This preview shows page 1. Sign up to view the full content.
Problem 6.1
[Difficulty: 2]
Given:
Velocity field
Find:
Acceleration of particle and pressure gradient at (1,1)
Solution:
NOTE: Units of B are s
1
not ft
1
s
1
Basic equations
For this flow
uxy
,
()
A
y
2
x
2
−
⋅
Bx
⋅
−
=
vxy
,
2
A
⋅
x
⋅
y
⋅
By
⋅
+
=
a
x
u
x
u
∂
∂
⋅
v
y
u
∂
∂
⋅
+
=
Ay
2
x
2
−
⋅
⋅
−
⎣
⎦
x
2
x
2
−
⋅
⋅
−
⎣
⎦
∂
∂
⋅
2A
⋅
x
⋅
y
⋅
⋅
+
y
2
x
2
−
⋅
⋅
−
⎣
⎦
∂
∂
⋅
+
=
a
x
B2
A
⋅
x
⋅
+
A
x
2
⋅
⋅
+
2
⋅
+
⋅
=
a
y
u
x
v
∂
∂
⋅
v
y
v
∂
∂
⋅
+
=
2
x
2
−
⋅
⋅
−
⎣
⎦
x
⋅
x
⋅
y
⋅
⋅
+
∂
∂
⋅
⋅
x
⋅
y
⋅
⋅
+
y
⋅
x
⋅
y
⋅
⋅
+
∂
∂
⋅
+
=
a
y
A
⋅
x
⋅
+
B
y
⋅
⋅
x
⋅
y
⋅
+
⋅
⋅
y
⋅
⋅
Ax
2
y
2
−
⋅
+
⎣
⎦
⋅
−
=
Hence at (1,1)
a
x
12
1
⋅
1
⋅
+
1
s
⋅
11
2
⋅
⋅
+
2
⋅
+
×
ft
s
⋅
=
a
x
9
ft
s
2
⋅
=
a
y
1
⋅
1
⋅
+
1
s
⋅
⋅
21
⋅
1
⋅
1
⋅
+
×
ft
s
⋅
⋅
1
⋅
1
s
⋅
⋅
2
1
2
−
⋅
+
⎣
⎦
×
ft
s
⋅
−
=
a
y
7
ft
s
2
⋅
=
aa
x
2
a
y
2
+
=
θ
atan
a
y
a
x
⎛
⎜
⎝
⎞
⎠
=
a
11.4
ft
s
2
⋅
=
θ
37.9 deg
⋅
=
For the pressure gradient
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 Lear
 Fluid Mechanics

Click to edit the document details