ME 152A (Fall 2008) – Prof. Sumita Pennathur
HW #3
1.
In this problem, consider a long duct of height,
2h
, as shown below,
Three velocity fields which can model the flow in the ducts are,
•
Uniform flow:
(
29
∞
=
U
y
u
•
Couette flow:
(
29
+
=
h
y
U
y
u
w
1
2
•
Poiseuille flow:
(
29

=
2
0
1
h
y
U
y
u
We assume that the other velocity components are zero. The uniform flow is representative of very
high Reynolds number (though without the boundary layers). Couette flow is the (laminar) flow that
results when the upper wall is moving at velocity
w
U
and the bottom wall is stationary. Poiseuille
flow is the (laminar) flow that results when a pressure drop is applied from endtoend.
a)
For all of the velocity distributions, sketch the streamlines.
b)
For all of the velocity distributions, calculate the vorticity.
c)
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 Spring '08
 Meinhart,C
 Fluid Dynamics, Fluid Mechanics, velocity distributions, Prof. Sumita Pennathur

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