drop over a given length of conduit of a known size is proportional to the velocity of flow. Pressure taps before and after the laminar flow elements facilitate the measurement of the differential pressure.
The entire unit is calibrated as a system enabling a high level of accuracy for the measured mass flow rate and simple operation. See Internet resources 1, 4, 6, 11–15, and 19 for commercial suppliers of mass flowmeters. And diffuse into the surrounding air. Finally, the water comes to full boiling with continuous and rapid vaporization. The temperature of the water at boiling is approximately 100 C or 212 F.
However, at high altitudes, the atmospheric pressure is noticeably lower and the boiling temperature is correspondingly lower. For example, Appendix Table E.3 shows that the atmospheric pressure at 5000 ft is only 12.2 psi (84.3 kPa). This is the approximate elevation of Denver, Colorado, often called the "Mile-High City", where water boils at approximately 94 C or 201 F. Relate this simple experiment with the conditions at the suction inlet of a pump. If the pump must pull fluid from below or if there are excessive energy losses in the suction line, the pressure at the pump may be sufficiently low to cause vapor bubbles to form in the fluid. Now consider what happens to the fluid as it begins its journey through the pump.
13.11, which shows the design of a radial centrifugal pump. The fluid enters the pump through the suction port at the central eye of the impeller and this where the lowest pressure occurs. The rotation of the impeller then accelerates the fluid outward along the vanes toward the casing, called a volute. Fluid pressure continues to rise throughout this process.
If vapor bubbles had formed in the suction port because of excessively low pressure there, they would collapse as they flowed into the higher-pressure zones. Collapsing bubbles release large amounts of energy, which effectively exerts impact forces on the impeller vanes and cause rapid surface erosion. When cavitation occurs, the performance of the pump is severely degraded as the volume flow rate delivered drops. The pump vibrates and becomes noisy, giving off a loud, rattling sound as if gravel was flowing with the fluid.
If this was allowed to continue, the pump would be destroyed in a short time. The pump should be promptly shut down and the cause of the cavitation should be identified and corrected before resuming operation. Obviously, it is preferred to ensure that cavitation does not occur under expected operating conditions as will be demonstrated in Sections 13.10 and 13.13. Cause the load to be moved at the desired speed.
Control is affected by adjustable internal restrictions that can be set during system operation. The restrictions cause energy losses and, therefore, there is a pressure drop across the valve. Energy is lost at the actuator as the fluid flows into the left end of the cylinder at A and out from the right end at B. On the return path, energy losses occur in the piping system. More energy losses occur in the directional control valve as the fluid passes back through the B port and on to the tank. The reasons for these losses are similar to those described in item 9.
This summary identifies 14 ways in which energy is either added to or lost from the hydraulic fluid in this relatively simple fluid power system. Each energy loss results in a pressure drop that could affect the performance of the system. However, designers of fluid power systems do not always analyze each pressure drop. The transient nature of the operation makes it critical that there is sufficient pressure and flow at the actuator under all reasonable conditions.
It is not uncommon for designers to provide extra capacity in the basic system design to overcome unforeseen circumstances. In the circuit just described, the critical pressure drops occur at the pressure relief valve, through the directional control valve, and through the flow control valve. These elements will be analyzed carefully. Other losses will often be only estimated in the initial design. In many cases, the actual configuration of the piping system is not defined during the design process, leaving it to skilled technicians to properly fit the components to the machine.
Then, when the system is in operation, some fine tuning will be done to ensure proper operation. This scenario applies most to systems designed for a special purpose when one or only a few systems will be built. When a system is designed for a production application or for a very critical application, more time spent on analysis and optimization of system performance is justified.
Examples are aircraft control systems and actuators for construction and agricultural equipment that are made in quantity. Table 6.2 shows the typical volume flow rate for centrifugal fire-fighting pumps is in the range of 1800 L/min to 9500 L/min. Specify the smallest suitable DN size of Schedule 40 steel pipe for each flow rate that will maintain the maximum velocity of flow at 2.0 m/s. Repeat Problem 6.47, but use Schedule 80 DN pipe.
Compute the resulting velocity of flow if 400 L/min of fluid flows through a DN 50 Schedule 40 pipe. Repeat Problem 6.49 for a DN 50 Schedule 80 pipe. Compute the velocity of flow through a 45-cm diameter pipe in ft/s if it is discharging water at 0.45 m3/s. Repeat Problem 6.51 for a 4-in Schedule 80 pipe. From the list of standard hydraulic steel tubing in Appendix G.2, select the smallest size that would carry 2.80 L/min of oil with a maximum velocity of 0.30 m/s.
A standard 6-in Schedule 40 steel pipe is carrying 95 gal/min of water. The pipe then branches into two standard 3-in pipes. If the flow divides evenly between the branches, calculate the velocity of flow in all three pipes. 7.2 Energy Losses and Additions The objective of this section is to describe, in general terms, the various types of devices and components of fluid flow systems. They occur in most fluid flow systems and they either add energy to the fluid, remove energy from the fluid, or cause undesirable losses of energy from the fluid. At this time we are only describing these devices in conceptual terms.
We discuss pumps, fluid motors, friction losses as fluid flows in pipes and tubes, energy losses from changes in the size of the flow path, and energy losses from valves and fittings. In later chapters, you will learn in more detail about how to compute the amount of energy losses in pipes and specific types of valves and fittings. You will learn the method of using performance curves for pumps to apply them properly. 6.3 are given in gal/min for the U.S. Customary System and in m3 / h for the SI system because most manufacturers rate their pumps in such units. Conversions to the standard units of ft3 / s and m3 / s must be done before using the flow rates in calculations in this book.
Introduction The objective of this book is to present the principles of fluid mechanics and the application of these principles to practical, applied problems. This book is directed to anyone in an engineering field where the ability to apply the principles of fluid mechanics is the primary goal. Those using this book are expected to have an understanding of algebra, trigonometry, and mechanics. After completing the book, the student should have the ability to design and analyze practical fluid flow systems and to continue learning in the field. Students could take other applied courses, such as those on fluid power, HVAC, and civil hydraulics, following this course.
Alternatively, this book could be used to teach selected fluid mechanics topics within such courses. 13.11 Discharge Line Details In general, the discharge line should be as short and direct as possible to minimize the head on the pump. Elbows should be of the standard or long-radius type if possible. Pipe size should be chosen according to velocity or allowable friction losses. Figure 6.3 in Chapter 6 includes recommendations for the ranges of desirable pipe sizes to carry a given volume flow rate.
In general, the larger sizes and lower velocities are recommended based on the ideal of minimizing the energy losses. Practical installation considerations and cost, however, may lead to the selection of smaller pipes with the resulting higher velocities. The discharge line should contain a valve close to the pump to allow service or pump replacement.
This valve acts with the valve in the suction line to isolate the pump. For low resistance, a gate or butterfly valve is preferred. If flow must be regulated during service, a globe valve is better because it allows a smooth throttling of the discharge.
This, in effect, increases the system head and causes the pump delivery to decrease to the desired value. The American Society of Mechanical Engineers , the American Water Works Association , the National Fire Protection Association , and others develop standards for such considerations. See References 1–17 and Internet resources 2–10. Other details and practical considerations of piping system design are discussed in References 3 and 6–11 and in the various Internet resources listed at the end of the chapter. The nominal size of the pipe or tubing is typically determined from flow considerations as outlined in this chapter.
The following equations are taken from Reference 1, and you are advised to consult that document for details and pertinent data. Reference 14 gives some discussion of the use of these equations along with example problems. These equations are based on the classic tangential stress analysis for thin-walled cylinders with internal pressure. Let's start with the fluid in the tank. Assume that it is at rest and that the tank is vented with atmospheric pressure above the surface of the fluid.
Density Of Air At Sea Level In Slugs Ft 3 As the pump draws fluid, we see that a suction line must accelerate the fluid from its resting condition in the tank to the velocity of flow in the suction line. Thus, there will be an entrance loss that depends on the configuration of the inlet. The pipe may simply be submerged in the hydraulic fluid or it may have a strainer at the inlet to keep foreign particles out of the pump and the valves. There will be friction losses in the pipe as the fluid flows to the suction port of the pump.
Along the way, there may be energy losses in any elbows or bends in the pipe. We must be concerned with the pressure at the inlet to the pump to ensure that cavitation does not happen and that there is an adequate supply of fluid. Specify the number, type, and size of all valves, elbows, and fittings. Specify the number of pumps, their types, capacities, head requirements, and power required. Specify the installation requirements for the pumps, including the complete suction line system.
Evaluate the NPSHA for your design, and demonstrate that your pump has an acceptable NPSH required. Determine the time required to fill and empty all tanks. Sketch the layout of your design in both a plan view and an elevation view . An isometric sketch may also be used. Include the analysis of all parts of the system, including energy losses due to friction and minor losses.
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