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applied fluid mechanics
Applied Fluid Mechanics 7th edition Robert L. Mott, Joseph A. Untener - Solutions
Compute the hydraulic radius for the section shown in Fig. 14.19 if water flows at a depth of 2.0 in. The section is that of a rain gutter for a house. 6 in 3.50 in 2 in 4 in
Repeat Problem 14.6 for a depth of 3.50 in.Repeat ProblemCompute the hydraulic radius for the section shown in Fig. 14.19 if water flows at a depth of 2.0 in. The section is that of a rain gutter for a house. 6 in 3.50 in 2 in 4 in
Compute the hydraulic radius for the channel shown in Fig. 14.20 if the water depth is 2.50 m. 25 m 0.6 m 0.5 m 1.0 m 2.
Water is flowing in a formed, unfinished concrete rectangular channel 3.5 m wide. For a depth of 2.0 m, calculate the normal discharge and the Froude number of the flow. The channel slope is 0.1 percent.
Determine the normal discharge for an aluminum rain spout with the shape shown in Fig. 14.19 that runs at the depth of 3.50 in. Use n = 0.013. The spout falls 4 in over a length of 60 ft. 6 in 3.50 in 2 in 4 in
A circular culvert under a highway is 6 ft in diameter and is made of corrugated metal. It drops 1 ft over a length of 500 ft. Calculate the normal discharge when the culvert runs half full.
A wooden flume is being built to temporarily carry 5000 L/min of water until a permanent drain can be installed. The flume is rectangular, with a 205-mm bottom width and a maximum depth of 250 mm. Calculate the slope required to handle the expected discharge.
A storm drainage channel in a city where heavy sudden rains occur has the shape shown in Fig. 14.20. It is made of unfinished concrete and has a slope of 0.5 percent. During normal times, the water remains in the small rectangular section. The upper section allows large volumes to be carried by the
Calculate the depth of flow of water in a rectangular channel 10 ft wide, made of brick in cement mortar, for a discharge of 150 ft3/s. The slope is 0.1 percent.
Calculate the depth of flow in a trapezoidal channel with a bottom width of 3 m and whose walls slope 40° with the horizontal. The channel is made of unfinished concrete and is laid on a 0.1-percent slope. The discharge is 15 m3/s.
A rectangular channel must carry 2.0 m3/s of water from a water-cooled refrigeration condenser to a cooling pond. The available slope is 75 mm over a distance of 50 m. The maximum depth of flow is 0.40 m. Determine the width of the channel if its surface is trowel-finished concrete.
The channel shown in Fig. 14.22 has a surface of floatfinished concrete and is laid on a slope that falls 0.1 m per 100 m of length. Calculate the normal discharge and the Froude number for a depth of 1.5 m. For that discharge, calculate the critical depth. 3.0 m
A square storage room is equipped with automatic sprinklers for fire protection that spray 1000 gal/min of water. The floor is designed to drain this flow evenly to troughs near each outside wall. The troughs are shaped as shown in Fig. 14.23. Each trough carries 250 gal/min, is laid on a 1-percent
The flow from two of the troughs described in Problem 14.20 passes into a sump, from which a round common clay drainage tile carries it to a storm sewer. Determine the size of tile required to carry the flow (500 gal/min) when running half full. The slope is 0.1 percent.Data from Problem 14.20A
For a rectangular channel with a bottom width of 1.00 m, compute the flow area and hydraulic radius for depths ranging from 0.10 m to 2.0 m. Plot a graph of area and hydraulic radius versus depth.
It is desired to carry 2.00 m3/s of water at a velocity of 3.0 m/s in a rectangular open channel. The bottom width is 0.80 m. Compute the depth of the flow and the hydraulic radius.
For the channel designed in Problem 14.23, compute the required slope if the channel is float-finished concrete.In ProblemIt is desired to carry 2.00 m3/s of water at a velocity of 3.0 m/s in a rectangular open channel. The bottom width is 0.80 m. Compute the depth of the flow and the hydraulic
It is desired to carry 2.00 m3/s of water at a velocity of 3.0 m/s in a rectangular open channel. Compute the depth and hydraulic radius for a range of designs for the channel, with bottom widths of 0.50 m to 2.00 m. Plot depth and hydraulic radius versus bottom width.
For each of the channels designed in Problem 14.25, compute the required slope if the channel is float-finished concrete. Plot slope versus bottom width.In ProblemIt is desired to carry 2.00 m3/s of water at a velocity of 3.0 m/s in a rectangular open channel. Compute the depth and hydraulic radius
A trapezoidal channel has a bottom width of 2.00 ft and a pitch of its sides of z = 1.50. Compute the flow area and hydraulic radius for a depth of 20 in.
For the channel described in Problem 14.27, compute the normal discharge that would be expected for a slope of 0.005 if the channel is made from formed unfinished concrete.In ProblemA trapezoidal channel has a bottom width of 2.00 ft and a pitch of its sides of z = 1.50. Compute the flow area and
A trapezoidal channel has a bottom width of 2.00 ft and a pitch of its sides of z = 1.50. Compute the flow area and hydraulic radius for depths ranging from 6.00 in to 24.00 in. Plot flow area and hydraulic radius versus depth.
For each channel designed in Problem 14.30, compute the normal discharge that would be expected for a slope of 0.005 if the channel is made from formed unfinished concrete.In ProblemA trapezoidal channel has a bottom width of 2.00 ft and a pitch of its sides of z = 1.50. Compute the flow area and
Compute the flow area and hydraulic radius for a circular drain pipe 375 mm in diameter for a depth of 225 mm.
Repeat Problem 14.32 for a depth of 135 mm.Repeat ProblemCompute the flow area and hydraulic radius for a circular drain pipe 375 mm in diameter for a depth of 225 mm.
For the channel designed in Problem 14.32, compute the normal discharge that is expected for a slope of 0.12 percent if the channel is made from painted steel.In ProblemCompute the flow area and hydraulic radius for a circular drain pipe 375 mm in diameter for a depth of 225 mm.
For the channel designed in Problem 14.33, compute the normal discharge that is expected for a slope of 0.12 percent if the channel is made from painted steel. Compare the result with that from Problem 14.34.In ProblemRepeat Problem 14.32 for a depth of 135 mm.Repeat ProblemCompute the flow area
Determine the maximum possible flow rate over a 60°V-notch weir if the width of the notch at the top is 12 in.
Plot a graph of Q versus H for a full-width weir with a crest length of 6 ft and whose crest is 2 ft from the channel bottom. Consider values of the head H from 0 to 12 inches in 2-in steps.
Repeat the calculations of Q versus H for a weir with the same dimensions as used in Problem 14.45 except that it is placed in a channel wider than 6 ft. It, thus, becomes a contracted weir.In ProblemPlot a graph of Q versus H for a full-width weir with a crest length of 6 ft and whose crest is 2
Compare the discharges over the following weirs when the head H is 18 in:a. Full-width rectangular: L = 3 ft, Hc = 4 ftb. Contracted rectangular: L = 3 ft, Hc = 4 ftc. 90 V-notch (top width also 3 ft)
Plot a graph of Q versus H for a 90° V-notch weir for values of the head from 0 to 12 in. in 2-in steps.
For a Parshall flume with a throat width of 9 in, calculate the head H corresponding to the minimum and maximum flows.
For a Parshall flume with a throat width of 8 ft, calculate the head H corresponding to the minimum and maximum flows. Plot a graph of Q versus H , using five values of H spaced approximately equally between the minimum and the maximum.
A flow rate of 50 ft3/s falls within the range of both the 4-ft- and the 10-ft-wide Parshall flume. Compare the head H for this flow rate in each size.
A long-throated flume is installed in a trapezoidal channel using design C from Table 14.5. Compute the discharge for a head of 0.84 ft.
A venturi meter similar to the one in Fig. 15.2 has an inlet diameter of 100 mm and a throat diameter of 50 mm. While it is carrying water at 80°C, a pressure difference of 55 kPa is observed between sections 1 and 2. Calculate the volume flow rate of water. Main pipe section Main pipe Throat
A long-throated flume is installed in a circular pipe using design B from Table 14.5. Compute the discharge for a head of 0.25 ft.
A long-throated flume is installed in a circular channel using design A from Table 14.5. Compute the discharge for a head of 0.09 ft.
For a long-throated flume of design B in a rectangular channel, compute the head corresponding to a volume flow rate of 1.25 ft3/s.
For a long-throated flume of design C in a circular channel, compute the head corresponding to a volume flow rate of 6.80 ft3/s.
Select a long-throated flume from Table 14.5 that will carry a range of flow from 30 gal/min to 500 gal/min. Compute the head for each of these flows and then compute the flow that would result from four additional heads spaced approximately equally between them.
Select a long-throated flume from Table 14.5 that will carry a range of flow from 50 m3/h to 180 m3/h. Compute the head for each of these flows and then compute the flow that would result from four additional heads spaced approximately equally between them.
A flow nozzle similar to that shown in Fig. 15.4 is used to measure the flow of water at 120°F. The pipe is 6-in Schedule 80 steel. The nozzle diameter is 3.50 in. Determine the pressure difference across the nozzle that would be measured for a flow of 1800 gal/min.Figure 15.4 D/2 3. Flow D. P2 to
A pitot-static tube is inserted into a pipe carrying methyl alcohol at 25°C. A differential manometer using mercury as the gage fluid is connected to the tube and shows a deflection of 225 mm. Calculate the velocity of flow of the alcohol.
A pitot-static tube is connected to a differential manometer using water at 40°C as the gage fluid. The velocity of air at 40°C and atmospheric pressure is to be measured, and it is expected that the maximum velocity will be 25 m/s. Calculate the expected manometer deflection.
A pitot-static tube is inserted in a pipe carrying water at 10°C. A differential manometer using mercury as the gage fluid shows a deflection of 106 mm. Calculate the velocity of flow.
A pitot-static tube is inserted into a duct carrying air at standard atmospheric pressure and a temperature of 80°F. A differential manometer reads 0.24 in of water. Calculate the velocity of flow.
For the system described in Problem 9.27, compute the pressure difference in both the small pipes and the large pipe between two points 50.0 ft apart if the pipes are horizontal. Use the roughness for steel pipe for all surfaces.
To what do the affinity laws refer in regard to pumps?
For a given centrifugal pump, if the speed of rotation of the impeller is cut in half, how does the capacity change?
For a given centrifugal pump, if the speed of rotation of the impeller is cut in half, how does the total head capability change?
For a given centrifugal pump, if the speed of rotation of the impeller is cut in half, how does the power required to drive the pump change?
For a given size of centrifugal pump casing, if the diameter of the impeller is reduced by 25 percent, how much does the capacity change?
For a given size of centrifugal pump casing, if the diameter of the impeller is reduced by 25 percent, how much does the total head capability change?
For a given size of centrifugal pump casing, if the diameter of the impeller is reduced by 25 percent, how much does the power required to drive the pump change?
Describe each part of this centrifugal pump designation: 1½ × 3 - 6.
For the line of pumps shown in Fig. 13.22, specify a suitable size for delivering 100 gal/min of water at a total head of 300 ft. 500 150 150 Impeller speed - 3500 r/min 400 E 100 100 300 2х3-10 14x3 - 10 3x4 - 10 200 50 50 1x -6 x3 - 6 100 2х3-6- 600 100 200 300 400 500 700 800 Capacity
For the line of pumps shown in Fig. 13.22, specify a suitable size for delivering 600 L/min of water at a total head of 25 m. 500 150 150 Impeller speed - 3500 r/min 400 E 100 100 300 2х3-10 14x3 - 10 3x4 - 10 200 50 50 1x -6 x3 - 6 100 2х3-6- 600 100 200 300 400 500 700 800 Capacity (gal/min)
For the 2 × 3 - 10 centrifugal pump performance curve shown in Fig. 13.28, describe the performance that can be expected from a pump with an 8-in impeller operating against a system head of 200 ft. Give the expected capacity, the power required, the efficiency, and the required NPSH.
For the 2 × 3 - 10 centrifugal pump performance curve shown in Fig. 13.28, at what head will the pump having an 8-in impeller operate at its highest efficiency? List the pump€™s capacity, power required, efficiency, and the required NPSH at that head. Impeller diameter 10 in
Using the result from Problem 13.26, describe how the performance of the pump changes if the system head increases by 15 percent.In ProblemFor the 2 × 3 - 10 centrifugal pump performance curve shown in Fig. 13.28, at what head will the pump having an 8-in impeller operate at its
For the 2 × 3 - 10 centrifugal pump performance curve shown in Fig. 13.28, list the total head and capacity at which the pump will operate at maximum efficiency for each of the impeller sizes shown. Impeller diameter 10 in 3136-41-46 140 2x3- 10 3500 RPM 450 151 54 56 57 58 58.7 400 9
For a given centrifugal pump and impeller size, describe how the NPSH required varies as the capacity increases.
State some advantages of using a variable-speed drive for a centrifugal pump that supplies fluid to a process requiring varying flow rates of a fluid as compared with adjusting throttling valves.
Describe how the capacity, efficiency, and power required for a centrifugal pump vary as the viscosity of the fluid pumped increases.
If two identical centrifugal pumps are connected in parallel and operated against a certain head, how would the total capacity compare with that of a single pump operating against the same head?
Describe the effect of operating two pumps in series.
For each of the following sets of operating conditions, list at least one appropriate type of pump. See Fig. 13.52.a. 500 gal/min of water at 80 ft of total headb. 500 gal/min of water at 800 ft of headc. 500 gal/min of a viscous adhesive at 80 ft of headd. 80 gal/min of water at 8000 ft of heade.
For the 1½ × 3 - 13 centrifugal pump performance curve shown in Fig. 13.34, determine the capacity that can be expected from a pump with a 12-in impeller operating against a system head of 550 ft. Then, compute the specific speed and specific diameter and locate the
For the 6 × 8 - 17 centrifugal pump performance curve shown in Fig. 13.32, determine the capacity that can be expected from a pump with a 15-in impeller operating against a system head of 200 ft. Then, compute the specific speed and specific diameter and locate the corresponding point on Fig.
Figure 13.52 shows that a mixed-flow pump is recommended for delivering 10 000 gal/min of water at a head of 40 ft. If such a pump operates with a specific speed of 5000, compute the appropriate operating speed of the pump. Flow (m3/h) 2.3 100 000 23 230 2300 23 000 30 000 Reciprocating 10 000 3000
Compute the specific speed for a pump operating at 1750 rpm delivering 5000 gal/min of water at a total head of 100 ft.
Compute the specific speed for a pump operating at 1750 rpm delivering 12 000 gal/min of water at a total head of 300 ft.
Compute the specific speed for a pump operating at 1750 rpm delivering 500 gal/min of water at a total head of 100 ft.
Compute the specific speed for a pump operating at 3500 rpm delivering 500 gal/min of water at a total head of 100 ft. Compare the result with that of Problem 13.40 and with Fig. 13.52. Flow (m3/h) 2.3 100 000 23 230 2300 23 000 30 000 Reciprocating 10 000 3000 Multistage centrifugal Rotary 1000
It is desired to operate a pump at 1750 rpm by driving it with a four-pole electric motor. For each of the following conditions, compute the specific speed using Eq. (13–17). Then, recommend whether to use an axial pump, a mixed-flow pump, a radial-flow pump, or none of these, based on the
For what point in a pumping system is the NPSH computed? Why?
Discuss why it is desirable to elevate the reservoir from which a pump draws liquid.
Discuss why it is desirable to use relatively large pipe sizes for the suction lines in pumping systems.
Discuss why an eccentric reducer should be used when it is necessary to decrease the size of a suction line as it approaches a pump.
If we assume that a given pump requires 7.50 ft of NPSH when operating at 3500 rpm, what would be the NPSH required at 2850 rpm?
Select a pump from the sample catalogue within the PIPE-FLO® demo software to run a system that pumps water at 30°C from a reservoir up into a storage tower, 20 m higher, at a rate of 1800 L/min. Position the pump at the same level as the reservoir. On the suction side, use 8 m of DN 100 Schedule
Work Problem 12.4 using PIPE-FLO® software. Display the volume flow rate in each branch and all other relevant values on the FLO-Sheet®.
Figure 12.15 represents the network for delivering coolant to five different machine tools in an automated machining system. The grid is a rectangle 7.5 m by 15 m. All pipes are drawn steel tubing with a 0.065-in wall thickness. Pipes 1 and 3 are 2-in diameter, pipe 2 is 1½-in diameter, and
Figure 12.14 represents the water distribution network in a small industrial park. The supply of 15.5 ft3/s of water at 60 F enters the system at A. Manufacturing plants draw off the indicated flows at points C, E, F, G, H, and I. Determine the flow in each pipe in the system. 15.5 ft/s 2) Pipe
Figure 12.13 represents a spray rinse system in which water at 15°C is flowing. All pipes are 3-in Type K copper tubing. Determine the flow rate in each pipe. 6000 L/min 10 m 15 m 10 m 6 m 6 m 15 m 15 m 15 m 1500 L/min 1500 L/min 1500 L/min 1500 L/min
The pump pictured in Fig. 11.12 delivers water from the lower reservoir to the upper reservoir at a rate of 220 gal/min. There are 10 ft of 3-in Schedule 40 steel pipe before the pump, and 32 ft after. There are three standard 90° elbows and a fully open gate valve. The depth of the fluid
For the system shown in Fig. 11.14, kerosene (sg = 0.82) at 20°C is to be forced from tank A to reservoir B by increasing the pressure in the sealed tank A above the kerosene. The total length of DN 50 Schedule 40 steel pipe is 38 m. The elbow is standard. Calculate the required pressure in
Figure 11.15 shows a portion of a hydraulic circuit. The pressure at point B must be 200 psig when the volume flow rate is 60 gal/min. The hydraulic fluid has a specific gravity of 0.90 and a dynamic viscosity of 6.0 × 10-5lbˆ™s/ft2. The total length of pipe between A and B
Figure 11.16 shows part of a large hydraulic system in which the pressure at B must be 500 psig while the flow rate is 750 gal/min. The fluid is a medium machine tool hydraulic oil. The total length of the 4-in pipe is 40 ft. The elbows are standard. Neglect the energy loss due to friction in the
Oil is flowing at the rate of 0.015 m3/s in the system shown in Fig. 11.17. Data for the system are as follows:– Oil specific weight = 8.80 kN/ m3– Oil kinematic viscosity = 2.12 × 10ˆ’5m2/s– Length of DN 150 pipe = 180 m– Length of
For the system shown in Fig. 11.18, calculate the vertical distance between the surfaces of the two reservoirs when water at 10°C flows from A to B at the rate of 0.03 m 3 /s. The elbows are standard. The total length of the 3-in pipe is 100 m. For the 6-in pipe it is 300 m. 3-in coated ductile
A liquid refrigerant flows through the system, shown in Fig. 11.19, at the rate of 1.70 L/min. The refrigerant has a specific gravity of 1.25 and a dynamic viscosity of 3 × 10ˆ’4Pa·s. Calculate the pressure difference between points A and B. The hydraulic tube is drawn
In a processing plant, ethylene glycol at 77°F is flowing in a 6-in coated ductile iron pipe having a length of 5000 ft. Over this distance, the pipe falls 55 ft and the pressure drops from 250 psig to 180 psig. Calculate the velocity of flow in the pipe.
Water at 15°C is flowing downward in a vertical tube 7.5 m long. The pressure is 550 kPa at the top and 585 kPa at the bottom. A ball-type check valve is installed near the bottom. The hydraulic tube is drawn steel, with a 32 mm OD and a 2.0 mm wall thickness. Compute the volume flow rate of the
Turpentine at 77°F is flowing from A to B in a 3-in coated ductile iron pipe. Point B is 20 ft higher than point A and the total length of the pipe is 60 ft. Two 90° long-radius elbows are installed between A and B. Calculate the volume flow rate of turpentine if the pressure at A is 120 psig and
A device designed to allow cleaning of walls and windows on the second floor of homes is similar to the system shown in Fig. 11.20. Determine the velocity of flow from the nozzle if the pressure at the bottom is (a) 20 psig and (b) 80 psig. The nozzle has a loss coefficient K of 0.15 based on the
Determine the required size of new Schedule 80 steel pipe to carry water at 160°F with a maximum pressure drop of 10 psi per 1000 ft when the flow rate is 0.5 ft3/s.
What size of standard hydraulic copper tube from Appendix G.2 is required to transfer 0.06 m3/s of water at 80°C from a heater where the pressure is 150 kPa to an open tank? The water flows from the end of the tube into the atmosphere. The tube is horizontal and 30 m long.
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