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engineering
mechanical engineering
Questions and Answers of
Mechanical Engineering
A uniform block of steel (SG =7.85) will float at a mercury-water interface as in the figure. What is the ratio of the distances a and b for this condition?
A spherical balloon is filled with helium at sea level. Helium and balloon material together weigh 500 N. If the net upward lift force on the balloon is also 500 N, what is the diameter of the
A balloon weighing 3.5 lbf is 6 ft in diameter. If filled with hydrogen at 18 psia and 60°F and released, at what U.S. standard altitude will it be neutral?
Suppose the balloon in Prob. 2.111 is constructed with a diameter of 14 m, is filled at sea level with hot air at 70°C and 1 atm, and released. If the hot air remains at 70°C, at what U.S. standard
A block of wood (SG = 0.6) floats in fluid X in Fig. P2.126 such that 75% of its volume is submerged in fluid X. Estimate the gage pressure of the air in the tank.
Consider a cylinder of specific gravity S
The iceberg of Fig. 2.20 can be idealized as a cube of side length L as shown. If seawater is denoted as S = 1, the iceberg has S = 0.88. Is it stable?
The iceberg of Prob. 2.128 may become unstable if its width decreases. Suppose that the height is L and the depth into the paper is L but the width decreases to H
Consider a wooden cylinder (SG =0.6) 1 m in diameter and 0.8 m long. Would this cylinder be stable if placed to float with its axis vertical in oil (SG = 0.85)?
A barge is 15 ft wide and floats with a draft of 4 ft. It is piled so high with gravel that its center of gravity is 3 ft above the waterline, as shown. Is it stable?
A solid right circular cone has SG =0.99 and floats vertically as shown. Is this a stable position?
Consider a uniform right circular cone of specific gravity S
When floating in water (SG = 1), an equilateral triangular body (SG = 0.9) might take two positions, as shown at right. Which position is more stable? Assume large body width into the paper.
Consider a homogeneous right circular cylinder of length L, radius R, and specific gravity SG, floating in water (SG = 1) with its axis vertical. Show that the body is stable if R/L> [2SG
Consider a homogeneous right circular cylinder of length L, radius R, and specific gravity SG = 0.5, floating in water (SG = 1) with its axis horizontal. Show that the body is stable if L/R > 2.0.
A tank of water 4 m deep receives a constant upward acceleration az. Determine(a) The gage pressure at the tank bottom if az = 5 m2/s; and(b) The value of az which causes the gage pressure at the
A 12 fluid ounce glass, 3 inches in diameter, sits on the edge of a merry-goround 8 ft in diameter, rotating at 12 r/min. How full can the glass be before it spills?
The tank of liquid in the figure P2.139 accelerates to the right with the fluid in rigid-body motion.(a) Compute ax in m/s2.(b) Why doesnt the solution to part (a) depend upon fluid
Suppose that the elliptical-end fuel tank in Prob. 2.101 is 10 m long and filled completely with fuel oil (ρ = 890 kg/m3). Let the tank be pulled along a horizontal road in rigid-body motion.
The same tank from Prob. 2.139 is now accelerating while rolling up a 30° inclined plane, as shown. Assuming rigid body motion, compute(a) The acceleration a,(b) Whether the acceleration is up or
The tank of water in Fig P2.142 is 12 cm wide into the paper. If the tank is accelerated to the right in rigid-body motion at 6 m/s2, compute(a) The water depth at AB, and(b) The water force on panel
The tank of water in Fig P2.143 is full and open to the atmosphere (patm = 15 psi = 2160 psf) at point A, as shown. For what acceleration ax, in ft/s2, will the pressure at point B in the figure be
Consider a hollow cube of side length 22 cm, full of water at 20°C, and open to patm = 1 atm at top corner A. The top surface is horizontal. Determine the rigid body accelerations for which the
A fish tank 16-in by 27-in by 14-inch deep is carried in a car which may experience accelerations as high as 6 m/s2. Assuming rigid-body motion, estimate the maximum water depth to avoid spilling.
The tank in Fig P2.146 is filled with water and has a vent hole at point A. It is 1 m wide into the paper. Inside is a 10-cm balloon filled with helium at 130 kPa. If the tank accelerates to the
The tank of water in Fig P2.147 accelerates uniformly by rolling without friction down the 30° inclined plane. What is the angle θ of the free surface? Can you explain this interesting
Modify Prob. 2.146 as follows: Let the 10-cm-diameter sphere be concrete (SG = 2.4) hanging by a string from the top. If the tank accelerates to the right at 5 m/s/s, at what angle will the balloon
The waterwheel in Fig P2.149 lifts water with 1-ft-diameter half-cylinder blades. The wheel rotates at 10 r/min, what is the water surface angle θ at pt A?
A cheap accelerometer can be made from the U-tube at right. If L = 18 cm and D = 5 mm, what will h be if ax = 6 m/s2?
The U-tube in Fig P2.151 is open at A and closed at D. What uniform acceleration ax will cause the pressure at point C to be atmospheric? The fluid is water.
A 16-cm-diameter open cylinder 27 cm high is full of water. Find the central rigid-body rotation rate for which(a) One third of the water will spill out; and(b) The bottom center of the can will be
Suppose the U-tube in Prob. 2.150 is not translated but instead is rotated about the right leg at 95 r/min. Find the level h in the left leg if L = 18 cm and D = 5 mm.
A very deep 18-cm-diameter can has 12 cm of water, overlaid with 10 cm of SAE 30 oil. It is rotated about the center in rigid-body motion at 150 r/min.(a) What will be the shapes of the
For what uniform rotation rate in r/min about axis C will the U-tube fluid in Fig. P2.155 take the position shown? The fluid is mercury at 20°C.
Suppose the U-tube of Prob. 2.151 is rotated about axis DC. If the fluid is water at 122°F and atmospheric pressure is 2116 psfa, at what rotation rate will the fluid begin to vaporize? At what
The 45° V-tube in Fig P2.157 contains water and is open at A and closed at C.(a) For what rigid-body rotation rate will the pressure be equal at points B and C?(b) For the condition of part (a),
It is desired to make a 3-mdiameter parabolic telescope mirror by rotating molten glass in rigid-body motion until the desired shape is achieved and then cooling the glass to a solid. The focus of
The three-legged manometer in Fig P2.159 is filled with water to a depth of 20 cm. All tubes are long and have equal small diameters. If the system spins at angular velocity Ω about the central
Discuss Newtons second law (the linear momentum relation) in these three forms:
Consider the angular-momentum relation in the formWhat does r mean in this relation? Is this relation valid in both solid and fluid mechanics? Is it related to the linear-momentum equation (Prob.
Discuss whether the following flows are steady or unsteady: (a) Flow near an automobile moving at 55 m/h; (b) Flow of the wind past a water tower; (c) Flow in a pipe as the downstream valve is
For steady laminar flow through a long tube (see Prob. 1.12), the axial velocity distribution is given by u = C (R2 − r2), where R is the tube outer radius and C is a constant. Integrate u(r)
A theory proposed by S. I. Pai in 1953 gives the following velocity values u(r) for turbulent (high-Reynolds number) airflow in a 4-cm-diameter tube: r, cm 0 0.25 0.5 0.75 1.0 1.25 1.5 1.75
When a gravity-driven liquid jet issues from a slot in a tank, as in Fig P3.6, an approximation for the exit velocity distribution is u≈ 2g (h−z), where h is the depth of the jet
In Chap. 8 a theory gives the velocities for flow past a cylinder:vr = Ucosθ (1−R2/r2 )vθ = −Usinθ (1+R2/r2)Compute the volume flow Q passing through surface CC in the
Three pipes steadily deliver water at 20°C to a large exit pipe in Fig. P3.8 The velocity V2 = 5 m/s, and the exit flow rate Q4 = 120 m3/h. Find (a) V1;(b) V3; and (c) V4 if it is known that
A laboratory test tank contains seawater of salinity S and density ρ. Water enters the tank at conditions (S1, ρ1, A1, V1) and is assumed to mix immediately in the tank. Tank water leaves
Water flowing through an 8-cm-diameter pipe enters a porous section, as in Fig. P3.10, which allows a uniform radial velocity vw through the wall surfaces for a distance of 1.2 m. If the entrance
A room contains dust at uniform concentration C = ρdust/ρ. It is to be cleaned by introducing fresh air at an inlet section Ai, Vi and exhausting the room air through an outlet section.
The pipe flow in Fig P3.12 fills a cylindrical tank as shown. At time t = 0, the water depth in the tank is 30 cm. Estimate the time required to fill the remainder of the tank.
Water at 20°C flows steadily at 40 kg/s through the nozzle in Fig P3.13, If D1 = 18 cm and D2 = 5 cm, compute the average velocity, in m/s, at (a) section 1 and (b) section 2.
The open tank in the figure contains water at 20°C. For incompressible flow, (a) Derive an analytic expression for dh/dt in terms of (Q1, Q2, Q3).b) If h is constant, determine V2 for the given
An incompressible fluid flows past an impermeable flat plate, as in Fig.P3.16, with a uniform inlet profile u = Uo and a cubic polynomial exit profileu ≈ Uo (3n n3 / 2) where n =
Water flows steadily through the round pipe in the figure. The entrance velocity is Vo. The exit velocity approximates turbulent flow, u = umax(1 − r/R) 1/7. Determine the ratio Uo/umax for
Incompressible steady flow in the inlet between parallel plates in Fig P3.17 is uniform, u = Uo = 8 cm/s, while downstream the flow develops into the parabolic laminar profile u = az (zo − z),
An incompressible fluid flows steadily through the rectangular duct in the figure. The exit velocity profile is given by u ≈ umax(1 y2/b2)(1 z2/h2). (a) Does this
Water from a storm drains flows over an outfall onto a porous bed which absorbs the water at a uniform vertical velocity of 8 mm/s, as shown in Fig. P3.19The system is 5 m deep into the paper. Find
Oil (SG-0.91) enters the thrust bearing at 250 N/hr and exits radially through the narrow clearance between thrust plates. Compute (a) the outlet volume flow in mL/s, and (b) the average outlet
A dehumidifier brings in saturated wet air (100 percent relative humidity) at 30°C and 1 atm, through an inlet of 8-cm diameter and average velocity 3 m/s. After some of the water vapor condenses
The converging-diverging nozzle shown in Fig P3.22 expands and accelerates dry air to supersonic speeds at the exit, where p2 = 8 kPa and T2 = 240 K. At the throat, p1 = 284 kPa, T1 = 665 K, and V1 =
The hypodermic needle in the figure contains a liquid (SG 1.05). If the serum is to be injected steadily at 6 cm3/s, how fast should the plunger be advanced (a) if leakage in the
Water enters the bottom of the cone in the figure at a uniformly increasing average velocity V = Kt. If d is very small, derive an analytic formula for the water surface rise h (t), assuming h = 0 at
As will be discussed in Chaps 7 and 8, the flow of a stream Uo past a blunt flat plate creates a broad low-velocity wake behind the plate. A simple model is given in Fig. P3.25, with only half of the
A thin layer of liquid, draining from an inclined plane, as in the figure, will have a laminar velocity profile u = Uo (2y/h − y2/h2), where Uo is the surface velocity. If the plane has width b
The cone frustum in the figure contains incompressible liquid to depth h. A solid piston of diameter d penetrates the surface at velocity V. Derive an analytic expression for the rate of rise dh/dt
According to Torricellis theorem, the velocity of a fluid draining from a hole in a tank is V ≈ (2gh) 1/2, where h is the depth of water above the hole, as in Fig. P3.28. Let the
In elementary compressible-flow theory (Chap. 9), compressed air will exhaust from a small hole in a tank at the mass flow rate m_ ≈C, where is the air density
A wedge splits a sheet of 20°C water, as shown in Fig. P3.30 Both wedge and sheet are very long into the paper. If the force required to hold the wedge stationary is F = 124 N per meter of
A bellows may be modeled as a deforming wedge-shaped volume as in Fig. P3.31 The check valve on the left (pleated) end is closed during the stroke. If b is the bellows width into the paper, derive
Water at 20°C flows through the piping junction in the figure, entering section 1 at 20 gal/min, the average velocity at section 2 is 2.5 m/s. A portion of the flow is diverted through the
In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig P3.33 contains 1200 holes of 5-mm diameter each per
A rocket motor is operating steadily, as shown in Fig. P3.34. The products of combustion flowing out the exhaust nozzle approximate a perfect gas with a molecular weight of 28. For the given
In contrast to the liquid rocket in Fig. P3.34, the solid-propellant rocket in Fig P3.35 is self-contained and has no entrance ducts. Using a control-volume analysis for the conditions shown in Fig
The jet pump in Fig P3.36 injects water at U1 = 40 m/s through a 3-in pipe and entrains a secondary flow of water U2 = 3 m/s in the annular region around the small pipe. The two flows become fully
A solid steel cylinder, 4.5 cm in diameter and 12 cm long, with a mass of 1500 grams, falls concentrically through a 5-cm-diameter vertical container filled with oil (SG = 0.89). Assuming the oil is
An incompressible fluid is squeezed between two disks by downward motion Vo of the upper disk. Assuming 1-dimensional radial outflow, find the velocity V(r).
For the elbow duct in Fig P3.39, SAE 30 oil at 20°C enters section 1 at 350 N/s, where the flow is laminar, and exits at section 2, where the flow is turbulent: u1 ≈ Vav1 (1-r2 / r2 1) u2
The water jet in Fig P3.40 strikes normal to a fixed plate. Neglect gravity and friction, and compute the force F in newtons required to hold the plate fixed.
In Fig P3.41 the vane turns the water jet completely around. Find the maximum jet velocity Vo for a force Fo.
A liquid of density ρ flows through the sudden contraction in Fig. P3.42 and exits to the atmosphere. Assume uniform conditions (p1, V1, D1) at section 1 and (p2, V2, D2) at section 2. Find an
Water at 20°C flows through a 5-cm-diameter pipe which has a 180° vertical bend, as in Fig P3.43The total length of pipe between flanges 1 and 2 is 75 cm. When the weight flow rate is 230
Consider uniform flow past a cylinder with a V-shaped wake, as shown. Pressures at (1) and (2) are equal. Let b be the width into the paper. Find a formula for the force F on the cylinder due to the
In Fig P3.45 a perfectly balanced 700-N weight and platform are supported by a steady water jet. What is the proper jet velocity?
When a jet strikes an inclined plate, it breaks into two jets of equal velocity V but unequal fluxes αQ at (2) and (1 α) Q at (3), as shown. Find α, assuming that the
The small boat is driven at steady speed Vo by compressed air issuing from a 3-cm-diameter hole at Ve = 343 m/s and pe = 1 atm, Te = 30°C. Neglect air drag. The hull drag is kVo 2, where k = 19 N
A liquid jet Vj of diameter Dj strikes a fixed cone and deflects back as a conical sheet at the same velocity. Find the cone angle θ for which the restraining force F = (3/2) ρAjVj 2.
The horizontal nozzle in Fig P3.49 has D1 = 12 in, D2 = 6 in, with p1 = 38 psia and V2 = 56 ft/s. For water at 20°C, find the force provided by the flange bolts to hold the nozzle fixed.
The jet engine in Fig P3.50 admits air at 20°C and 1 atm at (1), where A1 = 0.5 m2 and V1 = 250 m/s. The fuel-air ratio is 1:30. The air leaves section (2) at 1 atm, V2 = 900 m/s, and A2 = 0.4
A liquid jet of velocity Vj and area Aj strikes a single 180° bucket on a turbine wheel rotating at angular velocity Ω. Find an expression for the power P delivered. At what Ω is the
The vertical gate in a water channel is partially open, as in Fig. P3.52 Assuming no change in water level and a hydrostatic pressure distribution, derive an expression for the stream wise force Fx
Consider incompressible flow in the entrance of a circular tube, as in Fig. P3.53, the inlet flow is uniform, u1 = Uo. The flow at section 2 is developed pipe flow. Find the wall drag force F as a
For the pipe-flow reducing section of Fig P3.54, D1 = 8 cm, D2 = 5 cm, and p2 = 1 atm. All fluids are at 20°C. If V1 = 5 m/s and the manometer reading is h = 58 cm, estimate the total horizontal
Water at 20°C flows steadily through the box in Fig P3.56, entering station (1) at 2 m/s. Calculate the (a) horizontal; and (b) vertical forces required to hold the box stationary against the
The water tank in Fig P3.58 stands on a frictionless cart and feeds a jet of diameter 4 cm and velocity 8 m/s, which is deflected 60° by a vane. Compute the tension in the supporting cable.
In Fig P3.55 the jet strikes a vane which moves to the right at constant velocity Vc on a frictionless cart. Compute(a) The force Fx required to restrain the cart and(b) The power P delivered to the
Water flows through the duct in Fig P3.57, which is 50 cm wide and 1 m deep into the paper. Gate BC completely closes the duct when β = 90°. Assuming one-dimensional flow, for what angle
A pipe flow expands from (1) to (2), causing eddies as shown. Using the given CV and assuming p = p1 on the corner annular ring, show that the downstream pressure is given by, neglecting wall
Water at 20°C flows through the elbow in Fig P3.60 and exits to the atmosphere. The pipe diameter is D1 = 10 cm, while D2 = 3 cm. At a weight flow rate of 150 N/s, the pressure p1 = 2.3 atm
A 20°C water jet strikes a vane on a tank with frictionless wheels, as shown. The jet turns and falls into the tank without spilling. If θ = 30°, estimate the horizontal force F needed
The sluice gate in Fig P3.63 can control and measure flow in open channels. At sections 1 and 2, the flow is uniform and the pressure is hydrostatic. The channel width is b into the paper. Neglecting
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