Fluid Mechanics, 8 Ed
Fluid Mechanics, 8 Ed
8th Edition
ISBN: 9789385965494
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 6, Problem 6.88P
To determine

Estimate the appropriate number of passage.

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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 6 Solutions

Fluid Mechanics, 8 Ed

Ch. 6 - Water at 20°C flows upward at 4 m/s in a...Ch. 6 - Prob. 6.12PCh. 6 - Prob. 6.13PCh. 6 - Prob. 6.14PCh. 6 - Prob. 6.15PCh. 6 - Prob. 6.16PCh. 6 - P6.17 A capillary viscometer measures the time...Ch. 6 - P6.18 SAE 50W oil at 20°C flows from one tank to...Ch. 6 - Prob. 6.19PCh. 6 - The oil tanks in Tinyland are only 160 cm high,...Ch. 6 - Prob. 6.21PCh. 6 - Prob. 6.22PCh. 6 - Prob. 6.23PCh. 6 - Prob. 6.24PCh. 6 - Prob. 6.25PCh. 6 - Prob. 6.26PCh. 6 - Let us attack Prob. P6.25 in symbolic fashion,...Ch. 6 - Prob. 6.28PCh. 6 - Prob. 6.29PCh. 6 - Prob. 6.30PCh. 6 - A laminar flow element (LFE) (Meriam Instrument...Ch. 6 - SAE 30 oil at 20°C flows in the 3-cm.diametcr pipe...Ch. 6 - Prob. 6.33PCh. 6 - Prob. 6.34PCh. 6 - In the overlap layer of Fig. 6.9a, turbulent shear...Ch. 6 - Prob. 6.36PCh. 6 - Prob. 6.37PCh. 6 - Prob. 6.38PCh. 6 - Prob. 6.39PCh. 6 - Prob. 6.40PCh. 6 - P6.41 Two reservoirs, which differ in surface...Ch. 6 - Prob. 6.42PCh. 6 - Prob. 6.43PCh. 6 - P6.44 Mercury at 20°C flows through 4 m of...Ch. 6 - P6.45 Oil, SG = 0.88 and v = 4 E-5 m2/s, flows at...Ch. 6 - Prob. 6.46PCh. 6 - Prob. 6.47PCh. 6 - Prob. 6.48PCh. 6 - Prob. 6.49PCh. 6 - Prob. 6.50PCh. 6 - Prob. 6.51PCh. 6 - Prob. 6.52PCh. 6 - Water at 2OC flows by gravity through a smooth...Ch. 6 - A swimming pool W by Y by h deep is to be emptied...Ch. 6 - Prob. 6.55PCh. 6 - Prob. 6.56PCh. 6 - Prob. 6.57PCh. 6 - Prob. 6.58PCh. 6 - P6.59 The following data were obtained for flow of...Ch. 6 - Prob. 6.60PCh. 6 - Prob. 6.61PCh. 6 - Water at 20°C is to be pumped through 2000 ft of...Ch. 6 - Prob. 6.63PCh. 6 - Prob. 6.64PCh. 6 - Prob. 6.65PCh. 6 - Prob. 6.66PCh. 6 - Prob. 6.67PCh. 6 - Prob. 6.68PCh. 6 - P6.69 For Prob. P6.62 suppose the only pump...Ch. 6 - Prob. 6.70PCh. 6 - Prob. 6.71PCh. 6 - Prob. 6.72PCh. 6 - Prob. 6.73PCh. 6 - Prob. 6.74PCh. 6 - Prob. 6.75PCh. 6 - P6.76 The small turbine in Fig. P6.76 extracts 400...Ch. 6 - Prob. 6.77PCh. 6 - Prob. 6.78PCh. 6 - Prob. 6.79PCh. 6 - The head-versus-flow-rate characteristics of a...Ch. 6 - Prob. 6.81PCh. 6 - Prob. 6.82PCh. 6 - Prob. 6.83PCh. 6 - Prob. 6.84PCh. 6 - Prob. 6.85PCh. 6 - SAE 10 oil at 20°C flows at an average velocity of...Ch. 6 - A commercial steel annulus 40 ft long, with a = 1...Ch. 6 - Prob. 6.88PCh. 6 - Prob. 6.89PCh. 6 - Prob. 6.90PCh. 6 - Prob. 6.91PCh. 6 - Prob. 6.92PCh. 6 - Prob. 6.93PCh. 6 - Prob. 6.94PCh. 6 - Prob. 6.95PCh. 6 - Prob. 6.96PCh. 6 - Prob. 6.97PCh. 6 - Prob. 6.98PCh. 6 - Prob. 6.99PCh. 6 - Prob. 6.100PCh. 6 - Prob. 6.101PCh. 6 - *P6.102 A 70 percent efficient pump delivers water...Ch. 6 - Prob. 6.103PCh. 6 - Prob. 6.104PCh. 6 - Prob. 6.105PCh. 6 - Prob. 6.106PCh. 6 - Prob. 6.107PCh. 6 - P6.108 The water pump in Fig. P6.108 maintains a...Ch. 6 - In Fig. P6.109 there are 125 ft of 2-in pipe, 75...Ch. 6 - In Fig. P6.110 the pipe entrance is sharp-edged....Ch. 6 - For the parallel-pipe system of Fig. P6.111, each...Ch. 6 - Prob. 6.112PCh. 6 - Prob. 6.113PCh. 6 - Prob. 6.114PCh. 6 - Prob. 6.115PCh. 6 - Prob. 6.116PCh. 6 - Prob. 6.117PCh. 6 - Prob. 6.118PCh. 6 - Prob. 6.119PCh. 6 - Prob. 6.120PCh. 6 - Prob. 6.121PCh. 6 - Prob. 6.122PCh. 6 - Prob. 6.123PCh. 6 - Prob. 6.124PCh. 6 - Prob. 6.125PCh. 6 - Prob. 6.126PCh. 6 - Prob. 6.127PCh. 6 - In the five-pipe horizontal network of Fig....Ch. 6 - Prob. 6.129PCh. 6 - Prob. 6.130PCh. 6 - Prob. 6.131PCh. 6 - Prob. 6.132PCh. 6 - Prob. 6.133PCh. 6 - Prob. 6.134PCh. 6 - An airplane uses a pitot-static tube as a...Ch. 6 - Prob. 6.136PCh. 6 - Prob. 6.137PCh. 6 - Prob. 6.138PCh. 6 - P6.139 Professor Walter Tunnel needs to measure...Ch. 6 - Prob. 6.140PCh. 6 - Prob. 6.141PCh. 6 - Prob. 6.142PCh. 6 - Prob. 6.143PCh. 6 - Prob. 6.144PCh. 6 - Prob. 6.145PCh. 6 - Prob. 6.146PCh. 6 - Prob. 6.147PCh. 6 - Prob. 6.148PCh. 6 - Prob. 6.149PCh. 6 - Prob. 6.150PCh. 6 - Prob. 6.151PCh. 6 - Prob. 6.152PCh. 6 - Prob. 6.153PCh. 6 - Prob. 6.154PCh. 6 - Prob. 6.155PCh. 6 - Prob. 6.156PCh. 6 - Prob. 6.157PCh. 6 - Prob. 6.158PCh. 6 - Prob. 6.159PCh. 6 - Prob. 6.160PCh. 6 - Prob. 6.161PCh. 6 - Prob. 6.162PCh. 6 - Prob. 6.163PCh. 6 - Prob. 6.1WPCh. 6 - Prob. 6.2WPCh. 6 - Prob. 6.3WPCh. 6 - Prob. 6.4WPCh. 6 - Prob. 6.1FEEPCh. 6 - Prob. 6.2FEEPCh. 6 - Prob. 6.3FEEPCh. 6 - Prob. 6.4FEEPCh. 6 - Prob. 6.5FEEPCh. 6 - Prob. 6.6FEEPCh. 6 - Prob. 6.7FEEPCh. 6 - Prob. 6.8FEEPCh. 6 - Prob. 6.9FEEPCh. 6 - Prob. 6.10FEEPCh. 6 - Prob. 6.11FEEPCh. 6 - Prob. 6.12FEEPCh. 6 - Prob. 6.13FEEPCh. 6 - Prob. 6.14FEEPCh. 6 - Prob. 6.15FEEPCh. 6 - Prob. 6.1CPCh. 6 - Prob. 6.2CPCh. 6 - Prob. 6.3CPCh. 6 - Prob. 6.4CPCh. 6 - Prob. 6.5CPCh. 6 - Prob. 6.6CPCh. 6 - Prob. 6.7CPCh. 6 - Prob. 6.8CPCh. 6 - Prob. 6.9CPCh. 6 - A hydroponic garden uses the 10-m-long...Ch. 6 - It is desired to design a pump-piping system to...
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