This preview shows page 1. Sign up to view the full content.
Problem 2.25
[Difficulty: 3]
Given:
Flow field
Find:
Pathline for particle starting at (3,1); Streamlines through same point at t = 1, 2, and 3 s
Solution:
For particle paths
dx
dt
u
=
ax
⋅
t
⋅
=
an
d
dy
dt
v
=
b
=
Separating variables and integrating
dx
x
at
⋅
dt
⋅
=
or
ln x
()
1
2
a
⋅
t
2
⋅
c
1
+
=
dy
b dt
⋅
=
or
yb
t
⋅
c
2
+
=
Using initial condition (x,y) = (3,1) and the given values for a and b
c
1
ln 3 m
⋅
=
an
d
c
2
1m
⋅
=
The pathline is then
x3
e
0.05 t
2
⋅
⋅
=
and
y4
t
⋅
1
+
=
For streamlines (at any time t)
v
u
dy
dx
=
b
⋅
t
⋅
=
So, separating variables
dy
b
⋅
dx
x
⋅
=
Integrating
y
b
⋅
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