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applied fluid mechanics
Applied Fluid Mechanics 7th edition Robert L. Mott, Joseph A. Untener - Solutions
An air compressor delivers 2880 cfm of free air. Compute the flow rate of air in a pipe in which the pressure is 65 psig and the temperature is 95°F.
Specify a size of Schedule 40 steel pipe suitable for carrying 165 cfm (FAD) at 100 psig with no more than 5.0-psi pressure drop in 100 ft of pipe.
Specify a size of Schedule 40 steel pipe suitable for carrying 800 cfm (free air) to a reactor vessel in a chemical processing plant in which the pressure must be at least 100 psig at 70°F. The total length of pipe from the compressor to the reactor vessel is 350 ft. The line contains eight
For an aeration process, a sewage treatment plant requires 3000 cfm of compressed air. The pressure must be 80 psig, and the temperature must be 120°F. The compressor is located in a utility building, and 180 ft of pipe is required. The line also contains one fully open butterfly valve, 12 elbows,
Air flows from a reservoir in which the pressure is 40.0 psig and the temperature is 80°F to a pipe in which the pressure is 20.0 psig. The flow is to be considered adiabatic. Compute the specific weight of the air both in the reservoir and in the pipe.
Air flows from a reservoir in which the pressure is 275 kPa and the temperature is 25°C to a pipe in which the pressure is 140 kPa. The flow is to be considered adiabatic. Compute the specific weight of the air both in the reservoir and in the pipe.
Refrigerant 12 expands adiabatically from 35.0 psig at a temperature of 60°F to 3.6 psig. Compute the specific weight of the refrigerant at both conditions.
Oxygen is discharged from a tank in which the pressure is 125 psig and the temperature is 75F through a nozzle with a diameter of 0.120 in. The oxygen flows into the atmosphere, where the pressure is 14.40 psia. Compute the weight flow rate from the tank and the velocity of flow through the nozzle.
Repeat Problem 18.32, but change the pressure in the tank to 7.50 psig.Repeat ProblemOxygen is discharged from a tank in which the pressure is 125 psig and the temperature is 75F through a nozzle with a diameter of 0.120 in. The oxygen flows into the atmosphere, where the pressure is 14.40 psia.
A high-performance racing tire is charged with nitrogen at 50 psig and 70°F. At what weight flow rate would the nitrogen escape through a valve with a diameter of 0.062 in into the atmosphere at a pressure of 14.60 psia?
Repeat Problem 18.34 at internal pressures of 45 psig through 0 psig in 5.0-psig decrements. Plot a graph of weight flow rate versus the internal pressure in the tire.Repeat ProblemA high-performance racing tire is charged with nitrogen at 50 psig and 70°F. At what weight flow rate would the
Figure 18.14 shows a two-compartment vessel. The compartments are connected by a smooth convergent nozzle. The left compartment contains propane gas and is maintained at a constant 25.0 psig and 65°F. The right compartment starts at an equal 25.0-psig pressure, and then the pressure is
Air flows from a large tank through a smooth convergent nozzle into the atmosphere, where the pressure is 98.5 kPa absolute. The temperature in the tank is 95°C. Compute the minimum pressure in the tank required to produce sonic velocity in the nozzle.
For the conditions of Problem 18.37, compute the magnitude of the sonic velocity in the nozzle.In ProblemAir flows from a large tank through a smooth convergent nozzle into the atmosphere, where the pressure is 98.5 kPa absolute. The temperature in the tank is 95°C. Compute the minimum pressure in
For the conditions of Problem 18.37, compute the weight flow rate of air from the tank if the nozzle diameter is 10.0 mm.In ProblemAir flows from a large tank through a smooth convergent nozzle into the atmosphere, where the pressure is 98.5 kPa absolute. The temperature in the tank is 95°C.
A tank of Refrigerant 12 is at 150 kPa gage and 20°C. At what rate would the refrigerant flow from the tank into the atmosphere, where the pressure is 100.0 kPa absolute, through a smooth nozzle having a throat diameter of 8.0 mm?
For the tank described in Problem 18.40, compute the weight flow rate through the nozzle for tank gage pressures of 125 kPa, 100 kPa, 75 kPa, 50 kPa, and 25 kPa. Assume that the temperature in the tank is 20°C for all cases. Plot the weight flow rate versus tank pressure.In ProblemA tank of
Determine the velocity of flow and the friction loss as 1000 cfm of air flows through 75 ft of an 18-in-diameter round duct.
Repeat Problem 19.1 for duct diameters of 16, 14, 12, and 10 in. Then plot the velocity and friction loss versus duct diameter.Repeat ProblemDetermine the velocity of flow and the friction loss as 1000 cfm of air flows through 75 ft of an 18-in-diameter round duct.
Specify a diameter for a round duct suitable for carrying 1500 cfm of air with a maximum pressure drop of 0.10 inH2O per 100 ft of duct, rounding up to the next inch. For the actual size specified, give the friction loss per 100 ft of duct.
Repeat Problem 19.4 for duct diameters of 600, 700, 800, 900, and 1000 mm. Then plot the velocity and friction loss versus duct diameter.Repeat ProblemDetermine the velocity of flow and the friction loss as 3.0 m3/s of air flows through 25 m of a 500-mm-diameter round duct.
Specify a diameter for a round duct suitable for carrying 0.40 m3/s of air with a maximum pressure drop of 1.00 Pa/m of duct, rounding up to the next 50-mm increment. For the actual size specified, give the friction loss in Pa/m.
A heating duct for a forced-air furnace measures 10 × 30 in. Compute the circular equivalent diameter. Then determine the maximum flow rate of air that the duct could carry while limiting the friction loss to 0.10 inH2O per 100 ft.
A branch duct for a heating system measures 3 × 10 in. Compute the circular equivalent diameter. Then determine the maximum flow rate of air that the duct could carry while limiting the friction loss to 0.10 inH2O per 100 ft.
A ventilation duct in a large industrial warehouse measures 42 × 60 in. Compute the circular equivalent diameter. Then determine the maximum flow rate of air that the duct could carry while limiting the friction loss to 0.10 inH2O per 100 ft.
A heating duct for a forced-air furnace measures 250 × 500 mm. Compute the circular equivalent diameter. Then determine the maximum flow rate of air that the duct could carry while limiting the friction loss to 0.80 Pa/m.
A branch duct for a heating system measures 75 × 250 mm. Compute the circular equivalent diameter. Then determine the maximum flow rate of air that it could carry while limiting the friction loss to 0.80 Pa/m.
Specify a size for a rectangular duct suitable for carrying 1500 cfm of air with a maximum pressure drop of 0.10 inH2O per 100 ft of duct. The maximum vertical height of the duct is 12.0 in.
Specify a size for a rectangular duct suitable for carrying 300 cfm of air with a maximum pressure drop of 0.10 inH2O per 100 ft of duct. The maximum vertical height of the duct is 6.0 in.
Compute the pressure drop as 650 cfm of air flows through a three-piece 90 elbow in a 12-in-diameter round duct.
Repeat Problem 19.14, but use a five-piece elbow.Repeat ProblemCompute the pressure drop as 650 cfm of air flows through a three-piece 90 elbow in a 12-in-diameter round duct.
Compute the pressure drop as 1500 cfm of air flows through a wide-open damper installed in a 16-in-diameter duct.
Repeat Problem 19.16 with the damper partially closed at 10, 20, and 30.Repeat ProblemCompute the pressure drop as 1500 cfm of air flows through a wide-open damper installed in a 16-in-diameter duct.
A part of a duct system is a 10-by-22-in rectangular main duct carrying 1600 cfm of air. A tee to a branch duct, 10 × 10 in, draws 500 cfm from the main. The main duct remains the same size downstream from the branch. Determine the velocity of flow and the velocity pressure in all parts of the
For the conditions of Problem 19.18, estimate the loss in pressure as the flow enters the branch duct through the tee.In ProblemA part of a duct system is a 10-by-22-in rectangular main duct carrying 1600 cfm of air. A tee to a branch duct, 10 × 10 in, draws 500 cfm from the main. The main duct
For the conditions of Problem 19.18, estimate the loss in pressure for the flow in the main duct due to the tee.In ProblemA part of a duct system is a 10-by-22-in rectangular main duct carrying 1600 cfm of air. A tee to a branch duct, 10 × 10 in, draws 500 cfm from the main. The main duct remains
Compute the pressure drop as 0.20 m3/s of air flows through a three-piece 90° elbow in a 200-mm-diameter round duct.
Repeat Problem 19.21, but use a mitered elbow.Repeat ProblemCompute the pressure drop as 0.20 m3/s of air flows through a three-piece 90° elbow in a 200-mm-diameter round duct.
Compute the pressure drop as 0.85 m3/s of air flows through a damper set at 30° installed in a 400-mmdiameter duct.
A section of duct system consists of 42 ft of straight 12-indiameter round duct, a wide-open damper, two three-piece 90 elbows, and an outlet grille. Compute the pressure drop along this duct section for Q = 700 cfm.
A section of duct system consists of 38 ft of straight 12-by-20-in rectangular duct, a wide-open damper, three smooth 90 elbows, and an outlet grille. Compute the pressure drop along this duct section for Q = 1500 cfm.
Compute the hydraulic radius for the channel shown in Fig. 14.20 if the water depth is 0.50 m. 25 m 0.6 m 0.5 m 1.0 m 2.
Determine the required length of a contracted weir similar to that shown in Fig. 14.17 (b) to pass 15 ft3/s of water. The height of the crest is to be 3 ft from the channel bottom, and the maximum head above the crest is to be 18 in.
A long-throated flume is installed in a trapezoidal channel using design B from Table 14.5. Compute the discharge for a head of 0.65 ft.
A long-throated flume is installed in a rectangular channel using design C from Table 14.5. Compute the discharge for a head of 0.40 ft.
Air with a specific weight of 12.7 N/m3and a kinematic viscosity of 1.3 × 10ˆ’5m2/s is flowing through a flow nozzle similar to that shown in Fig. 15.4. A manometer using water as the gage fluid reads 81 mm of deflection. Calculate the volume flow rate if the nozzle diameter
The flow of kerosene is being measured with an orifice meter similar to that shown in Fig. 15.6. The pipe is a 2-in Schedule 40 pipe and the orifice diameter is 1.00 in. The kerosene is at 77°F. For a pressure difference of 0.53 psi across the orifice, calculate the volume flow rate of
A sharp-edged orifice is placed in a 10-in-diameter pipe carrying ammonia. If the volume flow rate is 25 gal/min, calculate the deflection of a water manometer (a) If the orifice diameter is 1.0 in (b) If the orifice diameter is 7.0 in. The ammonia has a specific gravity of 0.83 and a
A pitot-static tube is inserted into a duct carrying air at standard atmospheric pressure and a temperature of 50°C. A differential manometer reads 4.8 mm of water. Calculate the velocity of flow.
Calculate the force required to hold a flat plate in equilibrium perpendicular to the flow of water at 25 m/s issuing from a 75-mm-diameter nozzle.
What must be the velocity of flow of water from a 2-indiameter nozzle to exert a force of 300 lb on a flat wall?
Calculate the force exerted on a stationary curved vane that deflects a 1-in-diameter stream of water through a 90° angle. The volume flow rate is 150 gal/min.
A highway sign is being designed to withstand winds of 125 km/h. Calculate the total force on a sign 4 m by 3 m if the wind is flowing perpendicular to the face of the sign. Calculate the equivalent pressure on the sign in Pa. The air is at −10°C.
Compute the forces in the vertical and horizontal directions on the block shown in Fig. 16.12. The fluid stream is a 1.75-in-diameter jet of water at 60°F with a velocity of 25 ft/s. The velocity leaving the block is also 25 ft/s. 30°
Figure 16.13 shows a free stream of water at 180°F being deflected by a stationary vane through a 130 angle. The entering stream has a velocity of 22.0 ft/s. The cross-sectional area of the stream is constant at 2.95 in2throughout the system. Compute the forces in the horizontal and vertical
Compute the horizontal and vertical forces exerted on the vane shown in Fig. 16.14 due to a flow of water at 50°C. The velocity is constant at 15 m/s. 100-mm diameter 60°
In a plant where hemispherical cup-shaped parts are made, an automatic washer is being designed to clean the parts prior to shipment. One scheme being evaluated uses a stream of water at 180°F shooting vertically upward into the cup. The stream has a velocity of 30 ft/s and a diameter of 1.00
A stream of non-flammable oil (sg 0.90) is directed onto the center of the underside of a flat metal plate to keep it cool during a welding operation. The plate weighs 550 N. If the stream is 35 mm in diameter, calculate the velocity of the stream that will lift the plate. The stream strikes the
A 2-in-diameter stream of water having a velocity of 40 ft/s strikes the edge of a flat plate such that half the stream is deflected downward as shown in Fig. 16.16. Calculate the force on the plate and the moment due to the force at point A. 0,= Q,2 2-in diameter 4 in O3 = Q,/2
Figure 16.17 represents a type of flowmeter in which the flat vane is rotated on a pivot as it deflects the fluid stream. The fluid force is counterbalanced by a spring. Calculate the spring force required to hold the vane in a vertical position when water at 100 gal/min flows from the 1-in
Water is piped vertically from below a boat and discharged horizontally in a 4-in diameter jet with a velocity of 60 ft/s. Calculate the force on the boat.
For the louvers shown in Fig. 16.21 and described in Problem 16.24, compute the torque required to rotate the louvers when the angle θ = 20°. Pivot Incoming air stream Louvers are 20.0 in long 5.0 in typical Louver
A 2-in nozzle is attached to a hose with an inside diameter of 4 in. The resistance coefficient K of the nozzle is 0.12 based on the outlet velocity head. If the jet issuing from the nozzle has a velocity of 80 ft/s, calculate the force exerted by the water on the nozzle.
Seawater (sg 1.03) enters a heat exchanger through a reducing bend connecting a 4-in Type K copper tube with a 2-in Type K tube. The pressure upstream from the bend is 825 kPa. Calculate the force required to hold the bend in equilibrium. Consider the energy loss in the bend, assuming it has a
A reducer connects a standard 6-in Schedule 40 pipe to a 3-in Schedule 40 pipe. The walls of the conical reducer are tapered at an included angle of 40. The flow rate of water is 500 gal/min and the pressure ahead of the reducer is 125 psig. Considering the energy loss in the reducer, calculate
Calculate the force on a 45 elbow attached to an 8-in Schedule 80 steel pipe carrying water at 80F at 6.5 ft3/s. The outlet of the elbow discharges into the atmosphere. Consider the energy loss in the elbow.
Calculate the force required to hold a 90° elbow in place when attached to DN 150 Schedule 40 pipes carrying water at 125 m3/s and 1050 kPa. Neglect energy lost in the elbow.
Calculate the force required to hold a 180° close return bend in equilibrium. The bend is in a horizontal plane and is attached to a DN 100 Schedule 80 steel pipe carrying 2000 L/min of a hydraulic fluid at 2.0 MPa. The fluid has a specific gravity of 0.89. Neglect energy losses.
A bend in a tube causes the flow to turn through an angle of 135°. The pressure ahead of the bend is 275 kPa. If the standard hydraulic copper tube, 100 mm OD × 3.5 mm wall, carries 0.12 m3/s of carbon tetrachloride at 25°C, determine the force on the bend. Neglect energy losses.
A vehicle is to be propelled by a jet of water impinging on a vane as shown in Fig. 16.18. The jet has a velocity of 30 m/s and issues from a nozzle with a diameter of 200 mm. Calculate the force on the vehicle (a) If it is stationary (b) If it is moving at 12 m/s. 15°
A part of an inspection system in a packaging operation uses a jet of air to remove imperfect cartons from a conveyor line, as shown in Fig. 16.19. The jet is initiated by a sensor and timed so that the product to be rejected is in front of the jet at the right moment. The product is to be tipped
Shown in Fig. 16.20 is a small decorative wheel fitted with flat paddles so the wheel turns about its axis when acted on by a blown stream of air. Assuming that all the air in a 15-mm-diameter stream moving at 0.35 m/s strikes one paddle and is deflected by it at right angles, compute the force
For the wheel described in Problem 16.22, compute the force exerted on the paddle when the wheel rotates at 40 rpm.In ProblemShown in Fig. 16.20 is a small decorative wheel fitted with flat paddles so the wheel turns about its axis when acted on by a blown stream of air. Assuming that all the air
A set of louvers deflects a stream of warm air onto painted parts, as illustrated in Fig. 16.21. The louvers are rotated slowly to distribute the air evenly over the parts. Compute the torque required to rotate the louvers toward the stream of air when it is flowing at a velocity of 10 ft/s. Assume
For the louvers shown in Fig. 16.21 and described in Problem 16.24, compute the torque required to rotate the louvers for several settings of the angle u from 10 to 90. Plot a graph of torque versus angle. Pivot Incoming air stream Louvers are 20.0 in long 5.0 in typical Louver
Figure 16.22 shows a device for clearing debris using a 1½-in-diameter jet of air issuing from a blower nozzle. As shown, the jet is striking a rectangular box-shaped object sitting on a floor. If the air velocity is 25 ft/s and the entire jet is deflected by the box, what is the heaviest
Repeat Problem 16.27, except change the jet to water at 50°F and the diameter to 0.75 in.Repeat ProblemFigure 16.22 shows a device for clearing debris using a 1½-in-diameter jet of air issuing from a blower nozzle. As shown, the jet is striking a rectangular box-shaped object sitting on
Figure 16.23 is a sketch of a turbine in which the incoming stream of water at 15°C has a diameter of 7.50 mm and is moving with a velocity of 25 m/s. Compute the force on one blade of the turbine if the stream is deflected through the angle shown and the blade is stationary. Jet stream path
Repeat Problem 16.29 with the blade rotating as a part of the wheel at a radius of 200 mm and with a linear tangential velocity of 10 m/s. Also, compute the rotational speed of the wheel in rpm.Repeat ProblemFigure 16.23 is a sketch of a turbine in which the incoming stream of water at 15°C has
Repeat Problem 16.29, except with the blade rotating as a part of the wheel at a radius of 200 mm and with a linear tangential velocity ranging from 0 to 25 m/s in 5-m/s steps.Repeat ProblemFigure 16.23 is a sketch of a turbine in which the incoming stream of water at 15°C has a diameter of
Determine the terminal velocity (see Section 2.6.4, Chapter 2 ) of a 75-mm-diameter sphere made of solid aluminum (specific weight = 26.6 kN/m3) in free fall in (a) castor oil at 25°C, (b) water at 25°C, and (c) air at 20°C and standard atmospheric pressure. Consider the effect of buoyancy.
Calculate the moment at the base of a flagpole caused by a wind of 150 km/h. The pole is made of three sections, each 3 m long, of different-size Schedule 80 steel pipe. The bottom section is DN 150, the middle is DN 125, and the top is DN 100. The air is at 0°C and standard atmospheric pressure.
A pitcher throws a baseball without spin with a velocity of 20 m/s. If the ball has a circumference of 225 mm, calculate the drag force on the ball in air at 30°C.
A wing on a race car is supported by two cylindrical rods, as shown in Fig. 17.15. Compute the drag force exerted on the car due to these rods when the car is traveling through still air at ˆ’20°F at a speed of 150 mph. 2.0-in diameter 32 in Rod
In an attempt to decrease the drag on the car shown in Fig. 17.15 and described in Problem 17.14, the cylindrical rods are replaced by elongated elliptical cylinders having a length-to-breadth ratio of 8:1. By how much will the drag be reduced? Repeat for the Navy strut . 2.0-in diameter 32 in Rod
A parachute in the form of a hemispherical cup 1.5 m in diameter is deployed from a car trying for the land speed record. Determine the force exerted on the car if it is moving at 1100 km/h in air at atmospheric pressure and 20°C.
Calculate the required diameter of a parachute in the form of a hemispherical cup supporting a man weighing 800 N if the terminal velocity (see Section 2.6.4, Chapter 2)in air at 40°C is to be 5 m/s.
A ship tows an instrument in the form of a 30° cone, point first, at 7.5 m/s in seawater. If the base of the cone has a diameter of 2.20 m, calculate the force in the cable to which the cone is attached.
A highway sign is being designed to withstand winds of 125 km/h. Calculate the total force on a sign 4 m by 3 m if the wind is flowing perpendicular to the face of the sign. The air is at −10°C. Compare the force calculated for this problem with that for Problem 16.4. Discuss the reasons for the
Assuming that a semitrailer behaves as a square cylinder, calculate the force exerted if a wind of 20 km/h strikes it broadside. The trailer is 2.5 m by 2.5 m by 12 m. The air is at 0C and standard atmospheric pressure.
A type of level indicator incorporates four hemispherical cups with open fronts mounted as shown in Fig. 17.13. Each cup is 25 mm in diameter. A motor drives the cups at a constant rotational speed. Calculate the torque that the motor must produce to maintain the motion at 20 rpm when the cups are
Determine the wind velocity required to overturn the mobile home sketched in Fig. 17.14 if it is 10 m long and weighs 50 kN. Consider it to be a square cylinder. The width of each tire is 300 mm. The air is at 0°C. 2.5m Wind Direction 2.5 m 3 m 2 m
A bulk liquid transport truck incorporates a cylindrical tank 2 m in diameter and 8 m long. For the tank alone, calculate the pressure drag when the truck is traveling at 100 km/h in still air at 0°C.
An antenna in the shape of a cylindrical rod projects from the top of a locomotive. If the antenna is 42 in long and 0.200 in. in diameter, compute the drag force on it when the locomotive is traveling at 160 mph in still air at -20°F.
A ship tows an instrument package in the form of a hemisphere with an open back at a velocity of 25.0 ft/s through seawater at 77°F. The diameter of the hemisphere is 7.25 ft. Compute the force in the cable to which the package is attached.
Compute the hydraulic radius for a circular drain pipe running half full if its inside diameter is 300 mm.
A rectangular channel has a bottom width of 2.75 m. Compute the hydraulic radius when the fluid depth is 0.50 m.
A drainage structure for an industrial park has a trapezoidal cross-section similar to that shown in Fig. 14.2 (c). The bottom width is 3.50 ft and the sides are inclined at an angle of 60 from the horizontal. Compute the hydraulic radius for this channel when the fluid depth is 1.50 ft. х W- х
Repeat Problem 14.3 if the side slope is 45°.Repeat ProblemA drainage structure for an industrial park has a trapezoidal cross-section similar to that shown in Fig. 14.2 (c). The bottom width is 3.50 ft and the sides are inclined at an angle of 60 from the horizontal. Compute the hydraulic
Compute the hydraulic radius for a trapezoidal channel with a bottom width of 150 mm and with sides that pitch 15 mm horizontally for a vertical change of 10 mm. That is, the ratio of X D in Fig. 14.2 (c) is 1.50. The depth of the fluid in the channel is 62 mm. х W- х W- A = WD + XD WP = W + 2L
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