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Questions and Answers of Mechanical Engineering

Water at 20°C exits to the standard sea-level atmosphere through the split nozzle in Fig P3.62 Duct areas are A1 = 0.02 m2 and A2 = A3 = 0.008 m2. If p1 = 135 kPa (absolute) and the flow rate is
The 6-cm-diameter 20°C water jet in Fig P3.64 strikes a plate containing a hole of 4-cm diameter. Part of the jet passes through the hole, and part is deflected. Determine the horizontal force
The tank in Fig P3.66 weighs 500 N empty and contains 600 L of water at 20°C. Pipes 1 and 2 have D = 6 cm and Q = 300 m3/hr. What should the scale reading W be, in newtons?
The box in Fig P3.65 has three 0.5-in holes on the right side. The volume flows of 20°C water shown are steady, but the details of the interior are not known. Compute the force, if any, which
Gravel is dumped from a hopper, at a rate of 650 N/s, onto a moving belt, as in Fig P3.67. The gravel then passes off the end of the belt. The drive wheels are 80 cm in diameter and rotate clockwise
The rocket in Fig P3.68 has a supersonic exhaust, and the exit pressure pe is not necessarily equal to pa. Show that the force F required to hold this rocket on the test stand is F = ρeAeVe 2 +
A uniform rectangular plate, 40 cm long and 30 cm deep into the paper, hangs in air from a hinge at its top, 30-cm side. It is struck in its center by a horizontal 3-cmdiameter jet of water moving at
The dredger in Fig P3.70 is loading sand (SG = 2.6) onto a barge. The sand leaves the dredger pipe at 4 ft/s with a weight flux of 850 lbf/s. Estimate the tension on the mooring line caused by this
Suppose that a deflector is deployed at the exit of the jet engine of Prob. 3.50, as shown in Fig. P3.71 What will the reaction Rx on the test stand is now? Is this reaction sufficient to serve as a
A thick elliptical cylinder immersed in a water stream creates the idealized wake shown. Upstream and downstream pressures are equal, and Uo = 4 m/s, L = 80 cm. Find the drag force on the cylinder
A pump in a tank of water directs a jet at 45 ft/s and 200 gal/min against a vane, as shown in the figure, compute the force F to hold the cart stationary if the jet follows (a) path A; or (b) path
Water at 20°C flows down a vertical 6-cm-diameter tube at 300 gal/min, as in the figure the flow then turns horizontally and exits through a 90° radial duct segment 1 cm thick, as shown. If
A liquid jet of density r and area A strikes a block and splits into two jets, as shown in the figure. All three jets have the same velocity V. The upper jet exits at angle θ and area αA,
Water at 20°C flows steadily through a reducing pipe bend as in Fig P3.77 Known conditions are p1 = 350 kPa, D1 = 25 cm, V1 = 2.2 m/s, p2 = 120 kPa, and D2 = 8 cm. Neglecting bend and water
A two-dimensional sheet of water, 10 cm thick and moving at 7 m/s, strikes a fixed wall inclined at 20° with respect to the jet direction. Assuming frictionless flow, find(a) The normal force on
A fluid jet of diameter D1 enters a cascade of moving blades at absolute velocity V1 and angle β1, and it leaves at absolute velocity V1 and angle β2, as in Fig. P3.78. The blades move at
Air at 20°C and 1 atm enters the bottom of an 85° conical flow meter duct at a mass flow rate of 0.3 kg/s, as shown in the figure. It supports a centered conical body by steady annular flow
A river (1) passes over a €œdrowned€ weir as shown, leaving at a new condition(2). Neglect atmospheric pressure and assume hydrostatic pressure at(1) and(2). Derive an expression
Torricelli€™s idealization of efflux from a hole in the side of a tank is V≈ 2gh,as shown in Fig. P3.81. The tank weighs 150 N when empty and contains water at 20°C. The tank
The model car in Fig P3.82 weighs 17 N and is to be accelerated from rest by a 1-cm-diameter water jet moving at 75 m/s. Neglecting air drag and wheel friction, estimate the velocity of the car after
Air at 20°C and 1 atm flows in a 25-cm-diameter duct at 15 m/s, as in Fig P3.84The exit is choked by a 90° cone, as shown. Estimate the force of the airflow on the cone.
Gasoline at 20°C is flowing at V1 =12 m/s in a 5-cm-diameter pipe when it encounters a 1-m length of uniform radial wall suction. After the suction, the velocity has dropped to 10 m/s. If p1 =
The thin-plate orifice in Fig P3.85 causes a large pressure drop. For 20°C water flow at 500 gal/min, with pipe D 10 cm and orifice d 6 cm, p1 −p2
For the water-jet pump of Prob. 3.36, add the following data: p1 p2 25 lbf/in2, and the distance between sections 1 and 3 is 80 in. If the average wall shear stress
The boat in Fig P3.88 is jet-propelled by a pump which develops a volume flow rate Q and ejects water out the stem at velocity Vj. If the boat drag force is F = kV2, where k is a constant, develop a
Figure P3.87 simulates a manifold flow, with fluid removed from a porous wall or perforated section of pipe. Assume incompressible flow with negligible wall friction and small suction Vw _V1... If
Consider Fig. P3 36 as a general problem for analysis of a mixing ejector pump. If all conditions (p, ρ, V) are known at sections 1 and 2 and if the wall friction is negligible, derive formulas
As shown in Fig. P3.90, a liquid column of height h is confined in a vertical tube of cross-sectional area A by a stopper. At t = 0 the stopper is suddenly removed, exposing the bottom of the liquid
Extend Prob. 3.90 to include a linear (laminar) average wall shear stress of the form τ ≈ cV, where c is a constant. Find V (t), assuming that the wall area remains constant.
A more involved version of Prob. 3.90 is the elbow-shaped tube in Fig. P3.92, with constant cross-sectional area A and diameter D
Extend Prob. 3.92 to include a linear (laminar) average wall shear stress of the form τ ≈ cV, where c is a constant. Find V(t), assuming that the wall area remains constant.
Attempt a numerical solution of Prob. 3.93 for SAE 30 oil at 20°C. Let h = 20 cm, L = 15 cm and D = 4 mm. Use the laminar shear approximation from Sec. 6.4: τ ≈ 8μV/D, where μ
Attempt a numerical solution of Prob. 3.93 for mercury at 20°C. Let h = 20 cm, L = 15 cm, and D = 4 mm. For mercury the flow will be turbulent, with the wall shear stress estimated from Sec. 6.4:
Extend Prob. 3.90 to the case of the liquid motion in a frictionless U-tube whose liquid column is displaced a distance Z upward and then released, as in Fig. P3.96. Neglect the short horizontal leg
Extend Prob. 3.96 to include a linear (laminar) average wall shear stress resistance of the form τ ≈ 8μV/D, where μ is the fluid viscosity. Find the differential equation for
As an extension of Ex. 3.10, let the plate and cart be unrestrained, with frictionless wheels. Derive (a) the equation of motion for cart velocity Vc (t); and (b) the time required for the cart to
Let the rocket of Fig. E3.12 start at z = 0, with constant exit velocity and exit mass flow, and rise vertically with zero drag. (a) Show that, as long as fuel burning continues, the vertical height
Suppose that the solid-propellant rocket of Prob. 3.35 is built into a missile of diameter 70 cm and length 4 m. The system weighs 1800 N, which includes 700 N of propellant. Neglect air drag. If the
Modify Prob. 3.100 by accounting for air drags on the missile F ≈ CρD2V2, where C ≈ 0.02, ρ is the air density, D is the missile diameter, and V is the missile velocity. Solve
As can often be seen in a kitchen sink when the faucet is running, a high-speed channel flow (V1, h1) may €œjump€ to a low-speed, low-energy condition (V2, h2) as in Fig.
Suppose that the solid-propellant rocket of Prob. 3.35 is mounted on a 1000-kg car to propel it up a long slope of 15°. The rocket motor weighs 900 N, which includes 500 N of propellant. If the car
A rocket is attached to a rigid horizontal rod hinged at the origin as in Fig. P3.104. its initial mass is Mo, and its exit properties are m_ and Ve relative to the rocket. Set up the differential
Extend Prob. 3.104 to the case where the rocket has a linear air drag force F =cV, where c is a constant. Assuming no burnout, solve for ω(t) and find the terminal angular velocity, i.e., the
Extend Prob. 3.104 to the case where the rocket has a quadratic air drag force F =kV2, where k is a constant. Assuming no burnout, solve for ω(t) and find the terminal angular velocity, i.e.,
The cart in Fig P3.107 moves at constant velocity Vo = 12 m/s and takes on water with a scoop 80 cm wide which dips h = 2.5 cm into a pond. Neglect air drag and wheel friction. Estimate the force
A rocket sled of mass M is to be decelerated by a scoop, as in Fig. P3.108, which has width b into the paper and dips into the water a depth h, creating an upward jet at 60°. The rocket thrust is T
Apply Prob. 3.108 to the following data: Mo = 900 kg, b = 60 cm, h = 2 cm, Vo =120 m/s, with the rocket of Prob. 3.35 attached and burning. Estimate V after 3 sec.
The horizontal lawn sprinkler in Fig P3.110 has a water flow rate of 4.0 gal/min introduced vertically through the center. Estimate (a) the retarding torque required to keep the arms from rotating
In Prob. 3.60 find the torque caused around flange 1 if the center point of exit 2 is 1.2 m directly below the flange center.
The wye joint in Fig P3.112 splits the pipe flow into equal amounts Q/2, which exit, as shown, a distance Ro from the axis. Neglect gravity and friction. Find an expression for the torque T about the
Modify Ex. 3.15 so that the arm starts up from rest and spins up to its final rotation speed. The moment of inertia of the arm about O is Io. Neglect air drag. Find dω/dt and integrate to
The 3-arm lawn sprinkler of Fig P3.114 receives 20°C water through the center at 2.7 m3/hr, if collar friction is neglected, what is the steady rotation rate in rev/min for (a) θ = 0°;
The centrifugal pump of Fig P3.116 has a flow rate Q and exits the impeller at an angle θ2 relative to the blades, as shown. The fluid enters axially at section 1. Assuming incompressible flow
Water at 20°C flows at 30 gal/min through the 0.75-in-diameter double pipe bend of Fig P3.115, the pressures are p1 = 30 lbf/in2 and p2 = 24 lbf/in2. Compute the torque T at point B necessary to
A simple turbo machine is constructed from a disk with two internal ducts which exit tangentially through square holes, as in the figure. Water at 20C enters the disk at the center, as shown. The
Reverse the flow in Fig P3.116, so that the system operates as a radial-inflow turbine. Assuming that the outflow into section 1 has no tangential velocity, derive an expression for the power P
Revisit the turbine cascade system of Prob. 3.78, and derive a formula for the power P delivered, using the angular momentum theorem of Eq. (3.55).
A centrifugal pump delivers 4000 gal/min of water at 20°C with a shaft rotating at 1750 rpm. Neglect losses. If r1 = 6 in, r2 = 14 in, b1 = b2 = 1.75 in, Vt1 = 10 ft/s, and Vt2 = 110 ft/s, compute
The pipe bend of Fig. P3.121 has D1 = 27 cm and D2 = 13 cm. When water at 20°C flows through the pipe at 4000 gal/ min, p1 = 194 kPa (gage). Compute the torque required at point B to hold the
The waterwheel in Fig P3.123 is being driven at 200 r/min by a 150-ft/s jet of water at 20°C. The jet diameter is 2.5 in. Assuming no losses, what is the horsepower developed by the wheel? For
A rotating dishwasher arm delivers at 60°C to six nozzles, as in Fig. P3.124. The total flow rate is 3.0 gal/min. Each nozzle has a diameter of 3 16 in. If the nozzle flows are equal and friction
A liquid of density ρ flows through a 90° bend as in Fig. P3.125 and issues vertically from a uniformly porous section of length L. Neglecting weight, find a result for the support torque M
Extend Prob. 3.46 to the problem of computing the center of pressure L of the normal face Fn, as in Fig. P3.122. (At the center of pressure, no moments are required to hold the plate at rest.)
Given is steady isothermal flow of water at 20°C through the device in Fig. P3.126. Heat-transfer, gravity, and temperature effects are negligible. Known data are D1 = 9 cm, Q1 = 220 m3/h, p1 =
A power plant on a river, as in Fig P3.127, must eliminate 55 MW of waste heat to the river. The river conditions upstream are Q1 = 2.5 m3/s and T1 = 18°C. The river is 45 m wide and 2.7 m deep.
For the conditions of Prob. 3.127, if the power plant is to heat the nearby river water by no more than 12°C, what should be the minimum flow rate Q, in m3/s, through the plant heat exchanger? How
Multnomah Falls in the Columbia River Gorge has a sheer drop of 543 ft. Use the steady flow energy equation to estimate the water temperature rise, in °F, resulting.
When the pump in Fig P3.130 draws 220 m3/h of water at 20°C from the reservoir, the total friction head loss is 5 m. The flow discharges through a nozzle to the atmosphere Estimate the pump power
When the pump in Fig. P3.130 delivers 25 kW of power to the water, the friction head loss is 4 m. Estimate (a) the exit velocity; and (b) the flow rate.
Consider a turbine extracting energy from a penstock in a dam, as in the figure. For turbulent flow (Chap. 6) the friction head loss is hf = CQ2, where the constant C depends upon penstock dimensions
The long pipe in Fig 3.133 is filled with water at 20°C. When valve A is closed, p1 − p2 = 75 kPa. When the valve is open and water flows at 500 m3/h, p1 − p2 = 160 kPa. What is the
A 36-in-diameter pipeline carries oil (SG = 0.89) at 1 million barrels per day (bbl/day) (1 bbl = 42 U.S. gal). The friction head loss is 13 ft/1000 ft of pipe. It is planned to place pumping
The pump-turbine system in Fig P3.135 draws water from the upper reservoir in the daytime to produce power for a city. At night, it pumps water from lower to upper reservoirs to restore the
Water at 20°C is delivered from one reservoir to another through a long 8-cmdiameter pipe. The lower reservoir has a surface elevation z2 = 80 m. The friction loss in the pipe is correlated by the
A fireboat draws seawater (SG =1.025) from a submerged pipe and discharges it through a nozzle, as in Fig. P3.137. The total head loss is 6.5 ft. If the pump efficiency is 75 percent, what horsepower
Students in the fluid mechanics lab at Penn State University use the device in the figure to measure the viscosity of water: a tank and a capillary tube. The flow is laminar and has negligible
The horizontal pump in Fig P3.139 discharges 20°C water at 57 m3/h. Neglecting losses, what power in kW is delivered to the water by the pump?
Steam enters a horizontal turbine at 350 lbf/in2 absolute, 580°C, and 12 ft/s and is discharged at 110 ft/s and 25°C saturated conditions. The mass flow is 2.5 lbm/s, and the heat losses are 7
Water at 20°C is pumped at 1500 gal/min from the lower to the upper reservoir, as in Fig. P3.141. Pipe friction losses are approximated by hf ≈ 27V2 /(2g), where V is the average velocity
A typical pump has a head which, for a given shaft rotation rate, varies with the flow rate, resulting in a pump performance curve as in Fig. P3.142. Suppose that this pump is 75 percent efficient
The insulated tank in Fig P3.143 is to be filled from a high-pressure air supply. Initial conditions in the tank are T = 20°C and p = 200 kPa. When the valve is opened, the initial mass flow rate
The pump in Fig P3.144 creates a 20°C water jet oriented to travel a maximum horizontal distance. System friction head losses are 6.5 m. The jet may be approximated by the trajectory of
Kerosene at 20°C flows through the pump in Fig. P3.146 at 2.3 ft3/s. Head losses between 1 and 2 are 8 ft, and the pump delivers 8 hp to the flow. What should the mercury-manometer reading h ft
Repeat Prob. 3.49 by assuming that p1 is unknown and using Bernoulli€™s equation with no losses. Compute the new bolt force for this assumption. What is the head loss between 1 and 2 for
Reanalyze Prob. 3.54 to estimate the manometer reading h by Bernoulli€™s equation. For the reading h = 58 cm in Prob. 3.54, what is the head loss?
A jet of alcohol strikes the vertical plate in Fig. P3.149. A force F ≈ 425 N is required to hold the plate stationary. Assuming there are no losses in the nozzle, estimate (a) the mass flow
An airfoil at an angle of attack α, as in Fig P3.150, provides lift by a Bernoulli effect, because the lower surface slows the flow (high pressure) and the upper surface speeds up the flow (low
Water flows through a circular nozzle, exits into the air as a jet, and strikes a plate. The force required to hold the plate steady is 70 N. Assuming frictionless one-dimensional flow, estimate (a)
A free liquid jet, as in Fig P3.152, has constant ambient pressure and small losses; hence from Bernoulli’s equation z + V2/ (2g) is constant along the jet. For the fire nozzle in the figure, what
For the container of Fig P3.153 use Bernoulli€™s equation to derive a formula for the distance X where the free jet leaving horizontally will strike the floor, as a function of h and H. For
In Fig P3.154 the exit nozzle is horizontal. If losses are negligible, what should the water level h cm be for the free jet to just clear the wall?
Bernoulli€™s 1738 treatise Hydrodynamica contains many excellent sketches of flow patterns. One, however, redrawn here as Fig. P3.155 seems physically misleading. What is wrong with the
A blimp cruises at 75 mi/h through sea-level standard air. A differential pressure transducer connected between the nose and the side of the blimp registers 950 Pa. Estimate (a) the absolute pressure
The manometer fluid in Fig P3.157 is mercury. Estimate the volume flow in the tube if the flowing fluid is (a) gasoline and (b) nitrogen, at 20°C and 1 atm.
In Fig P3.158 the flowing fluid is CO2 at 20°C. Neglect losses. If p1 = 170 kPa and the manometer fluid is Merriam red oil (SG = 0.827), estimate (a) p2 and (b) the gas flow rate in m3/h.
Our D = 0.625-in-diameter hose is too short, and it is 125 ft from the d = 0.375-in-diameter nozzle exit to the garden. If losses are neglected, what is the minimum gage pressure required, inside the
A necked-down section in a pipe flow, called a venturi, develops a low throat pressure which can aspirate fluid upward from a reservoir, as in Fig. P3.161 Using Bernoulli€™s equation with
The air-cushion vehicle in Fig P3.160 brings in sea-level standard air through a fan and discharges it at high velocity through an annular skirt of 3-cm clearance. If the vehicle weighs 50 kN,
Suppose you are designing a 3 Ã— 6-ft air-hockey table, with 1/16-inch-diameter holes spaced every inch in a rectangular pattern (2592 holes total), the required jet speed from each hole
The liquid in Fig P3.163 is kerosine at 20°C. Estimate the flow rate from the tank for (a) no losses and (b) pipe losses hf ≈ 4.5V2/ (2g).

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