FLUID MECHANICS FUND. (LL)-W/ACCESS
4th Edition
ISBN: 9781266016042
Author: CENGEL
Publisher: MCG CUSTOM
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Chapter 9, Problem 88P
Consider steady, incompressible, parallel, laminar flow falling between two infinite vertical walls (Fig. 9-88). The distance between the walls is h, and gravity acts in the negative z-direction (downward in the figure). There is no applied (forced) pressure driving the flow-the fluid falls by gravity alone. The pressure is constant everywhere in the flow field. Calculate the velocity field and sketch the velocity profile using appropriate nondimensionalized variable.
FIGURE P9-88
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Question 4: Consider fully developed Couette flow - flow between
two infinite parallel plates separated by distance h, with the top
plate moving and the bottom plate stationary as illustrated. The flow
is steady, incompressible, and two dimensional in the xy-plane. The
velocity field is given by V = (u,v) = (V y/h)ỉ + 0ỷ, Generate an
expression for stream function Yalong the vertical dashed line in
the figure. For convenience, 4= 0 along the bottom wall of the channel. What is the value of Y
along the top wall?
Consider steady, incompressible, parallel, laminar flow of a viscous fluid falling between two infinite vertical walls. The distance between the walls is h, and gravity acts in the negative z-direction (downward in the figure). There is no applied (forced) pressure driving the flow—the fluid falls by gravity alone. The pressure is constant everywhere in the flow field. Calculate the velocity field and sketch the velocity profile using appropriate nondimensionalized variables.
Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite
parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a
forced pressure gradient dP/dx driving the flow as
illustrated in the figure (dP/dx is constant and
negative). The flow is steady, incompressible, and
two-dimensional in the xy-plane. The velocity
components are given by
1 dP
u = -(y² - hy); v = 0
2μ αχ
h
where μ is the fluid's viscosity. Is this flow rotational or irrotational?
u(y)
a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this
flow rotate clockwise or counterclockwise?
b. calculate the linear strain rates in the x- and y-directions, and
c. calculate the shear strain rate Exy.
d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,
Chapter 9 Solutions
FLUID MECHANICS FUND. (LL)-W/ACCESS
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