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mechanical engineering

Questions and Answers of Mechanical Engineering

Test the dimensional homogeneity of the boundary-layer x-momentum equation: ρu ∂u/ ∂τ + ρv ∂u/ ∂y = − ρgx + ∂τ / ∂y
Investigate the consistency of the Hazen-Williams formula from hydraulics: Q = 61.9D 2.63 (Δp/L) 0.54 What are the dimensions of the constant “61.9”? Can this equation be used with
(€œ*€ means €œdifficult€€”not just a plug-and-chug, that is) For small particles at low velocities, the first (linear) term in Stokes€™
Marangoni convection arises when a surface has a difference in surface tension along its length. The dimensionless Marangoni number M is a combination of thermal diffusivity α = k/ (ρcp)
(“C” means computer-oriented, although this one can be done analytically.) A baseball, with m = 145 g, is thrown directly upward from the initial position z = 0 and Vo = 45 m/s. The air drag on
The dimensionless Grashof number, Gr, is a combination of density ρ, viscosity μ, temperature difference ΔT, length scale L, the acceleration of gravity g, and the coefficient of
According to the theory of Chap. 8, as a uniform stream approaches a cylinder of radius R along the line AB shown in Fig P1.22, €“∞ u=U∞ (1−R2/x2); v=w=0
Consider carbon dioxide at 10 atm and 400°C. Calculate ρ and cp at this state and then estimate the new pressure when the gas is cooled isentropically to 100°C. Use two methods: (a) An ideal
A tank contains 0.9 m3 of helium at 200 kPa and 20°C. Estimate the total mass of this gas, in kg, (a) On earth; and (b) On the moon. Also, (c) How much heat transfer, in MJ, is required to
A tire has a volume of 3.0 ft3 and a ‘gage’ pressure of 32 psi at 75°F. If the ambient pressure is sea-level standard, what is the weight of air in the tire?
Given temperature and specific volume data for steam at 40 psia [Ref. 13]: T, °F: 400 500 600 700 800 V, ft3/lbm: 12.624 14.165 15.685 17.195 18.699 Is the ideal gas law reasonable
Wet air, at 100% relative humidity, is at 40°C and 1 atm. Using Dalton’s law of partial pressures, compute the density of this wet air and compare with dry air.
A tank holds 5 ft3 of air at 20°C and 120 psi (gage). Estimate the energy in ft-lbf required to compress this air isothermally from one atmosphere (14.7 psia = 2116 psfa).
Repeat Prob. 1.29 if the tank is filled with compressed water rather than air. Why is the result thousands of times less than the result of 215,000 ft⋅lbf in Prob. 1.29?
The density of water for 0°C < T < 100°C is given in Table A-1. Fit this data to a least-squares parabola, ρ = a + bT + cT2, and test its accuracy vis-a-vis Table A-1.Finally, compute ρ
A blimp is approximated by a prolate spheroid 90 m long and 30 m in diameter. Estimate the weight of 20°C gas within the blimp for (a) Helium at 1.1 atm; and (b) Air at 1.0 atm. What might the
Experimental data for density of mercury versus pressure at 20°C are as follows: p, atm: 1 500 1000 1500 2000 ρ, kg/m3: 13545 13573 13600 13625 13653 Fit this data to the
Consider steam at the following state near the saturation line: (p1, T1) = (1.31 MPa, 290°C). Calculate and compare, for an ideal gas (Table A.4) and the Steam Tables (or the EES software), (a) the
In Table A-4, most common gases (air, nitrogen, oxygen, hydrogen, CO, NO) have a specific heat ratio k = 1.40. Why do argon and helium have such high values? Why does NH3 have such a low value? What
The bulk modulus of a fluid is defined as B = ρ (∂ p/∂ρ) S. What are the dimensions of B? Estimate B (in Pa) for (a) N2O, and (b) Water, at 20°C and 1 atm.
A near-ideal gas has M = 44 and cv = 610 J/(kg⋅K). At 100°C, what are (a) Its specific heat ratio, and (b) Its speed of sound?
In Fig P1.38, if the fluid is glycerin at 20°C and the width between plates is 6 mm, what shear stress (in Pa) is required to move the upper plate at V = 5.5 m/s? What is the flow Reynolds number
Knowing μ ≈ 1.80E−5 Pa • s for air at 20°C from Table 1-4, estimate its viscosity at 500°C by (a) The Power-law, (b) The Sutherland law, and (c) The Law of Corresponding
Curve-fit the viscosity data for water in Table A-1 in the form of Andrade’s equation, μ ≈ Aexp (B/T) where T is in °K and A and B are curve-fit constants.
Some experimental values of μ for argon gas at 1 atm are as follows: T, °K: 300 400 500 600 700 800 μ, kg/m • s: 2.27E–5 2.85E–5 3.37E–5 3.83E–5 4.25E–5
Some experimental values of μ of helium at 1 atm are as follows: T, °K: 200 400 600 800 1000 1200 μ, kg/m ⋅ s: 1.50E–5 2.43E–5 3.20E–5 3.88E–5
Yaws et al. [ref. 34] suggest a 4-constant curve-fit formula for liquid viscosity: log10 μ≈A+B/T+CT+DT 2, with T in absolute unitsv (a) Can this formula be criticized on dimensional
The viscosity of SAE 30 oil may vary considerably, according to industry-agreed specifications [SAE Handbook, Ref. 26]. Comment on the following data and fit the data to Andrade’s equation from
A block of weight W slides down an inclined plane on a thin film of oil, as in Fig. P1.45 at right, the film contact area is A and its thickness h. Assuming a linear velocity distribution in the
Find the terminal velocity in Prob. P1.45 if m = 6 kg, A = 35 cm2, θ = 15°, and the film is 1-mm thick SAE 30 oil at 20°C.
A shaft 6.00 cm in diameter and 40 cm long is pulled steadily at V = 0.4 m/s through a sleeve 6.02 cm in diameter. The clearance is filled with oil, ν = 0.003 m2/s and SG = 0.88. Estimate the
A thin moving plate is separated from two fixed plates by two fluids of unequal viscosity and unequal spacing, as shown below. The contact area is A. Determine(a) The force required, and(b) Is there
An amazing number of commercial and laboratory devices have been developed to measure fluid viscosity, as described in Ref. 27. Consider a concentric shaft, as in Prob. 1.47, but now fixed axially
A simple viscometer measures the time t for a solid sphere to fall a distance L through a test fluid of density ρ. The fluid viscosity μ is then given by μ ≈ WnetI /3π DL
Use the theory of Prob. 1.50 for a shaft 8 cm long, rotating at 1200 r/min, with ri = 2.00 cm and ro = 2.05 cm. The measured torque is M = 0.293 N•m. What is the fluid viscosity? If the
The total error is dominated by the 8% error in the estimate of clearance, (Ro €“ Ri). We might state the experimental result for viscosity as the belt in Fig. P1.52 moves at steady
A solid cone of base ro and initial angular velocity ω o is rotating inside a conical seat. Neglect air drag and derive a formula for the cone’s angular velocity ω (t) if there is no
A disk of radius R rotates at angular velocity Ω inside an oil container of viscosity μ, as in Fig. P1.54. Assuming a linear velocity profile and neglecting shear on the outer disk edges,
Apply the rotating-disk viscometer of Prob. 1.54, to the particular case R = 5 cm, h = 1 mm, rotation rate 900 rev/min, measured torque M = 0.537 N•m. What is the fluid viscosity? If each parameter
For the cone-plate viscometer in Fig P1.56, the angle is very small, and the gap is filled with test liquid μ. Assuming a linear velocity profile, derive a formula for the viscosity μ in terms
Apply the cone-plate viscometer of Prob. 1.56 above to the special case R = 6 cm, θ = 3°, M = 0.157 N ⋅ m, and a rotation rate of 600 rev/min. What is the fluid viscosity? If each
The laminar-pipe-flow example of Prob. 1.14 leads to a capillary viscometer [27], using the formula μ = π ro 4Δp/ (8LQ). Given ro = 2 mm and L = 25 cm. The data are Q, m3/hr: 0.36
A solid cylinder of diameter D, length L, density ρ s falls due to gravity inside a tube of diameter Do. The clearance, (Do −D)
A highly viscous (non-turbulent) fluid fills the gap between two long concentric cylinders of radii a and b > a, respectively. If the outer cylinder is fixed and the inner cylinder moves steadily at
An air-hockey puck has m = 50 g and D = 9 cm. When placed on a 20°C air table, the blower forms a 0.12-mm-thick air film under the puck. The puck is struck with an initial velocity of 10 m/s. How
The hydrogen bubbles in Fig. 1.13 have D ≈ 0.01 mm. Assume an “air-water” interface at 30°C. What is the excess pressure within the bubble?
Derive Eq. (1.37) by making a force balance on the fluid interface in Fig. 1.9c.
A shower head emits a cylindrical jet of clean 20°C water into air. The pressure inside the jet is approximately 200 Pa greater than the air pressure. Estimate the jet diameter, in mm.
The system in Fig P1.65 is used to estimate the pressure p1 in the tank by measuring the 15-cm height of liquid in the 1-mm-diameter tube. The fluid is at 60°C. Calculate the true fluid height in
A thin wire ring, 3 cm in diameter, is lifted from a water surface at 20°C. What is the lift force required? Is this a good method? Suggest a ring material.
A vertical concentric annulus, with outer radius ro and inner radius ri, is lowered into fluid of surface tension Y and contact angle θ90. Derive an expression
Analyze the shape η(x) of the water-air interface near a wall, as shown. Assume small slope, R−1 ≈ d2η/dx2. The pressure difference across the interface is Δp ≈
A solid cylindrical needle of diameter d, length L, and density ρ n may €œfloat€ on a liquid surface. Neglect buoyancy and assume a contact angle of 0°. Calculate the
Derive an expression for the capillary height change h, as shown, for a fluid of surface tension Y and contact angle θ between two parallel plates W apart. Evaluate h for water at 20°C if W
A soap bubble of diameter D1 coalesces with another bubble of diameter D2 to form a single bubble D3 with the same amount of air. For an isothermal process, express D3 as a function of D1, D2, patm,
Early mountaineers boiled water to estimate their altitude. If they reach the top and find that water boils at 84°C, approximately how high is the mountain?
A small submersible moves at velocity V in 20°C water at 2-m depth, where ambient pressure is 131 kPa. Its critical cavitation number is Ca ≈ 0.25. At what velocity will cavitation bubbles
Oil, with a vapor pressure of 20 kPa, is delivered through a pipeline by equally spaced pumps, each of which increases the oil pressure by 1.3 MPa. Friction losses in the pipe are 150 Pa per meter of
A propeller is tested in a water tunnel at 20°C (similar to Fig. 1.12a). The lowest pressure on the body can be estimated by a Bernoulli-type relation, pmin = po − ρV2/2, where po = 1.5
Estimate the speed of sound of steam at 200°C and 400 kPa, (a) By an ideal-gas approximation (Table A.4); and (b) Using EES (or the Steam Tables) and making small isentropic changes in pressure
The density of gasoline varies with pressure approximately as follows: p, atm: 1 500 1000 1500 ρ, lbm/ft3: 42.45 44.85 46.60 47.98 Estimate (a) Its speed of sound, and (b)
Sir Isaac Newton measured sound speed by timing the difference between seeing a cannon’s puff of smoke and hearing its boom. If the cannon is on a mountain 5.2 miles away, estimate the air
Even a tiny amount of dissolved gas can drastically change the speed of sound of a gas-liquid mixture. By estimating the pressure-volume change of the mixture, Olson [40] gives the following
A two-dimensional steady velocity field is given by u = x2 – y2, v = –2xy. Find the streamline pattern and sketch a few lines. [Hint: The differential equation is exact.]
Repeat Ex. 1.13 by letting the velocity components increase linearly with time: V=Kxti−Kytj+0k
A velocity field is given by u = V cosθ, v = V sinθ, and w = 0, where V and θ are constants. Find an expression for the streamlines of this flow.
A two-dimensional unsteady velocity field is given by u = x (1 + 2t), v = y. Find the time-varying streamlines which pass through some reference point (xo, yo). Sketch some.
Modify Prob. 1.83 to find the equation of the pathline which passes through the point (xo, yo) at t = 0. Sketch this pathline.
Report to the class on the achievements of Evangelista Torricelli?
Report to the class on the achievements of Henri de Pitot?
Report to the class on the achievements of Antoine Chézy?
Report to the class on the achievements of Gotthilf Heinrich Ludwig Hagen?
Report to the class on the achievements of George Gabriel Stokes?
Report to the class on the achievements of Julius Weisbach?
Report to the class on the achievements of Moritz Weber?
Report to the class on the achievements of Theodor von Kármán?
Report to the class on the achievements of Ludwig Prandtl?
Report to the class on the achievements of Paul Richard Heinrich Blasius?
Report to the class on the achievements of John William Strutt, Lord Rayleigh?
Report to the class on the achievements of Osborne Reynolds?
Report to the class on the achievements of Daniel Bernoulli.?
Report to the class on the achievements of Leonhard Euler?
For the two-dimensional stress field in Fig. P2.1, letσ =3000 psf σyy=2000 psfσ xy = 500 psfFind the shear and normal stresses on plane AA cutting through at 30°.
For the stress field of Fig P2.1, change the known data to σxx = 2000 psf, σyy = 3000 psf, and σn (AA) = 2500 psf. Compute σxy and the shear stress on plane AA.
A vertical clean glass piezometer tube has an inside diameter of 1 mm. When a pressure is applied, water at 20°C rises into the tube to a height of 25 cm. After correcting for surface tension,
Given a flow pattern with isobars po − Bz + Cx2 = constant. Find an expression x = fcn (z) for the family of lines everywhere parallel to the local pressure gradient ∇p.
Atlanta, Georgia, has an average altitude of 1100 ft. On a U.S. standard day, pressure gage A reads 93 kPa and gage B reads 105 kPa. Express these readings in gage or vacuum pressure, whichever is
Express standard atmospheric pressure as a head, h = p/ρ g, in (a) feet of ethylene glycol; (b) inches of mercury; (c) meters of water; and (d) mm of methanol.
The deepest point in the ocean is 11034 m in the Mariana Tranch in the Pacific. At this depth γseawater ≈ 10520 N/m3, estimate the absolute pressure at this depth.
A diamond mine is 2 miles below sea level. (a) Estimate the air pressure at this depth. (b) If a barometer, accurate to 1 mm of mercury, is carried into this mine, how accurately can it estimate
Integrate the hydrostatic relation by assuming that the isentropic bulk modulus, B = ρ(∂p/∂ρ)s, is constant. Apply your result to the Mariana Trench, Prob. 2.7.
A closed tank contains 1.5 m of SAE 30 oil, 1 m of water, 20 cm of mercury, and an air space on top, all at 20°C. If pbottom = 60 kPa, what is the pressure in the air space?
In Fig P2.11, sensor A reads 1.5 kPa (gage). All fluids are at 20°C. Determine the elevations Z in meters of the liquid levels in the open piezometer tubes B and C.
In Fig. P2.12 the tank contains water and immiscible oil at 20°C. What is h in centimeters if the density of the oil is 898 kg/m3?
In Fig P2.13 the 20°C water and gasoline are open to the atmosphere and are at the same elevation. What is the height h in the third liquid?
The closed tank in Fig P2.14 is at 20°C. If the pressure at A is 95 kPa absolute, determine p at B (absolute). What percent error do you make by neglecting the specific weight of the air?
In Fig P2.15 all fluids are at 20°C. Gage A reads 15 lbf/in2 absolute and gage B reads 1.25 lbf/in2 less than gage C. Compute (a) The specific weight of the oil; and (b) The actual reading of
Suppose one wishes to construct a barometer using ethanol at 20°C (Table A-3) as the working fluid. Account for the equilibrium vapor pressure in your calculations and determine how high such a
All fluids in Fig P2.17 are at 20°C. If p = 1900 psf at point A, determine the pressures at B, C, and D in psf.
All fluids in Fig P2.18 are at 20°C. If atmospheric pressure = 101.33 kPa and the bottom pressure is 242 kPa absolute, what is the specific gravity of fluid X?

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