ME 309 Fall 2008
Section 2 (Merkle)
Homework # 17
Due Wed 8 Oct 2008
Problem 171
The radius of curvature of the streamlines in the converging inlet to a
water channel are approximated as
R = LR
0
/2y
and the velocity on each streamline is
uniform at
V
= 10
m/s
.
Find the pressure change from the centerline,
y = 0
, to the
channel wall,
y = L/
2, where
L=
200
mm,
and
R
0
= 0.5
m
.
Solution:
Given
:
Radius of curvature of SL’s at inlet
Speed along each
V
= 10
L =
0.1,
R = 0.5
Find
: pressure difference from centerline to wall
Assumptions
:
Steady, frictionless flow, incompressible, no body forces, constant
velocity along each streamline.
Analysis
:
Normal momentum equation:
R
V
n
p
2
ρ
=
∂
∂
Apply equation at inlet plane:
L
R
V
y
R
V
y
p
n
p
0
2
2
2
=
=
∂
∂

=
∂
∂
Separate variables and integrate:
dy
L
R
V
y
dp
0
2
2

=
or
2
0
2
0
y
L
R
V
p
p

=

Evaluate at outer wall:
2
0
2
0
2
/
/
9950
4
m
N
R
L
V
p
p
p
L

=

=

=
Α
(Note:
Minus sign implies pressure is lower on the wall than on the centerline.)
Problem 172
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 Spring '08
 MERKLE
 Fluid Dynamics, Force, Merkle, P2 − P1

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