Would love help with all 3 questions. Thank you!AME 30331
–
Fall 13
HW 9
Assigned 11/1
–
Due: 11/8
Problem 1
A source of strength
m
is located a distance
l
from a vertical solid wall
as shown on the right. The velocity potential for this incompressible,
irrotational flow is given by:
? ? ? ?
? ?
22
22
ln
ln
4
m
xl
y
xl
y
?
??
??
??
?
?
?
?
?
??
??
1- Show that there is no flow through the wall.
2- Determine the velocity distribution along the wall.
3- Determine the pressure distribution along the wall, assuming
pp
?
far from the source.
4- Show that the vorticity is zero everywhere.
Problem 2
A horizontal slice through a tornado is modeled by two distinct regions. The inner or core region
(
rR
??
) is modeled by solid body rotation (i.e., a rotational but inviscid region of flow). The
outer region (
rR
?
) is modeled as an irrotational region of flow.
The flow is two-dimensional in the
r
?
-plane, and the components of the velocity field are given
by:
r
v
?
2
rr
R
v
R
rR
r
?
?
?
??
?
?
?
?
?
?
?
,
where
?
is the magnitude of the angular velocity in the inner region. The ambient pressure (far
away from the tornado) is
p
?
.
This question was answered on: Sep 21, 2023
Solution~00021147636309.zip (25.37 KB)
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DATE ANSWEREDSep 21, 2023
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