EBK MUNSON, YOUNG AND OKIISHI'S FUNDAME
8th Edition
ISBN: 9781119547990
Author: HOCHSTEIN
Publisher: JOHN WILEY+SONS INC.
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Chapter 10.4, Problem 37P
To determine
The percentage reduction of flow rate.
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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 10 Solutions
EBK MUNSON, YOUNG AND OKIISHI'S FUNDAME
Ch. 10.2 - Prob. 1PCh. 10.2 - The flowrate per unit width in a wide channel is q...Ch. 10.2 - A rectangular channel 3 m wide carries 10 m3/s at...Ch. 10.2 - Prob. 4PCh. 10.2 - Prob. 5PCh. 10.2 - Prob. 6PCh. 10.2 - Prob. 7PCh. 10.2 - Prob. 8PCh. 10.2 - Prob. 9PCh. 10.2 - Prob. 10P
Ch. 10.2 - Prob. 11PCh. 10.3 - Water flows in a 10-m-wide open channel with a...Ch. 10.3 - Water flows in a 10-ft-wide rectangular channel...Ch. 10.3 - Water flows in a rectangular channel at a rate of...Ch. 10.3 - Water flows in a 5-ft-wide rectangular channel...Ch. 10.3 - Water flows over the bump in the bottom of the...Ch. 10.3 - Water in a rectangular channel flows into a...Ch. 10.3 - A channel has a rectangular cross section, a width...Ch. 10.3 - Prob. 19PCh. 10.3 - Prob. 20PCh. 10.3 - Prob. 23PCh. 10.3 - Prob. 24PCh. 10.3 - Prob. 25PCh. 10.3 - Prob. 26PCh. 10.3 - Prob. 27PCh. 10.3 - Prob. 28PCh. 10.3 - Prob. 29PCh. 10.4 - Water flows in a 5-m-wide channel with a speed...Ch. 10.4 - The following data are taken from measurements on...Ch. 10.4 - Prob. 32PCh. 10.4 - The following data are obtained for a particular...Ch. 10.4 - Prob. 34PCh. 10.4 - Prob. 35PCh. 10.4 - A 2-m-diameter pipe made of finished concrete lies...Ch. 10.4 - By what percent is the flowrate reduced in the...Ch. 10.4 - Prob. 38PCh. 10.4 - Prob. 39PCh. 10.4 - Prob. 40PCh. 10.4 - A trapezoidal channel with a bottom width of 3.0 m...Ch. 10.4 -
Water flows in a 2-m-diameter finished concrete...Ch. 10.4 - A round concrete storm sewer pipe used to carry...Ch. 10.4 - Find the discharge per unit width for a wide...Ch. 10.4 - Water flows down a wide rectangular channel having...Ch. 10.4 - Prob. 46PCh. 10.4 - Prob. 47PCh. 10.4 - Prob. 48PCh. 10.4 - Determine the flowrate for the symmetrical channel...Ch. 10.4 - (See The Wide World of Fluids article titled “Done...Ch. 10.4 - Prob. 51PCh. 10.4 - Prob. 52PCh. 10.4 - Prob. 53PCh. 10.4 - Prob. 54PCh. 10.4 - Prob. 55PCh. 10.4 - Prob. 56PCh. 10.4 - Prob. 57PCh. 10.4 - Prob. 58PCh. 10.4 - Prob. 59PCh. 10.4 - Prob. 60PCh. 10.4 - Prob. 61PCh. 10.4 - Prob. 62PCh. 10.4 - Prob. 63PCh. 10.4 - Water flows 1 m deep in a 2-m-wide finished...Ch. 10.4 - Uniform flow in a sluggish channel having a nearly...Ch. 10.4 - To prevent weeds from growing in a clean...Ch. 10.4 - Prob. 67PCh. 10.4 - Prob. 68PCh. 10.4 - Prob. 69PCh. 10.4 - Prob. 70PCh. 10.5 - Prob. 71PCh. 10.5 - Prob. 72PCh. 10.6 - Water flows upstream of a hydraulic jump with a...Ch. 10.6 - Prob. 75PCh. 10.6 - Prob. 76PCh. 10.6 - Prob. 77PCh. 10.6 - At a given location in a 12-ft-wide rectangular...Ch. 10.6 - Prob. 79PCh. 10.6 - Prob. 80PCh. 10.6 - Prob. 81PCh. 10.6 - A hydraulic engineer wants to analyze steady flow...Ch. 10.6 - Prob. 83PCh. 10.6 - A rectangular sharp-crested weir is used to...Ch. 10.6 - Prob. 85PCh. 10.6 - Prob. 87PCh. 10.6 - Prob. 88PCh. 10.6 - Prob. 89PCh. 10.6 - Prob. 90PCh. 10.6 - Prob. 91PCh. 10.7 - Prob. 1LLPCh. 10.7 - Prob. 2LLPCh. 10.7 - Prob. 3LLP
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