FUNDAMENTALS OF FLUID MECHANICS
8th Edition
ISBN: 9781119571490
Author: GERHART
Publisher: WILEY
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Chapter 6.5, Problem 46P
To determine
The wind speed at different locations of a category five hurricane.
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Question 1
Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
10 kN
X
x=0.0
x=2.0
2.0m
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x)) + 1(x) = 0.
dx
dx
What are the accompanying boundary conditions for this bar?
MacBook Air
a
会
DII
F5
F6
F7
F8
80
F3
F4
0/
20
[8 marksl
8
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Answer B
fem helpUsing the mesh in Figure 2, form the basis functions associated with element 2 and write the FEMapproximation over the element.
Chapter 6 Solutions
FUNDAMENTALS OF FLUID MECHANICS
Ch. 6.1 - Prob. 1PCh. 6.1 - The velocity in a certain flow field is given by...Ch. 6.1 - The flow in the plane two-dimensional channel...Ch. 6.1 - The three components of velocity in a flow field...Ch. 6.1 - Determine an expression for the vorticity of the...Ch. 6.1 - According to Eq. 6.134, the x-velocity in fully...Ch. 6.1 - For a certain incompressible, two-dimensional flow...Ch. 6.1 - An incompressible viscous fluid is placed between...Ch. 6.1 - A viscous fluid is contained in the space between...Ch. 6.1 - ..Air is delivered through a constant-diameter...
Ch. 6.2 - For a certain incompressible flow field it is...Ch. 6.2 - Prob. 12PCh. 6.2 - Prob. 14PCh. 6.2 - For each of the following stream functions, with...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - In a two-dimensional, incompressible flow field,...Ch. 6.2 - The stream function for an incompressible flow...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Consider the incompressible, two-dimensional flow...Ch. 6.3 - A fluid with a density of 2000 kg/m3 flows...Ch. 6.3 - Prob. 24PCh. 6.3 - Prob. 25PCh. 6.4 - The stream function for a given two-dimensional...Ch. 6.4 - Prob. 27PCh. 6.4 - Prob. 28PCh. 6.4 - Prob. 29PCh. 6.4 - The velocity potential for a certain inviscid flow...Ch. 6.4 - Prob. 31PCh. 6.4 - Prob. 32PCh. 6.4 - Prob. 33PCh. 6.4 - Prob. 34PCh. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.5 - Prob. 38PCh. 6.5 - Prob. 39PCh. 6.5 - Water flows through a two-dimensional diffuser...Ch. 6.5 - Prob. 41PCh. 6.5 - Prob. 42PCh. 6.5 - Prob. 43PCh. 6.5 - Prob. 44PCh. 6.5 - Prob. 45PCh. 6.5 - Prob. 46PCh. 6.5 - Consider the flow of a liquid of viscosity μ and...Ch. 6.5 - Prob. 48PCh. 6.5 - Show that the circulation of a free vortex for any...Ch. 6.5 - Prob. 50PCh. 6.6 - Potential flow against a flat plate (Fig. P6.51a)...Ch. 6.6 - Prob. 52PCh. 6.6 - Prob. 53PCh. 6.6 - Prob. 54PCh. 6.6 - Prob. 55PCh. 6.6 - Prob. 56PCh. 6.6 -
A 15-mph wind flows over a Quonset hut having a...Ch. 6.6 - Prob. 58PCh. 6.6 - Prob. 59PCh. 6.6 - Prob. 60PCh. 6.6 - Prob. 61PCh. 6.6 - Prob. 62PCh. 6.6 - The velocity potential for a cylinder (Fig. P6.63)...Ch. 6.6 - (See The Wide World of Fluids article titled “A...Ch. 6.6 - Prob. 65PCh. 6.6 - Air at 25 °C flows normal to the axis of an...Ch. 6.8 - Determine the shearing stress for an...Ch. 6.8 - Prob. 68PCh. 6.8 - The velocity of a fluid particle moving along a...Ch. 6.8 - “Stokes’s first problem” involves the...Ch. 6.9 - Oil (SAE 30) at 15.6 °C flows steadily between...Ch. 6.9 - Prob. 72PCh. 6.9 - Prob. 73PCh. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - (See The Wide World of Fluids article titled “10...Ch. 6.9 - The bearing shown in Fig. P6.76 consists of two...Ch. 6.9 - Prob. 77PCh. 6.9 - Prob. 78PCh. 6.9 - An incompressible, viscous fluid is placed between...Ch. 6.9 - Two immiscible, incompressible, viscous fluids...Ch. 6.9 - Prob. 81PCh. 6.9 - A viscous fluid (specific weight = 80 lb/ft3;...Ch. 6.9 - A flat block is pulled along a horizontal flat...Ch. 6.9 - A viscosity motor/pump is shown in Fig. P6.84. The...Ch. 6.9 - A vertical shaft passes through a bearing and is...Ch. 6.9 - A viscous fluid is contained between two long...Ch. 6.9 - Verify that the momentum correction factor β for...Ch. 6.9 - Verify that the kinetic energy correction factor α...Ch. 6.9 - A simple flow system to be used for steady-flow...Ch. 6.9 - (a) Show that for Poiseuille flow in a tube of...Ch. 6.9 - An infinitely long, solid, vertical cylinder of...Ch. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - A liquid (viscosity = 0.002 N · s/m2; density =...Ch. 6.9 - Fluid with kinematic viscosity ν flows down an...Ch. 6.9 - Blood flows at volume rate Q in a circular tube of...Ch. 6.9 - An incompressible Newtonian fluid flows steadily...Ch. 6.9 - Prob. 97PCh. 6.9 - Prob. 98PCh. 6.9 - Prob. 99PCh. 6.10 - Prob. 101PCh. 6.10 - Prob. 102PCh. 6.11 - Prob. 1LLPCh. 6.11 - Prob. 2LLPCh. 6.11 - Prob. 3LLP
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- answer pleasearrow_forwardFigure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6 0.4- 0.2 0.0 00 -0.2 -0.4 -0.6- 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps.arrow_forwardQuestion 2 Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three consecutive timesteps. 1.0 0.8- 0.6- 0.4- 0.2- 0.0- -0.2- -0.4- -0.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Figure 3: Advection equation, solution for three different timesteps. a) Provide an explanation what conditions and numerical setup could explain the curves. Identify which of the three curves is the first, second and third timestep. b) Consider explicit schemes with central and upwind discretisations. Explain how each of these candidate discretisations could produce the behaviour shown in Figure 3. c) Determine the CFL number that was used in the simulation for each of the candidate schemes for all possible updates. Assume that the timestep and mesh-width used are constant. Read the data to two digits of accuracy from Figure 4 shown at the end of the question, which is an enlarged version of Figure 3. Demonstrate your method and input data for one calculation, but then use a…arrow_forward
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