# FIGURE P8 50E FIGURE P8 62. Minor Losses

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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 0.10-m-long (L), 0.01-mdiameter (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 0.01-m-diameter, 0.10-m-long 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 entrance-length 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 0.01-m-diameter, 0.10-m-long will use CFD to predict the minor loss coefficient due to a bump in the pipe (simulating debris build-up 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 three-dimensional 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 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 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 1.00-m-diameter, 45.0-m-long 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 2-m-high open tanks filled with water on top of a 1-m-high 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 5-cm 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 90-ft-long, 2-in-diameter cast iron piping system that includes four standard flanged elbows, a well-rounded entrance, a sharp-edged 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 2.4-m-diameter tank is initially filled with water 4 m above the center of a sharp-edged 10-cm-diameter 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 Sharp-edged orifice 8 83 A 3-m-diameter tank is initially filled with water 2 m above the center of a sharp-edged 10-cm-diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a 100-m-long 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.

5 probe. Run FlowLab with template Pitot_static_position. This template calculates flow at 30 m/s over a Pitot-static 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 Pitot-static probe for each case. Using the Bernoulli approximation, calculate the free-stream 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 Pitot-static probe. For a certain run, the stagnation pressure is measured to be Pa gage and the static pressure is Pa gage. Calculate the wind-tunnel speed A Pitot-static probe is mounted in a 2.5-cm 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 3-cm-diameter pipe is to be measured with a 1.5-cm-diameter 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 10-cm-diameter 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 50-cm-diameter pipe is measured with an orifice meter with a 30-cm-diameter 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 5-cm-diameter 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 1.8-in-diameter 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 4-in-diameter 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 18-cm-diameter duct is measured with a Venturi

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