Consider the curved duct of Prob. 13–41, except allow the cross-sectional area to vary along the duct (A1 ≠ A2). (a) Write an expression for the horizontal force Fx of the fluid on the walls of the duct in terms of the given variables. (b) Verify your expression by plugging in the following values: ρ = 998.2 kg/m3, A1 = 0.025 m2, A2 = 0.015 m2, β1 = 1.02, β2 = 1.04, V1 = 20 m/s, P1,gage = 88.34 kPa, and P2,gage = 67.48 kPa.
> 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
> As a follow-up to Prob. 13–41, it turns out that for a large enough area ratio A2/A1, the inlet pressure is actually smaller than the outlet pressure! Explain how this can be true in light of the fact that there is friction and there ar
> A room is heated as a result of solar radiation coming in through the windows. Is this a heat or work interaction for the room?
> An incompressible fluid of density ρ and viscosity μ flows through a curved duct that turns the flow 180°. The duct cross-sectional area remains constant. The average velocity, momentum-flux correction factor, and gage
> Water enters a centrifugal pump axially at atmospheric pressure at a rate of 0.09 m3/s and at a velocity of 5 m/s and leaves in the normal direction along the pump casing, as shown in Fig. P13 40. Determine the force acting on the shaft (which is also t
> Express the conservation of momentum principle. What can you say about the momentum of a body if the net force acting on it is zero?
> A horizontal 4-cm-diameter water jet with a velocity of 18 m/s impinges normally upon a vertical plate of mass 750 kg. The plate rides on a nearly frictionless track and is initially stationary. When the jet strikes the plate, the plate begins to move in
> Water flowing in a horizontal 25-cm-diameter pipe at 8 m/s and 300 kPa gage enters a 90° bend reducing section, which connects to a 15-cm-diameter vertical pipe. The inlet of the bend is 50 cm above the exit. Neglecting any frictional and gravitational e
> Water is flowing through a 10-cm-diameter water pipe at a rate of 0.1 m3/s. Now a diffuser with an outlet diameter of 20 cm is bolted to the pipe in order to slow down water, as shown in Fig. P13–37. Disregarding frictional effects, det
> Reconsider the helicopter in Prob. 13–35, except that it is hovering on top of a 2200-m-high mountain where the air density is 0.987 kg/m3. Noting that the unloaded helicopter blades must rotate at 550 rpm to hover at sea level, determi
> An unloaded helicopter of mass 12,000 kg hovers at sea level while it is being loaded. In the unloaded hover mode, the blades rotate at 550 rpm. The horizontal blades above the helicopter cause a 18-m-diameter air mass to move downward at an average velo
> A 3-in-diameter horizontal water jet having a velocity of 90 ft/s strikes a curved plate, which deflects the water 180° at the same speed. Ignoring the frictional effects, determine the force required to hold the plate against the water stream
> A room is heated by an iron that is left plugged in. Is this a heat or work interaction? Take the entire room, including the iron, as the system.
> Reconsider Prob. 13–32. Using appropriate software, investigate the effect of the plate velocity on the force exerted on the plate. Let the plate velocity vary from 0 to 30 m/s, in increments of 3 m/s. Tabulate and plot your results. Data from Prob. 13-
> A 5-cm-diameter horizontal jet of water with a velocity of 30 m/s relative to the ground strikes a flat plate that is moving in the same direction as the jet at a velocity of 20 m/s. The water splatters in all directions in the plane of the plate. How mu
> Firefighters are holding a nozzle at the end of a hose while trying to extinguish a fire. If the nozzle exit diameter is 8 cm and the water flow rate is 12 m3/min, determine (a) the average water exit velocity and (b) the horizontal resistance force requ
> A 3-in-diameter horizontal jet of water, with velocity 140 ft/s, strikes a bent plate, which deflects the water by 135° from its original direction. How much force is required to hold the plate against the water stream, and what is its direction? Disrega
> Is momentum a vector? If so, in what direction does it point?
> A fan with 24-in-diameter blades moves 2000 cfm (cubic feet per minute) of air at 70°F at sea level. Determine (a) the force required to hold the fan and (b) the minimum power input required for the fan. Choose a control volume sufficiently large to cont
> Commercially available large wind turbines have blade span diameters larger than 100 m and generate over 3 MW of electric power at peak design conditions. Consider a wind turbine with a 75-m blade span subjected to 25-km/h steady winds. If the combined t
> Reconsider Prob. 13–26E. Using appropriate software, investigate the effect of the splitter angle on the force exerted on the splitter in the incoming flow direction. Let the half splitter angle vary from 0° to 180°
> A 100-ft3/s water jet is moving in the positive x-direction at 18 ft/s. The stream hits a stationary splitter, such that half of the flow is diverted upward at 45° and the other half is directed downward, and both streams have a final average
> Repeat Prob. 13–24 for the case of θ = 125°. Data from Prob. 13-24: A reducing elbow in a horizontal pipe is used to deflect water flow by an angle θ = 45° from the flow direction while a
> Consider an automobile traveling at a constant speed along a road. Determine the direction of the heat and work interactions, taking the following as the system: (a) the car radiator, (b) the car engine, (c) the car wheels, (d) the road, and (e) the air
> A reducing elbow in a horizontal pipe is used to deflect water flow by an angle θ = 45° from the flow direction while accelerating it. The elbow discharges water into the atmosphere. The cross sectional area of the elbow is 150 cm
> Water enters a 7-cm-diameter pipe steadily with a uniform velocity of 2 m/s and exits with the turbulent flow velocity distribution given by u = umax(1 − r/R)1/7. If the pressure drop along the pipe is 10 kPa, determine the drag force exerted on the pipe
> A horizontal water jet impinges against a vertical flat plate at 30 ft/s and splashes off the sides in the vertical plane. If a horizontal force of 500 lbf is required to hold the plate against the water stream, determine the volume flow rate of the wate
> Repeat Prob. 13–20 for the case of another (identical) elbow attached to the existing elbow so that the fluid makes a U-turn. Data from Prob. 13-20: A 90° elbow in a horizontal pipe is used to direct water flow upward at a r
> A 90° elbow in a horizontal pipe is used to direct water flow upward at a rate of 40 kg/s. The diameter of the entire elbow is 10 cm. The elbow discharges water into the atmosphere, and thus the pressure at the exit is the local atmospheric pr
> Express Newton’s first, second, and third laws.
> A 2.5-cm-diameter horizontal water jet with a speed of Vj = 40 m/s relative to the ground is deflected by a 60° stationary cone whose base diameter is 25 cm. Water velocity along the cone varies linearly from zero at the cone surface to the in
> A horizontal water jet from a nozzle of constant exit cross section impinges normally on a stationary vertical flat plate. A certain force F is required to hold the plate against the water stream. If the water velocity is doubled, will the necessary hold
> A horizontal water jet of constant velocity V from a stationary nozzle impinges normally on a vertical flat plate that rides on a nearly frictionless track. As the water jet hits the plate, it begins to move due to the water force. What is the highest ve
> A constant-velocity horizontal water jet from a stationary nozzle impinges normally on a vertical flat plate that rides on a nearly frictionless track. As the water jet hits the plate, it begins to move due to the water force. Will the acceleration of th
> When is the energy crossing the boundaries of a closed system heat and when is it work?
> If the mass of an object is 10 lbm, what is its weight, in lbf, at a location where g = 32.0 ft/s2?
> Describe body forces and surface forces, and explain how the net force acting on a control volume is determined. Is fluid weight a body force or surface force? How about pressure?
> In a given location, would a helicopter require more energy in summer or winter to achieve a specified performance? Explain.
> Does it take more, equal, or less power for a helicopter to hover at the top of a high mountain than it does at sea level? Explain.
> Describe in terms of momentum and airflow how a helicopter is able to hover.
> A rocket in space (no friction or resistance to motion) can expel gases relative to itself at some high velocity V. Is V the upper limit to the rocket’s ultimate velocity?
> Two firefighters are fighting a fire with identical water hoses and nozzles, except that one is holding the hose straight so that the water leaves the nozzle in the same direction it comes, while the other holds it backward so that the water makes a U-tu
> Express Newton’s second law of motion for rotating bodies. What can you say about the angular velocity and angular momentum of a rotating nonrigid body of constant mass if the net torque acting on it is zero?
> What is the hydraulic grade line? How does it differ from the energy grade line? Under what conditions do both lines coincide with the free surface of a liquid?
> The power generated by a wind turbine is proportional to the cube of the wind velocity. Inspired by the acceleration of a fluid in a nozzle, someone proposes to install a reducer casing to capture the wind energy from a larger area and accelerate it befo
> In a certain application, a siphon must go over a high wall. Can water or oil with a specific gravity of 0.8 go over a higher wall? Why?
> What is total energy? Identify the different forms of energy that constitute the total energy.
> A pump-storage plant uses a turbine to generate hydropower during the day, letting water from the upper reservoir flow through the turbine into the lower reservoir as sketched. The plant then pumps water back up to the upper reservoir during the night. I
> A wind tunnel draws atmospheric air at 20°C and 101.3 kPa with a large fan located near the exit of the tunnel. If the air velocity in the tunnel is 80 m/s, determine the pressure in the tunnel.
> An oil pump is drawing 18 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 2
> Reconsider Prob. 12–72. In order to drain the tank faster, a pump is installed near the tank exit. Determine the pump head input necessary to establish an average water velocity of 6.5 m/s when the tank is full. Data from Prob. 12-72:
> Reconsider Prob. 12–72. Using appropriate software, investigate the effect of the tank height on the initial discharge velocity of water from the completely filled tank. Let the tank height vary from 2 to 15 m in increments of 1 m, and
> A 3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. If the total irreversible head lo
> Air flows through a pipe at a rate of 120 L/s. The pipe consists of two sections of diameters 22 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Negle
