Applied Fluid Mechanics
7th Edition
ISBN: 9780133414622
Author: UNTENER
Publisher: YUZU
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Chapter 11, Problem 11.41PP
Repeat Problem 11.38, but replace the globe valve with a butterfly valve and use a DN
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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 11 Solutions
Applied Fluid Mechanics
Ch. 11 - Water at 10C flows from a large reservoir at the...Ch. 11 - For the system shown in Fig. 11.14, kerosene (...Ch. 11 - Figure 11.15 shows a portion of a hydraulic...Ch. 11 - Figure 11.16 shows part of a large hydraulic...Ch. 11 - Oil is flowing at the rate of 0.015m3/s in the...Ch. 11 - For the system shown in Fig. 11.18, calculate the...Ch. 11 - A liquid refrigerant flows through the system,...Ch. 11 - Water at 100F is flowing in a 4-in Schedule 80...Ch. 11 - A hydraulic oil is flowing in a drawn steel...Ch. 11 - In a processing plant, ethylene glycol at 77F is...
Ch. 11 - Water at 15C is flowing downward in a vertical...Ch. 11 - Turpentine at 77F is flowing from A to B in a 3...Ch. 11 - ]11.13 A device designed to allow cleaning of...Ch. 11 - Kerosene at 25C is flowing in the system shown in...Ch. 11 - Water at 40C is flowing from A to B through the...Ch. 11 - Oil with a specific gravity of 0.93 and a dynamic...Ch. 11 - Determine the required size of new Schedule 80...Ch. 11 - What size of standard hydraulic copper tube from...Ch. 11 - Water at 60F is to flow by gravity between two...Ch. 11 - The tank shown in Fig. 11.24 is to be drained to a...Ch. 11 - Figure 11.25 depicts gasoline flowing from a...Ch. 11 - For the system in Fig. 11.26, compute the pressure...Ch. 11 - For the system in Fig. 11.26, compute the total...Ch. 11 - For the system in Fig. 11.26 specify the size of...Ch. 11 - A manufacturer of spray nozzles specifies that the...Ch. 11 - Specify the size of new Schedule 40 steel pipe...Ch. 11 - Refer to Fig. 11.27. Water at 80C is being pumped...Ch. 11 - For the system shown in Fig. 11.27 and analyzed in...Ch. 11 - In a water pollution control project, the polluted...Ch. 11 - Repeat Problem 11.29, but use a 3-in Schedule 40...Ch. 11 - Water at 10C is being delivered to a tank on the...Ch. 11 - If the pressure at point A in Fig. 11.29 is 300...Ch. 11 - Change the design of the system in Fig. 11.29 to...Ch. 11 - It is desired to deliver 250 gal/min of ethyl...Ch. 11 - For the system shown in Fig. 11.30, compute the...Ch. 11 - Repeat Problem 11.35, but consider the valve to be...Ch. 11 - Repeat Problem 11.35, but consider the valve to be...Ch. 11 - Figure 11.31 depicts a DN 100 Schedule 40 steel...Ch. 11 - Repeat Problem 11.38 but replace the globe valve...Ch. 11 - Repeat Problem 11.38 but use a DN 125 Schedule 40...Ch. 11 - Repeat Problem 11.38, but replace the globe valve...Ch. 11 - It is desired to drive a small,...Ch. 11 - Figure 11.32 shows a pipe delivering water to the...Ch. 11 - Repeat Problem 11.43, except consider that there...Ch. 11 - A sump pump in a commercial building sits in a...Ch. 11 - For the system designed in Problem 11.45, compute...Ch. 11 - Figure 11.33 shows a part of a chemical processing...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - Analyze the system shown in Fig. 11.11 with...Ch. 11 - Create a program or a spreadsheet for analyzing...Ch. 11 - Create a program or a spreadsheet for determining...
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