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mechanical engineering

Questions and Answers of Mechanical Engineering

A ship is 125 m long and has a wetted area of 3500 m2. Its propellers can deliver a maximum power of 1.1 MW to seawater at 20°C. If all drag is due to friction, estimate the maximum ship speed, in
Air at 20C and 1 atm flows past a long flat plate, at the end of which is placed a narrow scoop, as shown in Fig. P7.37(a) Estimate the height h of the scoop if it is to extract 4 kg/s per
Atmospheric boundary layers are very thick but follow formulas very similar to those of flat-plate theory. Consider wind blowing at 10 m/s at a height of 80 m above a smooth beach. Estimate the wind
A hydrofoil 50 cm long and 4 m wide moves at 28 kn in seawater at 20°C. Using flat-plate theory with Retr = 5E5, estimate its drag, in N, for (a) a smooth wall and (b) a rough wall, ε =
Hoerner (Ref. 12) plots the drag of a flag in winds, based on total surface area 2bL, in the figure at right. A linear approximation is CD ≈ 0.01 + 0.05L/b, as shown. Test Reynolds numbers were
Repeat Prob. 7.20 with the sole change that the pitot probe is now 20 mm from the wall (10 times higher). Show that the flow there cannot possibly be laminar, and use smooth-wall turbulent flow
A four-bladed helicopter rotor rotates at n r/min in air with properties (ρ, μ). Each blade has chord length C and extends from the center of rotation out to radius R (the hub size is
In the flow of air at 20°C and 1 atm past a flat plate in Fig. P7.43, the wall shear is to be determined at position x by a floating element (a small area connected to a strain-gage force
Extensive measurements of wall shear stress and local velocity for turbulent airflow on the flat surface of the University of Rhode Island wind tunnel have led to the following proposed
A thin sheet of fiberboard weighs 90 N and lies on a rooftop, as shown in the figure. Assume ambient air at 20°C and 1 atm. If the coefficient of solid friction between board and roof is σ
A ship is 150 m long and has a wetted area of 5000 m2. If it is encrusted with barnacles, the ship requires 7000 hp to overcome friction drag when moving in seawater at 15 kn and 20°C. What is the
As a case similar to Example 7.5, Howarth also proposed the adverse-gradient velocity distribution U = Uo (1 − x2/L2) and computed separation at xsep/L = 0.271 by a series-expansion method.
In 1957 H. Görtler proposed the adverse-gradient test cases And computed separation for laminar flow at n = 1 to be xsep/L = 0.159. Compare with Thwaites’ method, assuming θo = 0.
Based on your understanding of boundary layers, which flow direction (left or right) for the foil shape in the figure will have less total drag?
For flow past a cylinder of radius R as in Fig P7.50, the theoretical in viscid velocity distribution along the surface is U =2Uosin(x/R), where Uo is the oncoming stream velocity and x is the arc
Clift et al. [46] give the formula F ≈ (6π /5) (4 + a/b) μUb for the drag of a prolate spheroid in creeping motion, as shown in Fig. P7.52. The half-thickness b is 4 mm. See also
Consider the flat-walled diffuser in Fig. P7.51, which is similar to that of Fig. 6.26a with constant width b, if x is measured from the inlet and the wall boundary layers are thin, show that the
From Table 7.2, the drag coefficient of a wide plate normal to a stream is approximately 2.0. Let the stream conditions be U∞ and p∞. If the average pressure on the front of the plate is
A chimney at sea level is 2 m in diameter and 40 m high and is subjected to 50 mi/h storm winds. What is the estimated wind-induced bending moment about the bottom of the chimney?
A ship tows a submerged cylinder, 1.5 m in diameter and 22 m long, at U = 5 m/s in fresh water at 20°C. Estimate the towing power in kW if the cylinder is (a) parallel, and (b) normal to the tow
A delivery vehicle carries a long sign on top, as in Fig. P7.56. If the sign is very thin and the vehicle moves at 65 mi/h, (a) Estimate the force on the sign with no crosswind. (b) Discuss the
The main cross-cable between towers of a coastal suspension bridge is 60 cm in diameter and 90 m long. Estimate the total drag force on this cable in crosswinds of 50 mi/h. Are these laminar-flow
A long cylinder of rectangular cross section, 5 cm high and 30 cm long, is immersed in water at 20°C flowing at 12 m/s parallel to the long side of the rectangle. Estimate the drag force on the
Joe can pedal his bike at 10 m/s on a straight, level road with no wind. The bike rolling resistance is 0.80 N/ (m/s), i.e. 0.8 N per m/s of speed. The drag area CDA of Joe and his bike is 0.422 m2.
A fishnet consists of 1-mm-diameter strings overlapped and knotted to form 1- by 1-cm squares. Estimate the drag of 1 m2 of such a net when towed normal to its plane at 3 m/s in 20°C seawater. What
A filter may be idealized as an array of cylindrical fibers normal to the flow, as in Fig. P7.61. Assuming that the fibers are uniformly distributed and have drag coefficients given by Fig 7.16a,
A sea-level smokestack is 52 m high and has a square cross-section. Its supports can withstand a maximum side force of 90 kN. If the stack is to survive 90 mi/h hurricane winds, what is its maximum
A parachutist jumps from a plane, using an 8.5-m-diameter chute in the standard atmosphere. The total mass of chutist and chute is 90 kg. Assuming a fully open chute in quasisteady motion, estimate
For those who think electric cars are sissy, Keio University in Japan has tested a 22-ft long prototype whose eight electric motors generate a total of 590 horsepower. The “Kaz” cruises at 180
As soldiers get bigger and packs get heavier, a parachutist and load can weigh as much as 400 lbf. The standard 28-ft parachute may descend too fast for safety. For heavier loads, the U.S. Army
A sphere of density ρ s and diameter D is dropped from rest in a fluid of density ρ and viscosity μ. Assuming a constant drag coefficient o Cd, derive a differential equation for the fall
A world-class bicycle rider can generate one-half horsepower for long periods. If racing at sea-level, estimate the velocity which this cyclist can maintain. Neglect rolling friction.
A baseball weighs 145 g and is 7.35 cm in diameter. It is dropped from rest from a 35-m-high tower at approximately sea level, Assuming a laminar-flow drag coefficient, estimate (a) Its terminal
Two baseballs from Prob. 7.68 are connected to a rod 7 mm in diameter and 56 cm long, as in Fig. P7.69What power, in W, is required to keep the system spinning at 400 r/min? Include the drag of the
A baseball from Prob. 7.68 is batted upward during a game at an angle of 45° and an initial velocity of 98 mi/h. Neglect spin and lift. Estimate the horizontal distance traveled, (a) Neglecting
A football weights 0.91 lbf and approximates an ellipsoid 6 in diameter and 12 in long (Table 7.3). It is thrown upward at a 45° angle with an initial velocity of 80 ft/s. Neglect spin and lift.
A settling tank for a municipal water supply is 2.5 m deep, and 20°C water flows through continuously at 35 cm/s. Estimate the minimum length of the tank which will ensure that all sediment (SG
A balloon is 4 m in diameter and contains helium at 125 kPa and 15°C. Balloon material and payload weigh 200 N, not including the helium. Estimate (a) The terminal ascent velocity in sea-level
It is difficult to define the “frontal area” of a motorcycle due to its complex shape. One then measures the drag-area, that is, CDA, in area units. Hoerner [12] reports the drag-area of a
Extend Problem 7.75 to make a smooth plot of tilt angle θ versus stream velocity U in the range 1 < U < 12 mi/h (use a spreadsheet). Comment on the effectiveness of this system as an
The helium-filled balloon in Fig P7.75 is tethered at 20°C and 1 atm with a string of negligible weight and drag. The diameter is 50 cm, and the balloon material weighs 0.2 N, not including the
To measure the drag of an upright person, without violating human-subject protocols, a life-sized mannequin is attached to the end of a 6-m rod and rotated at Ω = 80 rev/min, as in Fig. P7.77.
Apply Prob. 7.61 to a filter consisting of 300-μ m-diameter fibers packed 250 per square centimeter in the plane of Fig. P7.61. For air at 20°C and 1 atm flowing at 1.5 m/s, estimate the
A radioactive dust particle approximates a sphere with a density of 2400 kg/m3. How long, in days, will it take the particle to settle to sea level from 12 km altitude if the particle diameter is (a)
A heavy sphere attached to a string should hang at an angle θ when immersed in a stream of velocity U, as in Fig. P7.80. Derive an expression for θ as a function of the sphere and flow
A typical U.S. Army parachute has a projected diameter of 28 ft. For a payload mass of 80 kg, (a) What terminal velocity will result at 1000-m standard altitude? For the same velocity and payload,
The average skydiver, with parachute unopened, weighs 175 lbf and has a drag area CDA ≈ 9 ft2 spread-eagled and 1.2 ft2 falling feet-first (see Table 7.3). What is the minimum and maximum
A high-speed car has a drag coefficient of 0.3 and a frontal area of 1.0 m2. A parachute is to be used to slow this 2000-kg car from 80 to 40 m/s in 8 s. What should the chute diameter be? What
A Ping-Pong ball weighs 2.6 g and has a diameter of 3.8 cm. It can be supported by an air jet from a vacuum cleaner outlet, as in Fig. P7.84. For sea level standard air, what jet velocity is required
An aluminum cylinder (SG = 2.7) slides concentrically down a taut 1-mmdiameter wire as shown in the figure. Its length is L = 8 cm and its radius R = 1 cm. A 2-mm-diameter hole down the cylinder
Hoerner [Ref. 12 of Chap. 7, p. 3€“25] states that the drag coefficient of a flag of 2:1 aspect ratio is 0.11 based on platform area. URI has an aluminum flagpole 25 m high and 14 cm in
A tractor-trailer truck has a drag area CDA = 8 m2 bare and CDA = 6.7 m2 with a deflector added (Fig. 7.18b). Its rolling resistance is 50 N for each mi/h of speed. Calculate the total horsepower
A pickup truck has a clean drag-area CDA of 35 ft2. Estimate the horsepower required to drive the truck at 55 mi/h (a) clean and (b) with the 3- by 6-ft sign in Fig. P7.88 installed if the rolling
The new AMTRAK high-speed Acela train can reach 150 mi/h, which presently it seldom does, because of the curvy coastline tracks in New England. If 75% of the power expanded at this speed is due to
In the great hurricane of 1938, winds of 85 mi/h blew over a boxcar in Providence, Rhode Island. The boxcar was 10 ft high, 40 ft long, and 6 ft wide, with a 3-ft clearance above tracks 4.8 ft apart.
A cup anemometer uses two 5-cmdiameter hollow hemispheres connected to two 15-cm rods, as in Fig. P7.91. Rod drag is neglected, and the central bearing has a retarding torque of 0.004 N⋅m. With
A 1500-kg automobile uses its drag-area, CDA = 0.4 m2, plus brakes and a parachute, to slow down from 50 m/s. Its brakes apply 5000 N of resistance. Assume sea level standard air. If the automobile
A hot-film probe is mounted on a cone-and-rod system in a sea-level air stream of 45 m/s, as in Fig. P7.93. Estimate the maximum cone vertex angle allowable if the flow-induced bending moment at the
A rotary mixer consists of two 1-mlong half-tubes rotating around a central arm, as in Fig. P7.94. Using the drag from Table 7.2, derive an expression for the torque T required to drive the mixer at
An airplane weighing 28 kN, with a drag-area CDA = 5 m2, lands at sea level at 55 m/s and deploys a drag parachute 3 m in diameter. No other brakes are applied. (a) How long will it take the plane
A Savonius rotor (see Fig. 6.29b) can be approximated by the two open half tubes in Fig. P7.96 mounted on a central axis. If the drag of each tube is similar to that in Table 7.2, derive an
A simple measurement of automobile drag can be found by an unpowered coast down on a level road with no wind. Assume constant rolling resistance. For an automobile of mass 1500 kg and frontal area 2
A buoyant ball of specific gravity SG (b) How far will a 5-cm-diameter ball, with SG = 0.5 and CD = 0.47, penetrate if it enters at 10 m/s?
Two steel balls (SG = 7.86) are connected by a thin hinged rod of negligible weight and drag, as shown in Fig. P7.99. A stop prevents counterclockwise rotation. Estimate the sea-level air velocity U
Sand particles (SG = 2.7), approximately spherical with diameters from 100 to 250 μm, are introduced into an upward-flowing water stream. What is the minimum water velocity to carry all the
When immersed in a uniform stream, a heavy rod hinged at A will hang at Pode’s angle θ, after L. Pode (1951). Assume the cylinder has normal drag coefficient CDn and tangential coefficient
Suppose that the tractor-trailer truck of Prob. 7.100 is subjected to an unpowered, no-brakes no-deflector coast down on a sea-level road. The starting velocity is 65 mi/h. Solve, either analytically
A ship 50 m long, with a wetted area of 800 m2, has the hull shape of Fig. 7.19, with no bow or stern bulbs. Total propulsive power is 1 MW. For seawater at 20°C, plot the ship’s velocity V (in
A smooth steel ball 1-cm in diameter (W ≈ 0.04 N) is fired vertically at sea level at an initial velocity of 1000 m/s. Its drag coefficient is given by Fig. 7.20. Assuming a constant speed of
Repeat Prob. P7.106 if the body shot upward at 1000 m/s is a 9-mm steel bullet (W = 0.07 N) which approximates the pointed body of revolution in Fig. 7.20.
The data in Fig P7.108 are for lift and drag of a spinning sphere from Ref. 12, pp. 7€“20. Suppose a tennis ball (W ≈ 0.56 N, D ≈ 6.35 cm) is struck at sea level with initial
Repeat Prob. 7.108 above if the ball is instead struck with “underspin,” that is, with the front of the ball rotating upward.
A baseball pitcher throws a curveball with an initial velocity of 65 mi/h and a spin of 6500 r/min about a vertical axis. A baseball weighs 0.32 lbf and has a diameter of 2.9 in. Using the data of
A table tennis ball has a mass of 2.6 g and a diameter of 3.81 cm. It is struck horizontally at an initial velocity of 20 m/s while it is 50 cm above the table, as in Fig. P7.111. For sea-level air,
A smooth wooden sphere (SG = 0.65) is connected by a thin rigid rod to a hinge in a wind tunnel, as in Fig. P7.112. Air at 20°C and 1 atm flows and levitates the sphere.(a) Plot the angle θ
An auto has m = 1000 kg and a drag-area CDA = 0.7 m2, plus constant 70-N rolling resistance. The car coasts without brakes at 90 km/h climbing a hill of 10 percent grade (5.71°). How far up the
Suppose the car in Prob. 7.113 above is placed at the top of the hill and released from rest to coast down without brakes. What will be the car speed, in km/h, after dropping a vertical distance of
The Cessna Citation executive jet weighs 67 kN and has a wing area of 32 m2. It cruises at 10 km standard altitude with a lift coefficient of 0.21 and a drag coefficient of 0.015. Estimate (a) the
An airplane weighs 180 kN and has a wing area of 160 m2 and a mean chord of 4 m. The airfoil properties are given by Fig. 7.25. If the plane is designed to land at Vo = 1.2Vstall, using a split flap
Suppose the airplane of Prob. 7.116 takes off at sea level without benefit of flaps and with constant lift coefficient and take-off speed of 100 mi/h. (a) Estimate the take-off distance if the
Suppose the airplane of Prob. 7.116 is now fitted with all the best high-lift devices of Fig. 7.28. (a) What is its minimum stall speed in mi/h? (b) Estimate the stopping distance if the plane lands
An airplane has a mass of 5000 kg, a maximum thrust of 7000 N, and a rectangular wing with aspect ratio 6.0. It takes off at sea level with a 60° split flap as in Fig. 7.25. Assume all lift and drag
Show that, if Eqs. (7.70) and (7.71) are valid, the maximum lift-to-drag ratio occurs when CD = 2CD∞. What are (L/D) max and α for a symmetric wing when AR = 5.0 and CD∞ = 0.009?
In gliding (unpowered) flight, lift and drag are in equilibrium with the weight. Show, that with no wind, the craft sinks at an angle tanθ ≈ drag/lift. For a sailplane with m = 200 kg,
A boat of mass 2500 kg has two hydrofoils, each of chord 30 cm and span 1.5 meters, with CL,max = 1.2 and CD∞ = 0.08. Its engine can deliver 130 kW to the water. For seawater at 20°C, estimate
In prewar days there was a controversy, perhaps apocryphal, about whether the bumblebee has a legitimate aerodynamic right to fly. The average bumblebee (Bombus terrestris) weighs 0.88 g, with a wing
The bumblebee can hover at zero speed by flapping its wings. Using the data of Prob. 7.123, devise a theory for flapping wings where the down stroke approximates a short flat plate normal to the flow
In 2001, a commercial aircraft lost all power while flying at 33,000 ft over the open Atlantic Ocean, about 60 miles from the Azores Islands. The pilots, with admirable skill, put the plane into a
Prove that the streamlines ψ (r, θ) in polar coordinates, from Eq. (8.10), are orthogonal to the potential lines φ (r, θ).
The steady plane flow in the figure has the polar velocity components vθ = Ωr and vr = 0. Determine the circulation Γ around the path shown.
Using Cartesian coordinates, show that each velocity component (u, v, w) of a potential flow satisfies Laplace’s equation separately if 2φ = 0. Solution: This is true because the order of
Is the function 1/r a legitimate velocity potential in plane polar coordinates? If so, what is the associated stream function ψ ( r, θ ) ?
Consider the two-dimensional velocity distribution u = –By, v = +Bx, where B is a constant. If this flow possesses a stream function, find its form. If it has a velocity potential, find that also.
If the velocity potential of a realistic two-dimensional flow is φ = Cln(x2 + y2)1/2, where C is a constant, find the form of the stream function ψ ( x, y). Hint: Try polar coordinates.
Consider a flow with constant density and viscosity. If the flow possesses a velocity potential as defined by Eq. (8.1), show that it exactly satisfies the full Navier-Stokes equation (4.38). If this
For the velocity distribution of Prob. 8.5, u = €“By, v = +Bx, evaluate the circulation Γ around the rectangular closed curve defined by (x, y) = (1, 1), (3, 1), (3, 2), and (1, 2).
Consider the two-dimensional flow u = €“Ax, v = +Ay, where A is a constant. Evaluate the circulation Γ around the rectangular closed curve defined by (x, y) = (1, 1), (4, 1), (4, 3),
A mathematical relation sometimes used in fluid mechanics is the theorem of Stokes [1] where A is any surface and C is the curve enclosing that surface. The vector ds is the differential arc length
A power-plant discharges cooling water through the manifold in Fig. P8.11, which is 55 cm in diameter and 8 m high and is perforated with 25,000 holes 1 cm in diameter. Does this manifold simulate a
Consider the flow due to a vortex of strength K at the origin. Evaluate the circulation from Eq. (8.15) about the clockwise path from (a, 0) to (2a, 0) to (2a, 3π /2) to (a, 3π /2) and back to

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