Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 6, Problem 6.35P
In the overlap layer of Fig. 6.9a, turbulent shear is large. If we neglect viscosity, we can replace Eq. (6.24) with the approximate velocity-gradient function
Show by dimensional analysis that this leads to the logarithmic overlap relation (6.28).
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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.
The open tank in Fig. contains water at 20 ° C and isbeing filled through section 1. Assume incompressibleflow. First derive an analytic expression for the water-levelchange dh / dt in terms of arbitrary volume flows ( Q 1 , Q 2 ,Q 3 ) and tank diameter d . Then, if the water level h is constant,determine the exit velocity V 2 for the given data V 1 =3 m/s and Q 3 = 0.01 m 3 /s.
Chapter 6 Solutions
Fluid Mechanics
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