ME 330 Fluid Mechanics
Spring 2007
Department of Engineering
Western Kentucky University
CHAPTER 3C HW  Homework Solutions
Problem #’s 366, 3 68E and 370, Due February 9, 2007
366
Solution
A rectangular plate hinged about a horizontal axis along its upper edge
blocks a fresh water channel. The plate is restrained from opening by a fixed ridge at a
point
B
. The force exerted to the plate by the ridge is to be determined.
Assumptions
Atmospheric pressure acts on both sides of the plate, and thus it can be
ignored in calculations for convenience.
Properties
We take the density of water to be 1000 kg/m
3
throughout.
Analysis
The average pressure on a surface is the
pressure at the centroid (midpoint) of the surface, and is
determined to be
()
(
)
avg
32
2
2
2
1 kN
1000 kg/m
9 81 m/s
4 2 m
19 62 kN/m
1000 kg m/s
CC
PP
g
h
g
(
h
/
)
./
.
ρρ
==
=
⎛⎞
⎜⎟
⋅
⎝⎠
Then the resultant hydrostatic force on each wall becomes
2
avg
19 62 kN/m
4 m 5 m
392
kN
R
FP
A
.
×
=
The line of action of the force passes through the
pressure center, which is 2
h
/3 from the free surface,
m
2.667
3
m)
4
(
2
3
2
=
×
=
=
h
y
P
Taking the moment about point
A
and setting it equal to zero gives
AB
F
y
s
F
M
P
R
A
ridge
)
(
0
=
+
→
=
∑
Solving for
F
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 Spring '08
 an
 Force, FR Rsin, Fluid Mechanics Department of Engineering Western Kentucky University, Engineering Western Kentucky, Fluid Mechanics Department

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