16.100 Homework Assignment # 1
Fall 2005
Due: Monday, September 12, 9am
Reading Assignment
Anderson: Section 2.1 – 2.3; Section 2.92.13, Section 15.3
Problem 1
In this problem, consider a long duct of height,
, as shown below:
h
2
h
y
=
)
(
y
u
h
y
−
=
Three velocity fields which can model the flow in the ducts are:
Uniform flow:
∞
=
U
y
u
)
(
•
•
Couette flow:
+
=
h
y
U
y
u
w
1
2
)
(
Poiseuille flow:
−
=
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
U
and the bottom wall is stationary.
Poiseuille flow is the (laminar) flow that results when a pressure drop is applied from endtoend.
w
a)
For all of the velocity distributions, sketch the streamlines.
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 Fall '03
 willcox
 Dynamics, Fluid Dynamics, Aerodynamics, uθ, velocity distributions

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