EAS 4101 - Aerodynamics – Spring 2011
HW#8, 1/6
3/16/11, 8
th
Homework
1.
Given:
2 infinite plates, 2-D slot, with the stationary plate at
0
y
and one plate moving
at
y
h
with
a steady speed
Consider that the flow is steady and fully developed.
.
p
const
0
U
h
x
y
Find:
a)
Draw a schematic of this flow, clearly showing your coordinate system and list your
assumptions for this problem.
b)
Simplify the Navier Stokes and continuity equations, clearly stating why each term is
eliminated.
c)
List the boundary conditions for this problem.
d)
Solve for velocity component normal to the plates.
e)
Solve for velocity component parallel to the plates.
f)
Solve for the only non-zero shear stress component in this flow.
g)
Solve for the only non-zero vorticity component in this flow.
2.
Given:
2 infinite plates, 2-D slot, with the both plates stationary at
0
y
and at
y
h
.
There is a constant axial pressure gradient driving the flow,
dp
const
dx
Consider that the flow is steady and fully developed.
h
x
y
1
p
2
p
g
constant
dp
dx
Find:
a)
Draw a schematic of this flow, clearly showing your coordinate system and list your
assumptions for this problem.
b)
Simplify the Navier Stokes and continuity equations, clearly stating why each term is
eliminated.
c)
List the boundary conditions for this problem.
d)
Solve for velocity component normal to the plates.
e)
Solve for velocity component parallel to the plates.
f)
Solve for the only non-zero shear stress component in this flow.
g)
Solve for the only non-zero shear vorticity component in this flow.
3.

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