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applied fluid mechanics
Applied Fluid Mechanics 7th edition Robert L. Mott, Joseph A. Untener - Solutions
Using Eq. (9€“3), compute the distance y for which the local velocity U is equal to the average velocity v. v[1+ 1.43 Vỹ + 2.15Vf log10(y/r.). %3D
The result for Problem 9.12 predicts that the average velocity for turbulent flow will be found at a distance of 0.216ro from the wall of the pipe. Compute this distance for a 24-in Schedule 40 steel pipe. Then, if the pipe carries water at 50°F at a flow rate of 16.75 ft3/s, compute the velocity
Using Eq. (9€“4), compute the ratio of the average velocity to the maximum velocity of flow in smooth pipes with Reynolds numbers of 4000, 104, 105, and 106. Umax = v(1 + 1.43 VH)
Using Eq. (9€“4), compute the ratio of the average velocity to the maximum velocity of flow for the flow of a liquid through a concrete pipe with an inside diameter of 8.00 in with Reynolds numbers of 4000, 104, 105, and 106. Umax = v(1 + 1.43 VH)
Using Eq. (9-3), compute several points on the velocity profile for the flow of 400 gal/min of water at 50°F in a new, clean, 4-in Schedule 40 steel pipe. Make a plot similar to Fig. 9.7 with a fairly large scale.Figure 9.7 - 1.111 m/s max Pipe centerline 25 20 15 10 Pipe wall 40 .60 80 1.00 1.20
Repeat Problem 9.16 for the same conditions, except that the inside of the pipe is roughened by age so that ε = 5.0 × 10-3. Plot the results on the same graph as that used for the results of Problem 9.16.Repeat ProblemUsing Eq. (9-3), compute several points on the velocity profile for the flow of
For both situations described in Problems 9.16 and 9.17, compute the pressure drop that would occur over a distance of 250 ft of horizontal pipe.In ProblemsRepeat Problem 9.16 for the same conditions, except that the inside of the pipe is roughened by age so that ε = 5.0 ×
A shell-and-tube heat exchanger is made of two standard steel tubes, as shown in Fig. 9.13. The outer tube has an OD of 7/8 in and the OD for the inner tube is ½ in. Each tube has a wall thickness of 0.049 in. Calculate the required ratio of the volume flow rate in the shell to that in the
Figure 9.14 shows a heat exchanger in which each of two DN 150 Schedule 40 pipes carries 450 L/min of water. The pipes are inside a rectangular duct whose inside dimensions are 200 mm by 400 mm. Compute the velocity of flow in the pipes. Then, compute the required volume flow rate of water in the
Figure 9.15 shows the cross section of a shell-and-tube heat exchanger. Compute the volume flow rate required in each small pipe and in the shell to obtain an average velocity of flow of 25 ft/s in all parts. 15-in Schedule 40 pipes (3) 5-in Schedule 40 pipe
Air with a specific weight of 12.5 N/m3and a dynamic viscosity of 2.0 × 10-5Paˆ™s flows through the shaded portion of the duct shown in Fig. 9.16 at the rate of 150 m3/h. Calculate the Reynolds number of the flow. 100 mm 50 mm 25-mm outside diameter 50 mm
Carbon dioxide with a specific weight of 0.114 lb/ft3and a dynamic viscosity of 3.34 × 10-7lb-s/ft2flows in the shaded portion of the duct shown in Fig. 9.17. If the volume flow rate is 200 ft3/min, calculate the Reynolds number of the flow. 4-in outside diameter 6 in Z7777777/7777A
Water at 90°F flows in the space between 6-in Schedule 40 steel pipe and a square duct with inside dimensions of 10.0 in. The shape of the duct is similar to that shown in Fig. 9.10. Compute the Reynolds number if the volume flow rate is 4.00 ft3/s. 250 mm 150-mm diameter
Refer to the shell-and-tube heat exchanger shown in Fig. 9.13. The outer tube has an OD of 7/8 in and the OD of the inner tube is ½ in. Both tubes are standard steel tubes with 0.049-in wall thicknesses. The inside tube carries 4.75 gal/min of water at 200°F and the shell carries 30.0
Refer to Fig. 9.15, which shows three pipes inside a larger pipe. The inside pipes carry water at 200°F and the large pipe carries water at 60F. The average velocity of flow is 25.0 ft/s in each pipe; compute the Reynolds number for each. 1-in Schedule 40 pipes (3) 5-in Schedule 40 pipe
Water at 10°C is flowing in the shell shown in Fig. 9.18 at the rate of 850 L/min. The shell is a 50 mm OD × 1.5 mm wall copper tube and the inside tubes are 15 mm OD × 1.2 mm wall copper tubes. Compute the Reynolds number for the flow.
Figure 9.19 shows the cross section of a heat exchanger used to cool a bank of electronic devices. Ethylene glycol at 77°F flows in the shaded area. Compute the volume flow rate required to produce a Reynolds number of 1500. All dimen sions in inches
Figure 9.20 shows a liquid-to-air heat exchanger in which air flows at 50 m3/h inside a rectangular passage and around a set of five vertical tubes. Each tube is a standard hydraulic steel tube, 15 mm OD × 1.2 mm wall. The air has a density of 1.15 kg/m3and a dynamic viscosity of 1.63
Glycerin (sg = 1.26) at 40°C flows in the portion of the duct outside the square tubes shown in Fig. 9.21. Calculate the Reynolds number for a flow rate of 0.10 m3/s. Both 150 mm square outside -300 mm 450 mm-
Each of the square tubes shown in Fig. 9.21 carries 0.75 m3/s of water at 90°C. The thickness of the walls of the tubes is 2.77 mm. Compute the Reynolds number of the flow of water. Both 150 mm square outside -300 mm 450 mm-
A heat sink for an electronic circuit is made by machining a pocket into a block of aluminum and then covering it with a flat plate to provide a passage for cooling water as shown in Fig. 9.22. Compute the Reynolds number if the flow of water at 50°F is 78.0 gal/min. Electronic de vices 0.75-in
Figure 9.23 shows the cross section of a cooling passage for an odd-shaped device. Compute the volume flow rate of water at 50°F that would produce a Reynolds number of 1.5 × 105. 0.50 in 0.50 in 0.25-in radius 0.75-in radius 0.50 in
Figure 9.24 shows the cross section of a flow path machined from a casting using a ¾-in-diameter milling cutter. Considering all the fillets, compute the hydraulic radius for the passage, and then compute the volume flow rate of acetone at 77°F required to produce a Reynolds number for
The blade of a gas turbine engine contains internal cooling passages, as shown in Fig. 9.25. Compute the volume flow rate of air required to produce an average velocity of flow in each passage of 25.0 m/s. The air flow distributes evenly to all six passages. Then, compute the Reynolds number if the
For the system described in Problem 9.24, compute the pressure difference between two points 30.0 ft apart if the duct is horizontal. Use e = 8.5 × 10-5ft.In ProblemWater at 90°F flows in the space between 6-in Schedule 40 steel pipe and a square duct with inside dimensions of 10.0
For the shell-and-tube heat exchanger described in Problem 9.25, compute the pressure difference for both fluids between two points 5.25 m apart if the heat exchanger is horizontal.In ProblemRefer to the shell-and-tube heat exchanger shown in Fig. 9.13. The outer tube has an OD of 7/8 in and the OD
For the system described in Problem 9.26, compute the pressure drop for both fluids between two points 3.80 m apart if the duct is horizontal. Use the roughness for steel pipe for all surfaces.In ProblemRefer to Fig. 9.14, which shows two DN 150 Schedule 40 pipes inside a rectangular duct. Each
For the shell-and-tube heat exchanger described in Problem 9.28, compute the pressure drop for the flow of water in the shell. Use the roughness for copper for all surfaces. The length is 3.60 m.
For the heat exchanger described in Problem 9.29, compute the pressure drop for a length of 57 in.
For the glycerin described in Problem 9.31, compute the pressure drop for a horizontal duct 22.6 m long. All surfaces are copper.
For the flow of water in the square tubes described in Problem 9.32, compute the pressure drop over a length of 22.6 m. All surfaces are copper and the duct is horizontal.
If the heat sink described in Problem 9.33 is 105 in long, compute the pressure drop for the water. Use ε = 2.5 × 10-5 ft for the aluminum.
Compute the energy loss for the flow of water in the cooling passage described in Problem 9.34 if its total length is 45 in. Use ε for steel. Also compute the pressure difference across the total length of the cooling passage.
In Fig. 9.26, ethylene glycol (sg = 1.10) at 77°F flows around the tubes and inside the rectangular passage. Calculate the volume flow rate of ethylene glycol in gal/min required for the flow to have a Reynolds number of 8000. Then, compute the energy loss over a length of 128 in. All surfaces
Figure 9.27 shows a duct in which methyl alcohol at 25°C flows at the rate of 3000 L/min. Compute the energy loss over a 2.25-m length of the duct. All surfaces are smooth plastic. 100 mm 30 mm typical 100 mm 20 mm Methyl alcohol typical
A furnace heat exchanger has a cross section like that shown in Fig. 9.28. The air flows around the three thin passages in which hot gases flow. The air is at 140°F and has a density of 2.06 × 10-3slugs/ft3and a dynamic viscosity of 4.14 × 10-7lbˆ™s/ft2.
Figure 9.29 shows a system in which methyl alcohol at 77°F flows outside the three tubes while ethyl alcohol at 0°F flows inside the tubes. Compute the volume flow rate of each fluid required to produce a Reynolds number of 3.5 × 104in all parts of the system. Then, compute the
A simple heat exchanger is made by welding one-half of a 1¾-in drawn steel tube to a flat plate as shown in Fig. 9.30. Water at 40°F flows in the enclosed space and cools the plate. Compute the volume flow rate required so that the Reynolds number of the flow is 3.5 × 104.
Compute points on the velocity profile from the tube wall to the centerline of a plastic pipe, 125 mm OD × 7.4 mm wall, if the volume flow rate of gasoline (sg = 0.68) at 25°C is 3.0 L/min. Use increments of 8.0 mm and include the velocity at the centerline.
Compute points on the velocity profile from the pipe wall to the centerline of a 3/4-in Type K copper tube if the volume flow rate of water at 60°F is 0.50 gal/min. Use increments of 0.05 in and include the velocity at the centerline.
Compute points on the velocity profile from the pipe wall to the centerline of a 2-in Schedule 40 steel pipe if the volume flow rate of castor oil at 77°F is 0.25 ft3/s.
A large pipeline with a 1.200-m inside diameter carries oil similar to SAE 10 at 40°C (sg = 0.8). Compute the volume flow rate required to produce a Reynolds number of 3.60 × 104. Then, if the pipe is clean steel, compute several points of the velocity profile and plot the data in a manner
For the flow of 12.9 L/min of water at 75°C in a plastic pipe, 16 mm OD × 1.5 mm wall, compute the expected maximum velocity of flow from Eq. (9€“4). + 1.43 V) Umax = v(1 %3D
Compute points on the velocity profile from the tube wall to the centerline of a standard hydraulic steel tube, 50 mm OD × 1.5 mm wall, if the volume flow rate of SAE 30 oil (sg = 0.89) at 110°C is 25 L/min. Use increments of 4.0 mm and include the velocity at the centerline.
A small velocity probe is to be inserted through a pipe wall. If we measure from the outside of the DN 150 Schedule 80 pipe, how far (in mm) should the probe be inserted to sense the average velocity if the flow in the pipe is laminar?
If the accuracy of positioning the probe described in Problem 9.5 is plus or minus 5.0 mm, compute the possible error in measuring the average velocity.
An alternative scheme for using the velocity probe described in Problem 9.5 is to place it in the middle of the pipe, where the velocity is expected to be 2.0 times the average velocity. Compute the amount of insertion required to center the probe. Then, if the accuracy of placement is again plus
An existing fixture inserts the velocity probe described in Problem 9.5 exactly 60.0 mm from the outside surface of the pipe. If the probe reads 2.48 m/s, compute the actual average velocity of flow, assuming the flow is laminar. Then, check to see if the flow actually is laminar if the fluid is a
Convert 0.008 ft3/s to gal/min.
Convert 7.50 ft3/s to gal/min.
Convert 0.060 ft3/s to gal/min.
Convert 125 ft3/s to gal/min.
Convert 2.50 gal/min to ft3/s.
Convert 2500 gal/min to ft3/s.
Convert 20 gal/min to ft3/s.
Convert 459 gal/min to ft3/s.
Convert 5.26 × 10-6 m3/s to L/min.
Convert 3.58 × 10-3 m3/s to L/min.
Convert 84.3 gal/min to m3/s.
Convert 23.5 cm3/s to m3/s.
Convert 0.105 m3/s to L/min.
Convert 0.296 cm3/s to m3/s.
A pipeline is needed to transport medium fuel oil at 77°F. The pipeline needs to traverse 80 mi in total, and the initial proposal is to space pumping stations 2 mi apart. The line needs to carry 750 gal/min and would be made of 6-in Schedule 80 steel pipe. Calculate the pressure drop between
Linseed oil at 25°C flows at 3.65 m/s in a standard hydraulic copper tube, 20 mm OD × 1.2 mm wall. Compute the pressure difference between two points in the tube 17.5 m apart if the first point is 1.88 m above the second point.
Figure 8.20 shows a pump recirculating 300 gal/min of heavy machine tool lubricating oil at 104°F to test the oil’s stability. The total length of 4-in pipe is 25.0 ft and the total length of 3-in pipe is 75.0 ft. Compute the power delivered by the pump to the oil.
Gasoline at 50°F flows from point A to point B through 3200 ft of standard 10-in Schedule 40 steel pipe at the rate of 4.25 ft3/s. Point B is 85 ft above point A and the pressure at B must be 40.0 psig. Considering the friction loss in the pipe, compute the required pressure at A.
For the pump described in Problem 8.46, if the pressure at the pump inlet is -2.36 psig, compute the power delivered by the pump to the water.
Water at 60°F is being pumped from a stream to a reservoir whose surface is 210 ft above the pump. See Fig. 8.19. The pipe from the pump to the reservoir is an 8-in Schedule 40 steel pipe, 2500 ft long. If 4.00 ft3/s is being pumped, compute the pressure at the outlet of the pump. Consider the
In a chemical processing system, the flow of glycerin at 60F (sg = 1.24) in a copper tube must remain laminar with a Reynolds number approximately equal to but not exceeding 300. Specify the smallest standard Type K copper tube that will carry a flow rate of 0.90 ft3/s. Then, for a flow of 0.90
Figure 8.18 shows a system used to spray polluted water into the air to increase the water€™s oxygen content and to cause volatile solvents in the water to vaporize. The pressure at point B just ahead of the nozzle must be 25.0 psig for proper nozzle performance. The pressureat point A
Fuel oil (sg = 0.94) is being delivered to a furnace at a rate of 60 gal/min through a 1 ½-in Schedule 40 steel pipe. Compute the pressure difference between two points 40.0 ft apart if the pipe is horizontal and the oil is at 85°F.
For the system shown in Fig. 8.17, compute the power delivered by the pump to the water to pump 50 gal/min of water at 60°F to the tank. The air in the tank is at 40 psig. Consider the friction loss in the 225-ft-long discharge pipe, but neglect other losses. Then, redesign the system by using a
Water at 10°C flows at the rate of 900 L/min from the reservoir and through the pipe shown in Fig. 8.16. Compute the pressure at point B, considering the energy loss due to friction, but neglecting other losses.
For the pipeline described in Problem 8.39, consider that the oil is to be heated to 100C to decrease its viscosity.a. How does this affect the pump power requirement?b. At what distance apart could the pumps be placed with the same pressure drop as that from Problem 8.39?
A pipeline transporting crude oil (sg = 0.93) at 1200 L/min is made of DN 150 Schedule 80 steel pipe. Pumping stations are spaced 3.2 km apart. If the oil is at 10°C, calculate(a) The pressure drop between stations(b) The power required to maintain the same pressure at the inlet of each pump.
As a test to determine the effective wall roughness of an existing pipe installation, water at 10°C is pumped through it at the rate of 225 L/min. The pipe is standard steel tubing, 40 mm OD × 2.0 mm wall. Pressure gages located at 30 m apart in a horizontal run of the pipe read 1035 kPa and 669
Benzene at 60°C is flowing in a DN 25 Schedule 80 steel pipe at the rate of 20 L/min. The specific weight of the benzene is 8.62 kN/m3. Calculate the pressure difference between two points 100 m apart if the pipe is horizontal.
A 3-in Schedule 40 steel pipe is 5000 ft long and carries a lubricating oil between two points A and B such that the Reynolds number is 800. Point B is 20 ft higher than A. The oil has a specific gravity of 0.90 and a dynamic viscosity of 4 × 10-4 lb - s/ft2. If the pressure at A is 50 psig,
Glycerin at 25°C flows through a straight hydraulic copper tube, 80 mm OD × 2.8 mm wall, at a flow rate of 180 L/min. Compute the pressure difference between two points 25.8 m apart if the first point is 0.68 m below the second point.
Medium fuel oil at 25°C is to be pumped at a flow rate of 200 m3/h through a DN 125 Schedule 40 pipe over a total horizontal distance of 15 km. The maximum working pressure of the piping is to be limited to 4800 kPa gage and the pumps being used require an inlet pressure of at least 70 kPa
A tremendous amount of study has gone into the fluid effects of air over various spheres due to the impact on sports and recreation. Golf balls, for example, are dimpled due to the tremendous effect on flow characteristic and resulting drag force. Chapter 17 states that for a spherical body moving
In a given installation, it is determined that the pipe size used for the project was 1-in Schedule 40 pipe rather than the 2 in size that was specified. Some have said that it won’t be a problem since a factor of two was built into the system anyway. Others say it must be changed. If the run is
“Laminar” fountains have become quite popular due to the desirable aesthetics that result from a smooth shaped fluid held together with its own surface tension during flight. Check out videos of “laminar fountain” on the web. To convert turbulent to laminar flow a conduit is often
Use PIPE-FLO® to model a straight horizontal run of 100 ft of 1-in Schedule 40 pipe carrying 20 gal/min of 75°F water from a tank with a water level of 25 ft. Display the calculated pressure drop in the pipe, Reynolds number, and friction factor on the FLO-Sheet®.
Fuel oil is flowing in a 4-in Schedule 40 steel pipe at the maximum rate for which the flow is laminar. If the oil has a specific gravity of 0.895 and a dynamic viscosity of 8.3 × 10-4 lb - s/ft2, calculate the energy loss per 100 ft of pipe.
Water at 75°C is flowing in a standard hydraulic copper tube, 15 mm OD × 1.2 mm wall, at a rate of 12.9 L/min. Calculate the pressure difference between two points 45 m apart if the tube is horizontal.
Crude oil is flowing vertically downward through 60 m of DN 25 Schedule 80 steel pipe at a velocity of 0.64 m/s. The oil has a specific gravity of 0.86 and is at 0°C. Calculate the pressure difference between the top and bottom of the pipe.
A certain jet fuel has a kinematic viscosity of 1.20 centistokes. If the fuel is being delivered to the engine at 200 L/min through a 1-in steel tube with a wall thickness of 0.065 in, compute the Reynolds number for the flow.
In a soft-drink bottling plant, the concentrated syrup used to make the drink has a kinematic viscosity of 17.0 centistokes at 80°F. Compute the Reynolds number for the flow of 215 L/min of the syrup through a 1-in Type K copper tube.
In a dairy, milk at 100°F is reported to have a kinematic viscosity of 1.30 centistokes. Compute the Reynolds number for the flow of the milk at 45 gal/min through a 1¼-in steel tube with a wall thickness of 0.065 in.
The water line described in Problem 8.22 was a cold water distribution line. At another point in the system, the same-size tube delivers water at 180°F. Compute the range of volume flow rates for which the flow would be in the critical region.
The range of Reynolds numbers between 2000 and 4000 is described as the critical region because it is not possible to predict whether the flow is laminar or turbulent. One should avoid operation of fluid flow systems in this range. Compute the range of volume flow rates in gal/min of water at 60°F
A system is being designed to carry 500 gal/min of ethylene glycol at 77°F at a maximum velocity of 10.0 ft/s. Specify the smallest standard Schedule 40 steel pipe to meet this condition. Then, for the selected pipe, compute the Reynolds number for the flow.
After the press has run for some time, the lubricating oil described in Problem 8.19 heats to 212°F. Compute the Reynolds number for the oil flow at this temperature. Discuss the possible operating difficulty as the oil heats up.In ProblemThe lubrication system for a punch press delivers 1.65
The lubrication system for a punch press delivers 1.65 gal/min of a light lubricating oil (see Appendix C) through 5/16-in steel tubes having a wall thickness of 0.049 in. Shortly after the press is started, the oil temperature is 104°F. Compute the Reynolds number for the oil flow.
Repeat Problem 8.17 for an oil temperature of 0°C.Repeat ProblemRepeat Problem 8.15, except the tube is 50 mm OD × 1.5 mm wall thickness.Repeat ProblemSAE 30 oil (sg = 0.89) is flowing at 45 L/min through a 20 mm OD × 1.2 mm wall hydraulic steel tube. If the oil is at 110°C, is the flow laminar
Repeat Problem 8.15, except the tube is 50 mm OD × 1.5 mm wall thickness.Repeat ProblemSAE 30 oil (sg = 0.89) is flowing at 45 L/min through a 20 mm OD × 1.2 mm wall hydraulic steel tube. If the oil is at 110°C, is the flow laminar or turbulent?
Repeat Problem 8.15 for an oil temperature of 0°C.Repeat ProblemSAE 30 oil (sg = 0.89) is flowing at 45 L/min through a 20 mm OD × 1.2 mm wall hydraulic steel tube. If the oil is at 110°C, is the flow laminar or turbulent?
SAE 30 oil (sg = 0.89) is flowing at 45 L/min through a 20 mm OD × 1.2 mm wall hydraulic steel tube. If the oil is at 110°C, is the flow laminar or turbulent?
At approximately what volume flow rate will propyl alcohol at 77°F become turbulent when flowing in a 3-in Type K copper tube?
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