Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 8, Problem 8.50P
It is desired to simulate flow past a two-dimensional ridge or bump by using a streamline that passes above the flow over a cylinder, as in Fig. P8.50. The bump is to be a/2 high, where a is the cylinder radius. What is the elevation h of this streamline? What is Umax on the bump compared with stream velocity U?
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Q.4
A steady, uniform-density, 2-D flow is to be calculated on the square grid shown below.
The boundary velocities are given as; v₁ =30, V = 40,uc=100, u = 50, u = 200,
u, = 210, V = 0 and v₁ = 20. Among these numbers, there is some doubt about
correctness of the value of u,. If all other numbers are correct, what should be the correct
value of u,?
The internal velocities are governed by simplified momentum equations given by:
up = 70+0.5 (P₁-P₂)
u, = 10 +0.7 (P3-P4)
V =30+0.5(P3-P₁)
VG =18+0.8(P₁-P₂)
Write discretized continuity equation for each control volume. Derive the discretization
equation for pressure by substituting from momentum equations, following SIMPLER
calculation procedure. Solve the pressure equations to obtain P₁, P2, P3 and P₁. Hence
obtain values of up, u, V and VG
Q.4
A steady, uniform-density, 2-D flow is to be calculated on the square grid shown below.
The boundary velocities are given as; v₁ = 30, V = 40,uc=100, u = 50, u = 200,
u, = 210, v = 0 and v₁ = 20. Among these numbers, there is some doubt about
correctness of the value of u,. If all other numbers are correct, what should be the correct
value of u,?
The internal velocities are governed by simplified momentum equations given by:
up=70+0.5(P₁-P₂)
u, = 10+0.7 (P3-P4)
V=30+0.5(P₁-P₁)
V=18+0.8(P₁-P₂)
Write discretized continuity equation for each control volume. Derive the discretization
equation for pressure by substituting from momentum equations, following SIMPLER
calculation procedure. Solve the pressure equations to obtain P₁, P2, P3 and p₁. Hence
obtain values ofu,, U₁, V and V6.
Consider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.
Chapter 8 Solutions
Fluid Mechanics
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