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mechanical engineering

Thermodynamics An Interactive Approach 1st edition Subrata Bhattacharjee - Solutions

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 Q2 = Q3 = 275 m3/h, compute the force on the flange bolts at section 1.
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 required to hold the plate.
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 this water flow causes on the box.
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 at 150 r/min Neglecting system friction and air drag, estimate the power required to drive this belt.
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 + Ae (pe − pa). Is this force F what we term the thrust of the rocket?
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 8 m/s. If the gate has a mass of 16 kg, estimate the angle at which the plate will hang from the
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 loading process.
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 braking force during airplane landing?
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 per unit width into the paper. Also compute the dimensionless drag coefficient CD = 2F/(ρ Uo 2bL).
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 B. The tank holds 550 gallons of water at this instant.
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 the radial outflow is uniform and steady, estimate the forces (Fx, Fy, Fz) required to support this
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, the lower jet turns down at 90° and area (1 − α)A. (a) Derive a formula for the
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 weight, estimate the total force which must be resisted by the flange bolts.
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 the wall per meter of depth, and the widths of the sheet deflected(b) Upstream, and (c) downstream
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 velocity u. Derive a formula for the power P delivered to the blades as a function of these
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 around the cone and exits at the same velocity as it enters. Estimate the weight of the body in
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 for the force F exerted by the river on the obstacle. Neglect bottom friction.
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 bottom is on very smooth ice (static friction coefficient ζ ≈ 0.01). For what water depthh
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 it has moved forward 1 m.
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 = 120 kPa, estimate p2 if wall friction is neglected.
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 ≈145 kPa, if the wall friction is negligible, estimate the force of the water on the
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 between sections 1 and 3 is 7 lbf/ft2, estimate
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 formula for the steady forward speed V of the boat.
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 (p1, V1, Vw, D) are known, derive expressions for (a) V2 and (b) p2.
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 for estimating (a) V3 and (b) p3.
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 to atmospheric pressure. Using a control volume analysis of mass and vertical momentum, derive the
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 is the fluid viscosity. Account for the decrease in wall area wetted by the fluid. Solve for the time
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: τ ≈ 0.005ρV2, where ρ is the fluid density. Account for the decrease in wall area
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 and combine control-volume analyses for the left and right legs to derive a single differential
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 dV/dt and then solve for V (t), assuming an initial displacement z = zo, V = 0 at t = 0. The result
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 accelerate to 90% of jet velocity. (c) Compute numerical values for (b) using the data from Ex. 3.10
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 S(t) reached is given by S = Ve Mo/m ζ in ζ−ζ +1 where ζ = −1
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 missile is fired vertically from rest at sea level, estimate (a) Its velocity and height at fuel
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 numerically for (a) the velocity and altitude at burnout and (b) the maximum altitude attained.
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. P3.102The pressure at sections 1 and 2 is approximately hydrostatic, and wall friction is negligible. Use
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 starts from rest when the rocket is fired, and if air drag and wheel friction are neglected,
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 equation for rocket motion, and solve for the angular velocity  (t) of the rod. Neglect
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 final motion when the angular acceleration is zero. Apply to the case Mo = 6 kg, R = 3 m, m = 0.05
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 final motion when the angular acceleration is zero. Apply to the case Mo = 6 kg, R = 3 m, m = 0.05
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 required to keep the cart moving.
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 to the left. Let the initial velocity be Vo, and neglect air drag and wheel friction. Find an
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 and (b) the rotation rate (r/min) if there is no retarding torque.
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 x axis required to keep the system rotating at angular velocity Ω.
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 determine ω (t), assuming ω = 0 at t = 0.
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°; (b) θ = 40°?
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 at shaft angular velocity ω, derive a formula for the power P required to drive the impeller.
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 keep the pipe from rotating.
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 disk must drive, at 250 rev/min, a small device whose retarding torque is 1.5 N⋅m. What is 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 extracted by the turbine
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 absolute velocities (a) V1 and (b) V2, and (c) the ideal horsepower required.
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 bend stationary.
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 what speed Ω r/min will the horsepower developed be a maximum? Assume that there are many
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 is neglected, estimate the steady rotation rate of the arm, in r/min.
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 required at point O.
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.) Neglect friction. Express your result in terms of the sheet thickness h1 and the angle θ between the
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 = 150 kPa, D2 = 7 cm, Q2 = 100 m3/h, p2 = 225 kPa, D3 = 4 cm, and p3 = 265 kPa. Compute the rate of
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. If heat losses to the atmosphere and ground are negligible, estimate the downstream river conditions
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 will the value of Q affect the downstream conditions (Qo, To)?
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 in kW delivered to the water.
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 and water physical properties. Show that, for a given penstock and river flow Q, the maximum
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 friction head loss between 1 and 2, in m, for the flowing condition?
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 stations every 10 mi along the pipe. Estimate the horsepower which must be delivered to the oil by each
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 situation. For a design flow rate of 15,000 gal/ min in either direction, the friction head loss is 17 ft.
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 formula hloss ≈ 17.5(V2/2g), where V is the average velocity in the pipe. If the steady flow
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 motor is required to drive it?
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 entrance loss, in which case Chap. 6 theory shows that hf = 32μLV/ (ρgd2). Students measure water
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 Btu/lb of steam. If head losses are negligible, how much horsepower does the turbine develop?
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 in the pipe. If the pump is 75 percent efficient, what horsepower is needed to drive it?
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 and is used for the system in Prob. 3.141. Estimate (a) the flow rate, in gal/min, and (b) the
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 into the tank is 0.013 kg/s. Assuming an ideal gas, estimate the initial rate of temperature rise
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 frictionless particles. What power must be delivered by the pump? Fig P3.144
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 be?
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 the data of Prob. 3.49?
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 rate of alcohol and (b) the absolute pressure at section 1.
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 pressure). If the foil is 1.5 m long and 18 m wide into the paper, and the ambient air is 5000 m
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) the velocities at sections (1) and (2); (b) the mercury manometer reading h.
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 are (a) the minimum and (b) the maximum values of θ for which the water jet will clear the
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 what ratio h/H will X be maximum? Sketch the three trajectories for h/H = 0.4, 0.5, and 0.6.
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 drawing?
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 at the nose and (b) the absolute velocity of the air near the blimp side.
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 hose, to reach the garden?
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 no losses, derive an expression for the velocity V1 which is just sufficient to bring reservoir fluid
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, estimate (a) the required airflow rate and (b) the fan power in kW.
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 is 50 ft/s. You must select an appropriate blower. Estimate the volumetric flow rate (in ft3/min)
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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