FIGURE P8 50E FIGURE P8 62. Minor Losses


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1 8 48 Glycerin at 40 C with r 1252 kg/m 3 and m 0.27 kg/m s is flowing through a 4cmdiameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe Reconsider Prob Using EES (or other) software, investigate the effect of the pipe diameter on the pressure drop for the same constant flow rate. Let the pipe diameter vary from 1 to 10 cm in increments of 1 cm. Tabulate and plot the results, and draw conclusions. 8 50E Air at 1 atm and 60 F is flowing through a 1 ft 1ft square duct made of commercial steel at a rate of 1600 cfm. Determine the pressure drop and head loss per ft of the duct. 1 ft Air 1 ft 1600 ft 3 /min FIGURE P8 50E 8 51 Liquid ammonia at 20 C is flowing through a 30mlong section of a 5mmdiameter copper tube at a rate of 0.15 kg/s. Determine the pressure drop, the head loss, and the pumping power required to overcome the frictional losses in the tube. Answers: 4792 kpa, 734 m, 1.08 kw 8 52 Water (r kg/m 3 and m kg/m s) flows through a 0.01mdiameter pipe. The flow is steady, laminar, and fully developed. In this exercise, you will use CFD to calculate the Darcy friction factor f for fully developed laminar pipe flow, and compare to the analytical value obtained with the exact equation f = 64/Re. Run FlowLab with template Pipe_1D_Reynolds. Vary the Reynolds number from 100 to 2000, and record average velocity V and pressure gradient dp/dx for each case. From these data, calculate f and compare with the analytical value. Is there good agreement? Discuss In this exercise, we examine fully developed turbulent flow through a rough pipe. Run FlowLab with template Pipe_turbulent_rough. Run several cases, each with a diffferent value of normalized pipe roughness, e/d, but at the same Reynolds number. Calculate and tabulate Darcy friction factor f as a function of normalized toughness parameter e/d. Compare f with that predicted by the Colebrook equation for fully developed turbulent pipe flow in rough pipes. Discuss. Minor Losses 8 54C What is minor loss in pipe flow? How is the minor loss coefficient K L defined? C Define equivalent length for minor loss in pipe flow. How is it related to the minor loss coefficient? 8 56C The effect of rounding of a pipe inlet on the loss coefficient is (a) negligible, (b) somewhat significant, or (c) very significant. 8 57C The effect of rounding of a pipe exit on the loss coefficient is (a) negligible, (b) somewhat significant, or (c) very significant. 8 58C Which has a greater minor loss coefficient during pipe flow: gradual expansion or gradual contraction? Why? 8 59C A piping system involves sharp turns, and thus large minor head losses. One way of reducing the head loss is to replace the sharp turns by circular elbows. What is another way? 8 60C During a retrofitting project of a fluid flow system to reduce the pumping power, it is proposed to install vanes into the miter elbows or to replace the sharp turns in 90 miter elbows by smooth curved bends. Which approach will result in a greater reduction in pumping power requirements? 8 61 Water is to be withdrawn from a 5mhigh water reservoir by drilling a 1.5cmdiameter hole at the bottom surface. Disregarding the effect of the kinetic energy correction factor, determine the flow rate of water through the hole if (a) the entrance of the hole is wellrounded and (b) the entrance is sharpedged A horizontal pipe has an abrupt expansion from D 1 8 cm to D 2 16 cm. The water velocity in the smaller section is 10 m/s and the flow is turbulent. The pressure in the smaller section is P kpa. Taking the kinetic energy correction factor to be 1.06 at both the inlet and the outlet, determine the downstream pressure P 2, and estimate the error that would have occurred if Bernoulli s equation had been used. Answers: 432 kpa, 25.0 kpa Water D 1 = 8 cm 10 m/s 410 kpa FIGURE P8 62 D 2 = 16 cm 8 63 Consider flow from a water reservoir through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharpedged entrance (K L 0.5) is considerably less than the flow rate calculated assuming frictionless flow and thus zero loss for the hole. Disregarding the effect of the kinetic energy correction factor, obtain a relation for the equivalent diameter of the sharpedged hole for use in frictionless flow relations.
2 406 INTERNAL FLOW D Frictionless flow FIGURE P8 63 Actual flow D equiv 8 64 Repeat Prob for a slightly rounded entrance (K L 0.12) Water (r kg/m 3 and m kg/m s) flows into a 0.10mlong (L), 0.01mdiameter (D) pipe. We are interested in the minor loss coefficient due to entrance effects, and we model the entrance region using CFD. At the inlet, the velocity is uniform, which leads to a very high wall shear stress near the entrance. The pipe is long enough that the flow becomes fully developed before the pipe outlet. The flow is steady and laminar. Run FlowLab with template Pipe_2D_developing at a Reynolds number of 150 and record the pressure change P/L. Use the following steps to calculate the minor loss coefficient: (i) Calculate (analytically) the pressure drop that would occur for this same pipe if it were fully developed over the entire length. (ii) Subtract this from the actual pressure drop calculated from the CFD output; the difference represents the extra pressure drop due to entrance effects. (iii) Convert the extra pressure drop to a minor loss coefficient and compare with the minor loss coefficients for different types of pipe inlets given in the text. Discuss your results Water (r kg/m 3 and m kg/m s) flows through a 0.01mdiameter, 0.10mlong will use CFD to predict the minor loss coefficient due to the entrance region in the pipe. Specifically, run FlowLab with template Pipe_3d_Reynolds at Re = 100; this template simulates fully developed flow in the pipe. Record dp/dx and calculate the total pressure drop P in the pipe. Repeat at the same Reynolds number with template Pipe_3d_developing, which solves for flow in the same pipe but with an entrance region uniform flow at the inlet. In this case, the output is P per meter. Calculate P for this case and subtract P of the fully developed case. The difference is the pressure drop due solely to entrancelength effects. Calculate the minor loss coefficient K L and discuss your results Water (r kg/m 3 and m kg/m s) flows through a 0.01mdiameter, 0.10mlong will use CFD to predict the minor loss coefficient due to a bump in the pipe (simulating debris buildup or a deposit of solid material on the inner pipe wall). Specifically, run FlowLab with template Pipe_3d_developing at Re = 100; this template simu lates laminar flow in a pipe with a uniform velocity at the inlet. Record the pressure drop provided in the output as P per meter. Calculate P for this case. Repeat with template Pipe_3d_bump, which simulates the same flow in the same pipe but with a threedimensional bump along the inner pipe wall. Calculate the pressure drop by plotting the pressure along the axis and subtracting the outlet pressure from the inlet pressure. Subtract P for the case without the bump from P for the case with the bump. The difference is the pressure drop due solely to the effect of the bump. Calculate the minor loss coefficient K L and discuss your results Water (r kg/m 3 and m will use CFD to compare the length of the entrance region at two different Reynolds numbers. The flow at the pipe inlet is uniform, and the pipe is sufficiently long for the flow to become fully developed by the outlet. Run FlowLab with template Pipe_3d_developing at Re 20. Plot velocity profiles (XY Plots, select the appropriate plot, and Plot). Create a hardcopy (file) and attach to your homework. Approximately how many pipe diameters does it take for the flow to become fully developed? Repeat for Re = 100 and discuss your results Water (r kg/m 3 and m will use CFD to compare the pressure drop down the pipe for two cases a clean pipe and a pipe with a bump (simulating debris buildup or a deposit of solid material on the inner pipe wall). The flow at the pipe inlet is uniform, and the pipe is sufficiently long for the flow to become fully developed by the outlet. Run FlowLab with template Pipe_3d_developing at Re 100. Plot P gage versus x (XY Plots, select the appropriate plot, and Plot). Write the data to a file. Repeat for the case with the bump using template Pipe_3d_bump, again running at Re = 100. Plot P gage versus x for the two cases on the same plot for direct comparison. Discuss and explain the results Water (r kg/m 3 and m will use CFD to compare velocity profiles down the pipe for two cases a clean pipe and a pipe with a bump (simulating debris build up or a deposit of solid material on the inner pipe wall). The flow at the pipe inlet is uniform, and the pipe is sufficiently long for the flow to become fully developed by the outlet. Run FlowLab with template Pipe_3d_developing at Re 50. Plot velocity profiles at various axial locations down the pipe (XY Plots, select the appropriate plot, and Plot). Repeat for the case with the bump using the template Pipe_ 3d_bump, again running at Re = 50. Compare the two plots and discuss your results Air (r kg/m 3 and m kg/m s) flows through a 1.00mdiameter, 45.0mlong pipe. The flow is turbulent, but steady in the mean. In this
3 exercise, you will use CFD to predict the minor loss coefficient due to the entrance region in the pipe. Specifically, run FlowLab with template Pipe_turbulent_developed at Re 10,000; this template simulates fully developed flow in the pipe. Plot the axial pressure distribution (XY Plots, select the appropriate plot, and Plot). Write the data to a file and record the inlet and outlet pressures; using these data, calculate the total pressure drop P in the pipe. Repeat at the same Reynolds number with template Pipe_turbulent_developing, which solves for flow in the same pipe but with an entrance region uniform flow at the inlet. Calculate P for this case and subtract P of the fully developed case. The difference is the pressure drop due solely to entrance length effects. Calculate minor loss coefficient K L and discuss your results. Piping Systems and Pump Selection 8 72C A person filling a bucket with water using a garden hose suddenly remembers that attaching a nozzle to the hose increases the discharge velocity of water and wonders if this increased velocity would decrease the filling time of the bucket. What do you think would be the effect of attaching a nozzle to the hose on the filling time: increase it, decrease it, or have no effect? Why? 8 73C Consider two identical 2mhigh open tanks filled with water on top of a 1mhigh table. The discharge valve of one of the tanks is connected to a hose whose other end is left open on the ground while the other tank does not have a hose connected to its discharge valve. Now the discharge valves of both tanks are opened. Disregarding any frictional loses in the hose, which tank do you think empties completely first? Why? 8 74C A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in series. How would you compare the (a) flow rates and (b) pressure drops in these two pipes? 8 75C A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the (a) flow rates and (b) pressure drops in these two pipes? 8 76C A piping system involves two pipes of identical diameters but of different lengths connected in parallel. How would you compare the pressure drops in these two pipes? 8 77C Water is pumped from a large lower reservoir to a higher reservoir. Someone claims that if the head loss is negligible, the required pump head is equal to the elevation difference between the free surfaces of the two reservoirs. Do you agree? 8 78C A piping system equipped with a pump is operating steadily. Explain how the operating point (the flow rate and the head loss) is established. 8 79C For a piping system, define the system curve, the characteristic curve, and the operating point on a head versus flow rate chart The water needs of a small farm are to be met by pumping water from a well that can supply water continuously at a rate of 4 L/s. The water level in the well is 20 m below the ground level, and water is to be pumped to a large tank on a hill, which is 58 m above the ground level of the well, using 5cm internal diameter plastic pipes. The required length of piping is measured to be 420 m, and the total minor loss coefficient due to the use of elbows, vanes, etc. is estimated to be 12. Taking the efficiency of the pump to be 75 percent, determine the rated power of the pump that needs to be purchased, in kw. The density and viscosity of water at anticipated operation conditions are taken to be 1000 kg/m 3 and kg/m s, respectively. Is it wise to purchase a suitable pump that meets the total power requirements, or is it necessary to also pay particular attention to the large elevation head in this case? Explain. Answer: 6 kw 8 81E Water at 70 F flows by gravity from a large reservoir at a high elevation to a smaller one through a 90ftlong, 2indiameter cast iron piping system that includes four standard flanged elbows, a wellrounded entrance, a sharpedged exit, and a fully open gate valve. Taking the free surface of the lower reservoir as the reference level, determine the elevation z 1 of the higher reservoir for a flow rate of 10 ft 3 /min. Answer: 17.9 ft 8 82 A 2.4mdiameter tank is initially filled with water 4 m above the center of a sharpedged 10cmdiameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere. Neglecting the effect of the kinetic energy correction factor, calculate (a) the initial velocity from the tank and (b) the time required to empty the tank. Does the loss coefficient of the orifice cause a significant increase in the draining time of the tank? Water tank 2.4 m FIGURE P m Sharpedged orifice 8 83 A 3mdiameter tank is initially filled with water 2 m above the center of a sharpedged 10cmdiameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a 100mlong pipe. The friction coefficient of the pipe is taken to be and the effect of the kinetic energy correction factor can be neglected. Determine (a) the initial velocity from the tank and (b) the time required to empty the tank.
4 410 INTERNAL FLOW 8 99 Repeat Prob for cast iron pipes of the same diameter E A clothes dryer discharges air at 1 atm and 120 F at a rate of 1.2 ft 3 /s when its 5indiameter, wellrounded vent with negligible loss is not connected to any duct. Determine the flow rate when the vent is connected to a 15ftlong, 5indiameter duct made of galvanized iron, with three 90 flanged smooth bends. Take the friction factor of the duct to be 0.019, and assume the fan power input to remain constant. 3 cm and 5 cm. Water is to be pumped by a 68 percent efficient motor pump unit that draws 7 kw of electric power during operation. The minor losses and the head loss in the pipes that connect the parallel pipes to the two reservoirs are considered to be negligible. Determine the total flow rate between the reservoirs and the flow rates through each of the parallel pipes. Reservoir B z B = 9 m Hot air 3 cm 25 m Reservoir A z A = 2 m 5 cm Clothes drier FIGURE P8 100E 15 ft Gasoline (r 680 kg/m 3 and n m 2 /s) is transported at a rate of 400 L/s for a distance of 2 km. The surface roughness of the piping is 0.03 mm. If the head loss due to pipe friction is not to exceed 8 m, determine the minimum diameter of the pipe In large buildings, hot water in a water tank is circulated through a loop so that the user doesn t have to wait for all the water in long piping to drain before hot water starts coming out. A certain recirculating loop involves 40mlong, 1.2cmdiameter cast iron pipes with six 90 threaded smooth bends and two fully open gate valves. If the average flow velocity through the loop is 2 m/s, determine the required power input for the recirculating pump. Take the average water temperature to be 60 C and the efficiency of the pump to be 70 percent. Answer: kw Reconsider Prob Using EES (or other) software, investigate the effect of the average flow velocity on the power input to the recirculating pump. Let the velocity vary from 0 to 3 m/s in increments of 0.3 m/s. Tabulate and plot the results Repeat Prob for plastic (smooth) pipes Water at 20 C is to be pumped from a reservoir (z A 2 m) to another reservoir at a higher elevation (z B 9 m) through two 25mlong plastic pipes connected in parallel. The diameters of the two pipes are 5 in Pump FIGURE P8 105 Flow Rate and Velocity Measurements 8 106C What are the primary considerations when selecting a flowmeter to measure the flow rate of a fluid? 8 107C Explain how flow rate is measured with a Pitotstatic tube, and discuss its advantages and disadvantages with respect to cost, pressure drop, reliability, and accuracy C Explain how flow rate is measured with obstructiontype flowmeters. Compare orifice meters, flow nozzles, and Venturi meters with respect to cost, size, head loss, and accuracy C How do positive displacement flowmeters operate? Why are they commonly used to meter gasoline, water, and natural gas? 8 110C Explain how flow rate is measured with a turbine flowmeter, and discuss how they compare to other types of flowmeters with respect to cost, head loss, and accuracy C What is the operating principle of variablearea flowmeters (rotameters)? How do they compare to other types of flowmeters with respect to cost, head loss, and reliability? 8 112C What is the difference between the operating principles of thermal and laser Doppler anemometers? 8 113C What is the difference between laser Doppler velocimetry (LDV) and particle image velocimetry (PIV)? Air (r kg/m 3 and m kg/m s) flows over a d 5mmdiameter Pitotstatic probe that is aligned directly into the flow. Your job is to determine how far (L) downstream from the nose to place the static pressure holes around the circumference of the
5 probe. Run FlowLab with template Pitot_static_position. This template calculates flow at 30 m/s over a Pitotstatic probe and includes viscous losses. Vary the static pressure tap location from L/d = 0.5 to 20, and record the stagnation and static pressures as calculated on the surface of the Pitotstatic probe for each case. Using the Bernoulli approximation, calculate the freestream velocity based on these pressures, and compare with the known inlet velocity. At approximately what L/d is the error less than 1.5 percent? Discuss your results. 4 in 1.8 in 7 in Air (r kg/m 3 and m kg/m s) flows in a wind tunnel, and the wind tunnel speed is measured with a Pitotstatic probe. For a certain run, the stagnation pressure is measured to be Pa gage and the static pressure is Pa gage. Calculate the windtunnel speed A Pitotstatic probe is mounted in a 2.5cm inner diameter pipe at a location where the local velocity is approximately equal to the average velocity. The oil in the pipe has density r 860 kg/m 3 and viscosity m kg/m s. The pressure difference is measured to be 95.8 Pa. Calculate the volume flow rate through the pipe in cubic meters per second Calculate the Reynolds number of the flow of Prob Is it laminar or turbulent? The flow rate of ammonia at 10 C (r kg/m 3 and m kg/m s) through a 3cmdiameter pipe is to be measured with a 1.5cmdiameter flow nozzle equipped with a differential pressure gage. If the gage reads a pressure differential of 6 kpa, determine the flow rate of ammonia through the pipe, and the average flow velocity The flow rate of water through a 10cmdiameter pipe is to be determined by measuring the water velocity at several locations along a cross section. For the set of measurements given in the table, determine the flow rate. FIGURE P8 120E 8 121E Repeat Prob E for a differential height of 10 in The flow rate of water at 20 C (r 998 kg/m 3 and m kg/m s) through a 50cmdiameter pipe is measured with an orifice meter with a 30cmdiameter opening to be 250 L/s. Determine the pressure difference indicated by the orifice meter and the head loss A Venturi meter equipped with a differential pressure gage is used to measure the flow rate of water at 15 C (r kg/m 3 ) through a 5cmdiameter horizontal pipe. The diameter of the Venturi neck is 3 cm, and the measured pressure drop is 5 kpa. Taking the discharge coefficient to be 0.98, determine the volume flow rate of water and the average velocity through the pipe. Answers: 2.35 L/s and 1.20 m/s 5 cm 3 cm r, cm V, m/s E An orifice with a 1.8indiameter opening is used to measure the mass flow rate of water at 60 F (r lbm/ft 3 and m lbm/ft s) through a horizontal 4indiameter pipe. A mercury manometer is used to measure the pressure difference across the orifice. If the differential height of the manometer is 7 in, determine the volume flow rate of water through the pipe, the average velocity, and the head loss caused by the orifice meter. FIGURE P8 123 P Differential pressure gage Reconsider Prob Letting the pressure drop vary from 1 kpa to 10 kpa, evaluate the flow rate at intervals of 1 kpa, and plot it against the pressure drop The mass flow rate of air at 20 C (r kg/m 3 ) through a 18cmdiameter duct is measured with a Venturi
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