Problem *5.30
[Difficulty: 3]
Given:
Stream function for an incompressible flow field:
ψ
5
A
x
2A
y
A2
m
s
Find:
(a) Sketch streamlines
ψ
= 0 and
ψ
= 5
(b) Velocity vector at (0, 0)
(c) Flow rate between streamlines passing through points (2, 2) and (4, 1)
Solution:
We will generate the velocity field from the stream function.
x
v
y
u
Governing
Equations:
(Definition of stream function)
Assumptions:
Incompressible flow (
ρ
is constant)
Flow is only in the xy plane
For
ψ
= 0:
05
A
x
y
Solving for y:
y
5
2
x
For
ψ
= 5:
55
A
x
y
Solving for y:
y
5
2
x
5
2
m
2
s
s
2m
5
2
x
5
2
m
4
2
0
2
4
10
5
5
10
x (m)
y (m)
Here is the plot of the two streamlines:
ψ
=0 is in red;
ψ
= 5 is in blue
Generating
the velocity components from the stream function derivatives:
This is the end of the preview. Sign up
to
access the rest of the document.
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

Click to edit the document details