How is the friction factor for flow in a pipe related to the pressure loss? How is the pressure loss related to the pumping power requirement for a given mass flow rate?
> Water is to be withdrawn from an 8-m-high water reservoir by drilling a 2.2-cm-diameter hole at the bottom surface.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
> Repeat Prob. 14–55 for a slightly rounded entrance (KL = 0.12). Data from Prob. 14-55: 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
> The engine of a 1500-kg automobile has a power rating of 75 kW. Determine the time required to accelerate this car from rest to a speed of 100 km/h at full power on a level road. Is your answer realistic?
> 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 sharp-edged entrance (KL = 0.5) is considerably less than the flow rat
> A horizontal pipe has an abrupt expansion from D1 = 5 cm to D2 = 10 cm. The water velocity in the smaller section is 8 m/s and the flow is turbulent. The pressure in the smaller section is P1 = 410 kPa. Taking the kinetic energy correction factor to b
> 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 redu
> 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 with circular elbows. What is another way?
> Which has a greater minor loss coefficient during pipe flow: gradual expansion or gradual contraction? Why?
> The effect of rounding of a pipe exit on the loss coefficient is (a) negligible, (b) somewhat significant, or (c) very significant.
> Show that the Reynolds number for flow in a circular pipe of diameter D can be expressed as Re = 4m/(πDμ).
> Define equivalent length for minor loss in pipe flow. How is it related to the minor loss coefficient?
> What is minor loss in pipe flow? How is the minor loss coefficient KL defined?
> Consider the fully developed flow of glycerin at 40°C through a 70-m-long, 4-cm-diameter, horizontal, circular pipe. If the flow velocity at the centerline is measured to be 6 m/s, determine the velocity profile and the pressure difference acr
> A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag and assuming that the avera
> Liquid ammonia at −20°C is flowing through a 20-m-long section of a 5-mm-diameter copper tube at a rate of 0.09 kg/s. Determine the pressure drop, the head loss, and the pumping power required to overcome the frictional losses in the tube.
> Reconsider Prob. 14–44. Using appropriate 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 dra
> Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/m·s is flowing through a 6-cm-diameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe.
> In an air heating system, heated air at 40°C and 105 kPa absolute is distributed through a 0.2 m × 0.3 m rectangular duct made of commercial steel at a rate of 0.5 m3/s. Determine the pressure drop and head loss through a 40-m-long section of the duct.
> Oil with a density of 850 kg/m3 and kinematic viscosity of 0.00062 m2/s is being discharged by a 8-mm-diameter, 40-m-long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 4 m. Disr
> Air at 1 atm and 60°F is flowing through a 1 ft × 1 ft square duct made of commercial steel at a rate of 1600 cfm. Determine the pressure drop and head loss per ft of the duct.
> Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/m·s is flowing through a 3-cm-diameter, 25-m-long pipe that discharges into the atmosphere at 100 kPa. The flow rate through the pipe is 0.075 L/s. (a) Determine the absolute pressure 25 m before the p
> Consider a person walking first in air and then in water at the same speed. For which motion will the Reynolds number be higher?
> Consider an air solar collector that is 1 m wide and 4 m long and has a constant spacing of 3 cm between the glass cover and the collector plate. Air flows at an average temperature of 45°C at a rate of 0.12 m3/s through the 1-m-wide edge of t
> Air enters a 10-m-long section of a rectangular duct of cross section 15 cm × 20 cm made of commercial steel at 1 atm and 35°C at an average velocity of 5 m/s. Disregarding the entrance effects, determine the fan power needed to o
> List the forms of energy that contribute to the internal energy of a system.
> The acceleration of high-speed aircraft is sometimes expressed in g’s (in multiples of the standard acceleration of gravity). Determine the upward force, in N, that a 90-kg man would experience in an aircraft whose acceleration is 6 g’s.
> Repeat Prob. 14–36 for turbulent flow in smooth pipes for which the friction factor is given as f = 0.184Re−0.2. What would your answer be for fully turbulent flow in a rough pipe?
> Consider laminar flow of a fluid through a square channel with smooth surfaces. Now the average velocity of the fluid is doubled. Determine the change in the head loss of the fluid. Assume the flow regime remains unchanged.
> Water at 10°C (ρ = 999.7 kg/m3 and μ = 1.307 × 10−3 kg/m·s) is flowing steadily in a 0.12-cm diameter, 15-m-long pipe at an average velocity of 0.9 m/s. Determine (a) the pressure drop, (b) the head loss, and (c) the pumping power requirement to overcome
> Repeat Prob. 14–33 for a pipe of inner radius 7 cm. Data from Prob. 14-33: The velocity profile in fully developed laminar flow in a circular pipe of inner radius R = 2 cm, in m/s, is given by u(r) = 4(1 − r2/R2). Det
> The velocity profile in fully developed laminar flow in a circular pipe of inner radius R = 2 cm, in m/s, is given by u(r) = 4(1 − r2/R2). Determine the average and maximum velocities in the pipe and the volume flow rate.
> In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the centerline) is measured to be 11 m/s. Determine the velocity at the center of the pipe.
> Heated air at 1 atm and 100°F is to be transported in a 400-ft-long circular plastic duct at a rate of 12 ft3/s. If the head loss in the pipe is not to exceed 50 ft, determine the minimum diameter of the duct.
> Water at 70°F passes through 0.75-in-internal-diameter copper tubes at a rate of 0.5 lbm/s. Determine the pumping power per ft of pipe length required to maintain this flow at the specified rate.
> What is the physical significance of the Reynolds number? How is it defined for (a) flow in a circular pipe of inner diameter D and (b) flow in a rectangular duct of cross section a × b?
> Water at 15°C (ρ = 999.1 kg/m3 and μ = 1.138 × 10−3 kg/m·s) is flowing steadily in a 30-m-long and 6-cm diameter horizontal pipe made of stainless steel at a rate of 10 L/s.
> How much work, in kJ, can a spring whose spring constant is 3 kN/cm produce after it has been compressed 3 cm from its unloaded length?
> The velocity profile for the fully developed laminar flow of a Newtonian fluid between two large parallel plates is given by where 2h is the distance between the two plates, u0 is the velocity at the center plane, and y is the vertical coordinate from th
> What is the physical mechanism that causes the friction factor to be higher in turbulent flow?
> What is turbulent viscosity? What causes it?
> How is head loss related to pressure loss? For a given fluid, explain how you would convert head loss to pressure loss.
> Consider fully developed laminar flow in a circular pipe. If the viscosity of the fluid is reduced by half by heating while the flow rate is held constant, how does the head loss change?
> Consider laminar flow of air in a circular pipe with perfectly smooth surfaces. Do you think the friction factor for this flow is zero? Explain.
> Explain why the friction factor is independent of the Reynolds number at very large Reynolds numbers.
> Consider fully developed laminar flow in a circular pipe. If the diameter of the pipe is reduced by half while the flow rate and the pipe length are held constant, the head loss will (a) double, (b) triple, (c) quadruple, (d) increase by a factor of 8, o
> Consider fully developed flow in a circular pipe with negligible entrance effects. If the length of the pipe is doubled, the head loss will (a) double, (b) more than double, (c) less than double, (d) reduce by half, or (e) remain constant.
> Why are liquids usually transported in circular pipes?
> Determine the torque applied to the shaft of a car that transmits 225 hp and rotates at a rate of 3000 rpm.
> Discuss whether fully developed pipe flow is one-, two-, or three-dimensional.
> How does the wall shear stress τw vary along the flow direction in the fully developed region in (a) laminar flow and (b) turbulent flow?
> Someone claims that in fully developed turbulent flow in a pipe, the shear stress is a maximum at the pipe wall. Do you agree with this claim? Explain.
> Someone claims that the shear stress at the center of a circular pipe during fully developed laminar flow is zero. Do you agree with this claim? Explain.
> Someone claims that the average velocity in a circular pipe in fully developed laminar flow can be determined by simply measuring the velocity at R/2 (midway between the wall surface and the centerline). Do you agree? Explain.
> Someone claims that the volume flow rate in a circular pipe with laminar flow can be determined by measuring the velocity at the centerline in the fully developed region, multiplying it by the cross-sectional area, and dividing the result by 2. Do you ag
> In the fully developed region of flow in a circular pipe, does the velocity profile change in the flow direction?
> Repeat Prob. 14–109 for a sharp-edged entrance to the pipe with KL = 0.5. Is this “minor loss” truly “minor” or not? Data from Prob. 14-109: The water at 20Â
> Reconsider Prob. 14–109. Using appropriate software, investigate the effect of the discharge pipe diameter on the time required to empty the pool completely. Let the diameter vary from 1 to 10 cm, in increments of 1 cm. Tabulate and plo
> A construction crane lifts a prestressed concrete beam weighing 3 short tons from the ground to the top of piers that are 24 ft above the ground. Determine the amount of work done considering (a) the beam and (b) the crane as the system. Express your ans
> Shown here is a cool picture of water being released at 300,000 gallons per second in the spring of 2008. This was part of a revitalization effort for the ecosystem of the Grand Canyon and the Colorado River. Estimate the Reynolds number of the pipe flow
> The water at 20°C in a 10-m-diameter, 2-m-high aboveground swimming pool is to be emptied by unplugging a 5-cm-diameter, 25-m-long horizontal plastic pipe attached to the bottom of the pool. Determine the initial rate of discharge of water thr
> Reconsider Prob. 14–106E. The office worker who set up the siphoning system purchased a 12-ft long reel of the plastic tube and wanted to use the whole thing to avoid cutting it in pieces, thinking that it is the elevation difference th
> Reconsider Prob. 14–106E. Using appropriate software, investigate the effect of the hose diameter on the time required to fill a glass when the bottle is full. Let the diameter vary from 0.2 to 2 in, in increments of 0.2 in. Tabulate an
> The drinking water needs of an office are met by large water bottles. One end of a 0.35-in diameter, 6-ft-long plastic hose is inserted into the bottle placed on a high stand, while the other end with an on/off valve is maintained 3 ft below the bottom o
> In Prob. 14–104, the pipe diameter is tripled in order to reduce the pipe losses. Determine the percent increase in the net power output as a result of this modification. Data from Prob. 14-104: In a hydroelectric power plant, water at 20°C is supplied
> In a hydroelectric power plant, water at 20°C is supplied to the turbine at a rate of 0.55 m3/s through a 200-m-long, 0.35-m-diameter cast iron pipe. The elevation difference between the free surface of the reservoir and the turbine discharge is 140 m, a
> Repeat Prob. 14–102E for plastic (smooth) pipes. Data from Prob. 14-102: A water fountain is to be installed at a remote location by attaching a cast iron pipe directly to a water main through which water is flowing at 70°F
> A water fountain is to be installed at a remote location by attaching a cast iron pipe directly to a water main through which water is flowing at 70°F and 60 psig. The entrance to the pipe is sharp edged, and the 70-ft-long piping system invol
> Reconsider Prob. 14–100. In order to reduce the head losses in the piping and thus the power wasted, someone suggests doubling the diameter of the 83-m-long compressed air pipes. Calculate the reduction in wasted power, and determine if this is a worthwh
> A car is accelerated from rest to 85 km/h in 10 s. Would the energy transferred to the car be different if it were accelerated to the same speed in 5 s?
> The compressed air requirements of a textile factory are met by a large compressor that draws in 0.6 m3/s air at atmospheric conditions of 20°C and 1 bar (100 kPa) and consumes 300 kW electric power when operating. Air is compressed to a gage pressure of
> What is hydraulic diameter? How is it defined? What is it equal to for a circular pipe of diameter D?
> How is the hydrodynamic entry length defined for flow in a pipe? Is the entry length longer in laminar or turbulent flow?
> In the application of the momentum equation, explain why we can usually disregard the atmospheric pressure and work with gage pressures only.
> Write the momentum equation for steady one dimensional flow for the case of no external forces, and explain the physical significance of its terms.
> What is the importance of the momentum-flux correction factor in the momentum analysis of flow systems? For which type(s) of flow is it significant and must it be considered in analysis: laminar flow, turbulent flow, or jet flow?
> Water shoots out of a large tank sitting on a cart with frictionless wheels. The water jet velocity is Vj = 7.00 m/s, its cross sectional area is Aj = 20.0 mm2, and the momentum-flux correction factor of the jet is 1.04. The water is deflected 135Â
> Nearly frictionless vertical guide rails maintain a plate of mass mp in a horizontal position, such that it can slide freely in the vertical direction. A nozzle directs a water stream of area A against the plate’s underside. The water j
> A soldier jumps from a plane and opens his parachute when his velocity reaches the terminal velocity VT. The parachute slows him down to his landing velocity of VF. After the parachute is deployed, the air resistance is proportional to the velocity squar
> Consider steady developing laminar flow of water in a constant-diameter horizontal discharge pipe attached to a tank. The fluid enters the pipe with nearly uniform velocity V and pressure P1. The velocity profile becomes parabolic after a certain distanc
> A small electrical motor produces 5 W of mechanical power. What is this power in (a) N, m, and s units; and (b) kg, m, and s units?
> Repeat Prob. 13–59 for a height of 8 m from the nozzle. Data from Prob. 13-59: A 7-cm-diameter vertical water jet is injected upwards by a nozzle at a speed of 15 m/s. Determine the maximum weight of a flat plate that can be supported by this water jet
> Explain the importance of the Reynolds transport theorem in fluid mechanics, and describe how the linear momentum equation is obtained from it.
> A 7-cm-diameter vertical water jet is injected upwards by a nozzle at a speed of 15 m/s. Determine the maximum weight of a flat plate that can be supported by this water jet at a height of 2 m from the nozzle.
> An engineering student considers using a fan as a levitation demonstration. She plans to face the box-enclosed fan so the air blast is directed facedown through a 2-ft-diameter blade span area. The system weighs 3 lbf, and the student will secure the sys
> Indiana Jones needs to ascend a 10-m-high building. There is a large hose filled with pressurized water hanging down from the building top. He builds a square platform and mounts four 4-cm diameter nozzles pointing down at each corner. By connecting hose
> Water is flowing into and discharging from a pipe U-section as shown in Fig. P13–56. At flange (1), the total absolute pressure is 200 kPa, and 55 kg/s flows into the pipe. At flange (2), the total pressure is 150 kPa. At location (3),
> A 5-cm-diameter horizontal jet of water, with velocity 30 m/s, strikes the tip of a horizontal cone, which deflects the water by 60° from its original direction. How much force is required to hold the cone against the water stream?
> A 60-kg ice skater is standing on ice with ice skates (negligible friction). She is holding a flexible hose (essentially weightless) that directs a 2-cm-diameter stream of water horizontally parallel to her skates. The water velocity at the hose outlet i
> A spacecraft cruising in space at a constant velocity of 2000 ft/s has a mass of 25,000 lbm. To slow down the spacecraft, a solid fuel rocket is fired, and the combustion gases leave the rocket at a constant rate of 150 lbm/s at a velocity of 5000 ft/s i
> Reconsider Prob. 13–51. Using appropriate software, investigate the effect of thrust reverser angle on the braking force exerted on the airplane. Let the reverser angle vary from 0° (no reversing) to 180° (full rev
> A gas in a piston–cylinder device is compressed, and as a result its temperature rises. Is this a heat or work interaction?
> Consider an airplane with a jet engine attached to the tail section that expels combustion gases at a rate of 18 kg/s with a velocity of V = 300 m/s relative to the plane. During landing, a thrust reverser (which serves as a brake for the aircraft and fa
> A tripod holding a nozzle, which directs a 5-cm-diameter stream of water from a hose, is shown in Fig. P13–50. The nozzle mass is 10 kg when filled with water. The tripod is rated to provide 1800 N of holding force. A firefighter was st
> How do surface forces arise in the momentum analysis of a control volume? How can we minimize the number of surface forces exposed during analysis?
> A 16-cm-diameter horizontal water jet with a speed of Vj = 20 m/s relative to the ground is deflected by a 40° cone moving to the left at Vc = 10 m/s. Determine the external force, F, needed to maintain the motion of the cone. Disregard the gr
> Repeat Prob. 13–47 by taking into consideration the weight of the elbow whose mass is 5 kg. Data from Prob. 13-47: Water flowing steadily at a rate of 0.16 m3/s is deflected downward by an angled elbow as shown in Fig. P13â€
> Water flowing steadily at a rate of 0.16 m3/s is deflected downward by an angled elbow as shown in Fig. P13–47. For D = 30 cm, d = 10 cm, and h = 50 cm, determine the force acting on the flanges of the elbow and the angle its line of ac
> An 8-cm-diameter horizontal water jet having a velocity of 35 m/s strikes a vertical stationary flat plate. The water splatters in all directions in the plane of the plate. How much force is required to hold the plate against the water stream?
> A sluice gate, which controls flow rate in a channel by simply raising or lowering a vertical plate, is commonly used in irrigation systems. A force is exerted on the gate due to the difference between the water heights y1 and y2 and the flow velocities
> Water of density ρ = 998.2 kg/m3 flows through a fireman’s nozzle—a converging section of pipe that accelerates the flow. The inlet diameter is d1 = 0.100 m, and the outlet diameter is d2 = 0.050 m. The aver
