THINKING LIKE AN ENGINEER W/ACCESS
17th Edition
ISBN: 9781323522127
Author: STEPHAN
Publisher: PEARSON C
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Chapter 7, Problem 28RQ
Ideal gas" constant (R) [atm L/(mol K )]
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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 7 Solutions
THINKING LIKE AN ENGINEER W/ACCESS
Ch. 7.1 - Express the following values using an appropriate...Ch. 7.1 - Indicate if the following units are correctly...Ch. 7.3 - Comprehension Check 7-3 The highest mountain in...Ch. 7.3 - To be considered a full-time employee, companies...Ch. 7.4 - In January 2008, Scientific American reported that...Ch. 7.4 - Officially, a hurricane is a tropical storm with...Ch. 7.4 - Many toilets in commercial establishments have a...Ch. 7.5 - Comprehension Check 7-8 A hogshead is a unit of...Ch. 7.5 - Comprehension Check 7-9 In NCAA basketball, a...Ch. 7.5 - A boat is traveling at 20 knots. Convert this...
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