Problem 2.13
[Difficulty: 3]
Given:
Flow field
Find:
Plot of velocity magnitude along axes, and y = x; Equations of streamlines
Solution:
On the x axis, y = 0, so
u
q x
⋅
2
π
⋅
x
2
y
2
+
(
)
⋅
−
=
q
2
π
⋅
x
⋅
−
=
v
q y
⋅
2
π
⋅
x
2
y
2
+
(
)
⋅
−
=
0
=
1
−
0.5
−
0
0.5
1
100
−
50
−
50
100
x (km)
u (m/s)
Plotting
The velocity is very high close to the origin, and falls off to zero.
It is also along the axis.
This can be plotted in
Excel
.
On the y axis, x = 0, so
u
q x
⋅
2
π
⋅
x
2
y
2
+
(
)
⋅
−
=
0
=
v
q y
⋅
2
π
⋅
x
2
y
2
+
(
)
⋅
−
=
q
2
π
⋅
y
⋅
−
=
1
−
0.5
−
0
0.5
1
100
−
60
−
20
−
20
60
100
y (km)
v (m/s)
Plotting
The velocity is again very high close to the origin, and falls off to zero.
It is also along the axis.
This can also be plotted in
Excel.

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