16.100 Homework Assignment # 6
Due: Monday, October 31 9am
Reading Assignment
Anderson, 3
rd
edition: Chapter 15, Sections 14, 7
Chapter 16, pages 745751, 781786
Problem 1
y
0
U
Consider an initially stationary, long flat plate.
At time
t
=
0 , the plate is set in motion at
velocity
U
.
As time evolves, the air above the plate will begin to move as the viscous effects
diffuse the momentum away from the plate. We will define the height of the boundary layer of
nonnegligible momentum,
0
)
(
t
δ
, as the ylocation at which the velocity is only 1% of the wall
velocity.
Assume the flow is incompressible.
a) Apply the conservation of mass in differential form (i.e. not integral form) to show that
the vertical velocity,
v
, is zero everywhere in the flow for all time.
b) Next, show that the conservation of xmomentum can be reduced to the following form:
2
2
y
u
t
u
∂
∂
=
∂
∂
ν
(1)
c) Show that the following xvelocity is a solution to Equation (1) and that it satisfies the
initial and boundary conditions:
()
∫
−
≡
≡
−
=
η
ξ
π
0
0
2
2
4
1
d
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 Fall '03
 willcox
 Dynamics, Mass, Aerodynamics, Shear Stress, Velocity

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