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Problem 6.104
[Difficulty: 2]
Given:
Stream function
Find:
Velocity potential
Solution:
Basic equations: Incompressibility because
ψ
exists
u
y
ψ
∂
∂
=
v
x
ψ
∂
∂
−
=
u
x
φ
∂
∂
−
=
v
y
φ
∂
∂
−
=
Irrotationality
x
v
∂
∂
y
u
∂
∂
−
0
=
We have
ψ
xy
,
()A
x
2
⋅
y
⋅
By
3
⋅
−
=
Then
uxy
,
()
y
ψ
,
∂
∂
=
,
() A
x
2
⋅
3B
⋅
y
2
⋅
−
=
vxy
,
x
ψ
,
∂
∂
−
=
,
() 2
−
A
⋅
x
⋅
y
⋅
=
Then
x
,
∂
∂
y
,
∂
∂
−
6B
⋅
y
⋅
2A
⋅
y
⋅
−
=
but
⋅
⋅
−
0
1
ms
⋅
=
hence flow is IRROTATIONAL
Hence
u
x
φ
∂
∂
−
=
so
φ
,
x
,
⌠
⎮
⌡
d
−
fy
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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