Fluid Mechanics, 8 Ed
8th Edition
ISBN: 9789385965494
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 2, Problem 2.100P
Pressurized water fills the tank in Fig, P2.100. Compute the net hydrostatic force on the conical surface ABC.
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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 2 Solutions
Fluid Mechanics, 8 Ed
Ch. 2 - Prob. 2.1PCh. 2 - For the two-dimensional stress field shown in Fig....Ch. 2 - A vertical, clean, glass piezometer tube has an...Ch. 2 - P2.4 Pressure gages, such as the bourdon gage in...Ch. 2 - Quito, Ecuador, has an average altitude of 9350...Ch. 2 - Prob. 2.6PCh. 2 - La Paz, Bolivia, is at an altitude of...Ch. 2 - P2.8 Suppose, which is possible, that there is a...Ch. 2 - A storage tank, 26 ft in diameter and 36 ft high,...Ch. 2 - P2.10 A large open tank is open to sea-level...
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - The system in Fig. P2.18 is at 20°C. If...Ch. 2 - Prob. 2.19PCh. 2 - The hydraulic jack in Fig. P2.20 is filled with...Ch. 2 - At 20°C gage A reads 350 kPa absolute. What is the...Ch. 2 - The fuel gage for a gasoline tank in a car reads...Ch. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26PCh. 2 - P2.27 Conduct an experiment to illustrate...Ch. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - Prob. 2.30PCh. 2 - In Fig. P2.31 all fluids arc at 20°C. Determine...Ch. 2 - For the inverted manometer of Fig. P2.32, all...Ch. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Water flows upward in a pipe slanted at 30°, as in...Ch. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - If the pressure in container A in Fig. P2.38 is...Ch. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - P2.41 The system in Fig. P2.41 is at 20°C....Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - In Fig. P2.46 both ends of the manometer are open...Ch. 2 - Prob. 2.47PCh. 2 - The system in Fig. P2.4H is open to 1 atm on the...Ch. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Gate AB in Fig. P2.51 is 1.2 m long and 0.8 m into...Ch. 2 - Example 2.5 calculated the force on plate AB and...Ch. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Gate AB in Fig. P2.55 is 5 ft wide into the paper,...Ch. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 2 - Gate AB has length L and width b into the paper,...Ch. 2 - Prob. 2.60PCh. 2 - Gale AB in Fig. P2.61 is homogeneous mass of 180...Ch. 2 - Gale AB in Fig. P2.62 is 15 ft long and 8 ft wide...Ch. 2 - The tank in Fig. P2.63 has a 4-cm-diameter plug at...Ch. 2 - Prob. 2.64PCh. 2 - Prob. 2.65PCh. 2 - Prob. 2.66PCh. 2 - Prob. 2.67PCh. 2 - P2.68 Isosceles triangle gate AB in Fig. P2.68 is...Ch. 2 - P2.69 Consider the slanted plate AB of length L in...Ch. 2 - Prob. 2.70PCh. 2 - Prob. 2.71PCh. 2 - Prob. 2.72PCh. 2 - P2.73 Gate AB is 5 ft wide into the paper and...Ch. 2 - Prob. 2.74PCh. 2 - Prob. 2.75PCh. 2 - Prob. 2.76PCh. 2 - P2.77 The circular gate ABC in Fig. P2.77 has l-m...Ch. 2 - Prob. 2.78PCh. 2 - Prob. 2.79PCh. 2 - Prob. 2.80PCh. 2 - Prob. 2.81PCh. 2 - Prob. 2.82PCh. 2 - Prob. 2.83PCh. 2 - Prob. 2.84PCh. 2 - P2.85 Compute the horizontal and vertical...Ch. 2 - Prob. 2.86PCh. 2 - The bottle of champagne (SG = 0.96) in Fig. P2.87...Ch. 2 - Prob. 2.88PCh. 2 - Prob. 2.89PCh. 2 - The lank in Fig. P2.90 is 120 cm long into the...Ch. 2 - The hemispherical dome in Fig. P2.91 weighs 30 kN...Ch. 2 - A 4-m-diameter water lank consists of two half...Ch. 2 - Prob. 2.93PCh. 2 - Prob. 2.94PCh. 2 - Prob. 2.95PCh. 2 - Prob. 2.96PCh. 2 - Prob. 2.97PCh. 2 - Prob. 2.98PCh. 2 - The mega-magnum cylinder in Fig. P2.99 has a...Ch. 2 - Pressurized water fills the tank in Fig, P2.100....Ch. 2 - Prob. 2.101PCh. 2 - Prob. 2.102PCh. 2 - Prob. 2.103PCh. 2 - Prob. 2.104PCh. 2 - P2.105 it is said that Archimedes discovered the...Ch. 2 - Prob. 2.106PCh. 2 - Prob. 2.107PCh. 2 - P2.108 A 7-cm-diameter solid aluminum ball (SG =...Ch. 2 - Prob. 2.109PCh. 2 - Prob. 2.110PCh. 2 - P2.111 A solid wooden cone (SG = 0.729) floats in...Ch. 2 - The uniform 5-m-long round wooden rod in Fig....Ch. 2 - Prob. 2.113PCh. 2 - Prob. 2.114PCh. 2 - P2.115 The 2-in by 2-in by 12-ft spar buoy from...Ch. 2 - Prob. 2.116PCh. 2 - The solid sphere in Fig. P2.117 is iron ( SG7.9 )....Ch. 2 - Prob. 2.118PCh. 2 - Prob. 2.119PCh. 2 - Prob. 2.120PCh. 2 - Prob. 2.121PCh. 2 - Prob. 2.122PCh. 2 - Prob. 2.123PCh. 2 - Prob. 2.124PCh. 2 - Prob. 2.125PCh. 2 - Prob. 2.126PCh. 2 - Prob. 2.127PCh. 2 - Prob. 2.128PCh. 2 - Prob. 2.129PCh. 2 - Prob. 2.130PCh. 2 - Prob. 2.131PCh. 2 - Prob. 2.132PCh. 2 - Prob. 2.133PCh. 2 - Prob. 2.134PCh. 2 - P2.135 Consider a homogeneous right circular...Ch. 2 - Prob. 2.136PCh. 2 - Prob. 2.137PCh. 2 - Prob. 2.138PCh. 2 - P2.139 The tank of liquid in Kg. P2.139...Ch. 2 - P2.140 The U-tube in Fig, P2.140 is moving to the...Ch. 2 - The same tank from Prob. P2.139 is now moving with...Ch. 2 - Prob. 2.142PCh. 2 - Prob. 2.143PCh. 2 - Prob. 2.144PCh. 2 - A fish tank 14 in deep by 16 by 27 in is to be...Ch. 2 - Prob. 2.146PCh. 2 - Prob. 2.147PCh. 2 - Prob. 2.148PCh. 2 - Prob. 2.149PCh. 2 - Prob. 2.150PCh. 2 - Prob. 2.151PCh. 2 - P2.152 A 16-cm-diamctcr open cylinder 27 cm high...Ch. 2 - Prob. 2.153PCh. 2 - Prob. 2.154PCh. 2 - Prob. 2.155PCh. 2 - Prob. 2.156PCh. 2 - Prob. 2.157PCh. 2 - Prob. 2.158PCh. 2 - Prob. 2.159PCh. 2 - Prob. 2.160PCh. 2 - Prob. 2.161PCh. 2 - Prob. 2.1WPCh. 2 - Prob. 2.2WPCh. 2 - W2.3 Consider a submerged curved surface that...Ch. 2 - Prob. 2.4WPCh. 2 - Prob. 2.5WPCh. 2 - W2.6 Consider a balloon of mass m floating...Ch. 2 - Prob. 2.7WPCh. 2 - W2.8 Repeat your analysis of Prob. W2.7 to let the...Ch. 2 - Prob. 2.9WPCh. 2 - Prob. 2.1FEEPCh. 2 - FE2.2 On a sea-level standard day, a pressure...Ch. 2 - Prob. 2.3FEEPCh. 2 - In Fig, FE2,3, if the oil in region B has SG = 0,8...Ch. 2 - Prob. 2.5FEEPCh. 2 - Prob. 2.6FEEPCh. 2 - Prob. 2.7FEEPCh. 2 - Prob. 2.8FEEPCh. 2 - Prob. 2.9FEEPCh. 2 - Prob. 2.10FEEPCh. 2 - Prob. 2.1CPCh. 2 - Prob. 2.2CPCh. 2 - Prob. 2.3CPCh. 2 - Prob. 2.4CPCh. 2 - Prob. 2.5CPCh. 2 - Prob. 2.6CPCh. 2 - Prob. 2.7CPCh. 2 - Prob. 2.8CPCh. 2 - Prob. 2.9CPCh. 2 - Prob. 2.1DPCh. 2 - Prob. 2.2DPCh. 2 - The Leary Engineering Company (see Popular...
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