EBK FLUID MECHANICS
2nd Edition
ISBN: 9780134626055
Author: HIBBELER
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 4, Problem 81P
To determine
The density of the mixture leaving and required average velocity of the mixture from the tank at point C.
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The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
Chapter 4 Solutions
EBK FLUID MECHANICS
Ch. 4 - Prob. 1FPCh. 4 - Air flows through the triangular duct at 0.7 kg/s...Ch. 4 - Water has an average velocity of 8 m/s through the...Ch. 4 - Crude oil flows through the pipe at 0.02 m3/s. If...Ch. 4 - Determine the mass flow of air having a...Ch. 4 - Prob. 6FPCh. 4 - The velocity of the steady flow at A and B is...Ch. 4 - Prob. 8FPCh. 4 - As air exits the tank at 0.05 kg/s, it is mixed...Ch. 4 - Water flows along the triangular channel having...
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Kerosene flows through the nozzle at 0.25 m3/s....Ch. 4 - At two specific instants during a heartbeat, the...Ch. 4 - Prob. 25PCh. 4 - The radius of the circular duct varies as m,...Ch. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - The average velocities of water flowing steadily...Ch. 4 - Air flows through the tapered duct, and during...Ch. 4 - Prob. 31PCh. 4 - Air is pumped into the tank, and at the instant...Ch. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Compressed air is being released from the tank,...Ch. 4 - Prob. 36PCh. 4 - Prob. 38PCh. 4 - Water flows through the pipe at A at 60 kg/s, and...Ch. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Nitrogen flows into the tank at A at VA = 3 m/s,...Ch. 4 - Nitrogen flows into the tank at A at VA = 3 m/s,...Ch. 4 - The flat strip is sprayed with paint using the six...Ch. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Drilling fluid is pumped down through the center...Ch. 4 - Drilling fluid is pumped down through the center...Ch. 4 - Oil flows into the pipe at A with an average...Ch. 4 - The unsteady flow of glycerin is such that at A it...Ch. 4 - The unsteady flow of glycerin is such that at A it...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - The cylindrical plunger traveling at Vp =...Ch. 4 - The cylindrical plunger traveling at Vp =...Ch. 4 - Prob. 56PCh. 4 - The pressure vessel of a nuclear reactor is filled...Ch. 4 - With every breath, air enters the trachea, its...Ch. 4 - A liquid flows through the drainpipe such that it...Ch. 4 - Oil flows into a mixing tank through pipe A with...Ch. 4 - Oil flows into the mixing tank through pipe A at...Ch. 4 - Water flows into the tank through two pipes. At A...Ch. 4 - Gasoline flows into the tank through two pipes. At...Ch. 4 - Prob. 64PCh. 4 - The cylindrical syringe is actuated by applying a...Ch. 4 - Prob. 66PCh. 4 - The tank contains air at a temperature of 20°C and...Ch. 4 - The natural gas (methane) and crude oil mixture...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - Prob. 74PCh. 4 - Kerosene flows into the 4-ft-diameter cylindrical...Ch. 4 - Prob. 76PCh. 4 - Water flows into the cylindrical tank through...Ch. 4 - Water flows into the cylindrical tank through...Ch. 4 - The cylinder is pushed down into the tube at a...Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - Oil flows into the trapezoidal container at a...Ch. 4 - Oil flows into the conical frustum at a constant...Ch. 4 - Water in the triangular trough is at a depth of y...Ch. 4 - Prob. 88PCh. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Hydrogen is pumped into the closed cylindrical...Ch. 4 - Hydrogen is pumped into the closed cylindrical...Ch. 4 - Prob. 94PCh. 4 - A part is manufactured by placing molten plastic...
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