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Problem 6.10
[Difficulty: 2]
Given:
Velocity field
Find:
Expression for pressure field; evaluate at (2,2)
Solution:
Basic equations
Given data
A4
1
s
⋅
=
B2
1
s
⋅
=
x2
m
⋅
=
y2
m
⋅
=
ρ
1500
kg
m
3
⋅
=
p
0
200 kPa
⋅
=
For this flow
uxy
,
()A
x
⋅
By
⋅
+
=
vxy
,
()B
x
⋅
Ay
⋅
−
=
Note that
x
,
()
∂
∂
y
,
∂
∂
+
0
=
x
,
∂
∂
y
,
∂
∂
−
0
=
Then
a
x
xy
,
()u
x
y
,
x
,
∂
∂
⋅
,
y
,
∂
∂
⋅
+
=
a
x
,
()x
A
2
B
2
+
⋅
=
a
x
,
4
0
m
s
2
=
a
y
,
x
y
,
x
,
∂
∂
⋅
,
y
,
∂
∂
⋅
+
=
a
y
,
()y
A
2
B
2
+
⋅
=
a
y
,
4
0
m
s
2
=
The momentum equation becomes
x
p
∂
∂
ρ
−
a
x
⋅
=
y
p
∂
∂
ρ
−
a
y
⋅
=
and
pd
x
x
p
∂
∂
⋅
dy
y
p
∂
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 Fall '07
 Lear
 Fluid Mechanics

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