Problem 6.2
[2]
Given:
Velocity field
Find:
Acceleration of particle and pressure gradient at (0.7,2)
Solution:
Basic equations
For this flow
uxy
,
()A
x
⋅
By
⋅
−
=
vxy
,
() A
−
y
⋅
=
a
x
u
x
u
∂
∂
⋅
v
y
u
∂
∂
⋅
+
=
Ax
⋅
⋅
−
()
x
⋅
⋅
−
∂
∂
⋅
A
−
y
⋅
y
⋅
⋅
−
∂
∂
⋅
+
=
a
x
A
2
x
⋅
=
a
y
u
x
v
∂
∂
⋅
v
y
v
∂
∂
⋅
+
=
⋅
⋅
−
x
A
−
y
⋅
∂
∂
⋅
A
−
y
⋅
y
A
−
y
⋅
∂
∂
⋅
+
=
a
y
A
2
y
⋅
=
Hence at (0.7,2)
a
x
1
s
⎛
⎝
⎞
⎠
2
0.7
×
m
⋅
=
a
x
0.7
m
s
2
=
a
y
1
s
⎛
⎝
⎞
⎠
2
2
×
m
⋅
=
a
y
2
m
s
2
=
aa
x
2
a
y
2
+
=
θ
atan
a
y
a
x
⎛
⎜
⎝
⎞
⎟
⎠
=
a
2.12
m
s
2
=
θ
70.7 deg
⋅
=
For the pressure gradient
x
p
∂
∂
ρ
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This note was uploaded on 08/25/2011 for the course AME 331 taught by Professor Zohar during the Fall '08 term at Arizona.
 Fall '08
 ZOHAR

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