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MEEN 344: Section 502
HW Problem Set #5
(Due on 10/10/06)
1.
For a flow in the xy plane, the x component of velocity is given by
()
uA
x
yB
=−
, where
A = 2 m
1
s
1
, B = 2m, and x and y are measured in meters.
Find a possible y component
for steady, incompressible flow.
Is it also valid for unsteady, incompressible flow? Why?
How many y components are possible?
2.
Consider the velocity field
22
ˆˆ
(2
)(
2
)
VA
x x
y
iAx
yyj
=+
−
+
G
in the xy plane, where A =
0.5 m
1
s
1
, and the coordinates are measured in meters.
Is this a possible incompressible
flow field? Calculate the acceleration of a fluid particle at point (x,y) = (2,1).
3.
Consider the incompressible flow of a fluid through a nozzle as shown below.
The area
of the nozzle is given by
0
(1
)
AA b
x
and the inlet velocity varies according to
0
)
t
UU
e
λ
−
, where A
0
= 1 m
2
, L = 5 m, b = 0.1 m
1,
λ
= 0.1 s
1
, and U
0
= 5 m/s.
Find
and plot the acceleration on the centerline, with time as a parameter.
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 Fall '08
 SCHOBEIRI

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