EAS 4101  Aerodynamics – Spring 2011
HW#8, 1/6
3/16/11, 8
th
Homework
1.
Given:
2 infinite plates, 2D slot, with the stationary plate at
0
y
and one plate moving
at
yh
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 nonzero shear stress component in this flow.
g)
Solve for the only nonzero vorticity component in this flow.
2.
Given:
2 infinite plates, 2D slot, with the both plates stationary at
0
y
and at
.
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 nonzero shear stress component in this flow.
g)
Solve for the only nonzero shear vorticity component in this flow.
3.
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View Full DocumentEAS 4101  Aerodynamics – Spring 2011
HW#8, 2/6
Given:
A long, wide belt inclined at an angle
with respect to the horizontal is submerged
in a liquid of density
and viscosity
.
The belt is moving with a steady speed
U
such that a thin film of liquid is pulled upward along the belt.
Sufficiently far along the belt, the film possesses a constant thickness
and the flow
is fully developed.
.
p
const
Find:
h)
Draw a schematic of this flow, clearly showing your coordinate system and list your
assumptions for this problem.
i)
Simplify the Navier Stokes and continuity equations, clearly stating why each term is
eliminated.
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 Spring '08
 Sheplak
 Fluid Dynamics, Boundary conditions, Navier Stokes

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