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Problem 6.2
[Difficulty: 2]
Given:
Velocity field
Find:
Acceleration of particle and pressure gradient at (2,2)
Solution:
Basic equations
Given data
A1
1
s
⋅
=
B3
1
s
⋅
=
x2
m
⋅
=
y2
m
⋅
=
ρ
999
kg
m
3
⋅
=
For this flow
uxy
,
()A
x
⋅
By
⋅
+
=
vxy
,
()B
x
⋅
Ay
⋅
−
=
a
x
u
x
u
∂
∂
⋅
v
y
u
∂
∂
⋅
+
=
Ax
⋅
⋅
+
()
x
⋅
⋅
+
∂
∂
⋅
Bx
⋅
⋅
−
y
⋅
⋅
+
∂
∂
⋅
+
=
a
x
A
2
B
2
+
x
⋅
=
a
y
u
x
v
∂
∂
⋅
v
y
v
∂
∂
⋅
+
=
⋅
⋅
+
x
⋅
⋅
−
∂
∂
⋅
⋅
⋅
−
y
⋅
⋅
−
∂
∂
⋅
+
=
a
y
A
2
B
2
+
y
⋅
=
Hence at (2,2)
a
x
19
+
1
s
2
×
m
⋅
=
a
x
20
m
s
=
a
y
+
1
s
2
×
m
⋅
=
a
y
20
m
s
=
aa
x
2
a
y
2
+
=
θ
atan
a
y
a
x
⎛
⎜
⎝
⎞
⎠
=
a
28.28
m
s
=
θ
45 deg
⋅
=
For the pressure gradient
x
p
∂
∂
ρ
g
x
⋅
ρ
a
x
⋅
−
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 Fall '07
 Lear
 Fluid Mechanics

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