Due:
In class, Friday
November 2, 2007
Name
For instructor or TA use only:
Problem
Score
Points
1
15
2
15
3
10
4
15
5
10
6
35
ME 521
Fall Semester, 2007
Homework Set # 8
Professor J. M. Cimbala
Total:
100
1
.
(15 pts)
Consider the following velocity potential function for a steady, incompressible, irrotational, twodimensional
flow field in cylindrical (
r
,
θ
) coordinates:
()
2
,c
a
rU
r
r
o
s
φ
⎛⎞
=+
⎜⎟
⎝⎠
, where
a
is a constant.
(
a
) Write the CauchyRiemann conditions in
r

coordinates, and then use them to generate an expression for stream
function
ψ
(
r
,
).
(
b
) Sketch some streamlines and equipotential lines for this flow field. For consistency, use solid lines for the streamlines
and dashed lines for the equipotential lines. [A neat handdrawn sketch is acceptable, but some of you may prefer to
generate the sketch electronically – also acceptable.] What kind of classical flow field does this model?
Hint
: There is
something special about radius
r
=
a
; calculate the value of stream function
along
r
=
a
to help you interpret what
kind of flow this represents.
Note
: Be sure to sketch streamlines and equipotential lines for both
r
<
a
and
r
>
a
.
(
c
) Calculate velocity components
u
r
and
u
for any arbitrary location (
r
,
) in the flow field. Calculate velocity components
u
r
and
u
along
r
=
a
, and calculate the minimum and maximum speed (magnitude of velocity) along
r
=
a
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 CIMBALA
 Fluid Dynamics, Taylor Series, Cartesian Coordinate System, potential flow, flow field

Click to edit the document details