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Problem 5.19
[Difficulty: 2]
Given:
The list of velocity fields provided above
Find:
Which of these fields possibly represent incompressible flow
Solution:
We will check these flow fields against the continuity equation
0
1
1
t
V
z
V
r
V
r
r
r
z
r
Governing
Equations:
(Continuity equation)
Assumptions:
(1) Incompressible flow (
ρ
is constant)
(2) Two dimensional flow (velocity is not a function of z)
Based on the two assumptions listed above, the continuity equation reduces to:
r
rV
r
θ
V
θ
0
This is the criterion against which we will check all of the flow fields.
a)
V
r
r
θ
t
()
K
r
V
θ
r
θ
t
()
0
r
rV
r
r
θ
t
()
0
θ
V
θ
r
θ
t
()
0
Hence
r
rV
r
θ
V
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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

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