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Problem 3.66
[Difficulty: 3]
Given:
Geometry of gate
h
D
F
R
y
F
A
y’
Find:
Force at A to hold gate closed
Solution:
Basic equation
dp
dh
ρ
g
⋅
=
Σ
M
z
0
=
Computing equations
F
R
p
c
A
⋅
=
y'
y
c
I
xx
Ay
c
⋅
+
=
I
xx
wL
3
⋅
12
=
Assumptions:
Static fluid;
ρ
= constant; p
atm
on other side; no friction in hinge
For incompressible fluid
p
ρ
g
⋅
h
⋅
=
where p is gage pressure and h is measured downwards
The hydrostatic force on the gate is that on a rectangle of size L and width w.
Hence
F
R
p
c
A
⋅
=
ρ
g
⋅
h
c
⋅
A
⋅
=
ρ
g
⋅
D
L
2
sin 30 deg
⋅
()
⋅
+
⎛
⎝
⎞
⎠
⋅
L
⋅
w
⋅
=
F
R
1000
kg
m
3
⋅
9.81
×
m
s
2
⋅
1.5
3
2
sin 30 deg
⋅
+
⎛
⎝
⎞
⎠
×
m
⋅
3
×
m
⋅
3
×
m
⋅
Ns
2
⋅
kg m
⋅
×
=
F
R
199 kN
⋅
=
The location of this force is given by
y'
y
c
I
xx
c
⋅
+
=
where
y' and y
c
are measured along the plane of the gate to the free surface
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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, Gate

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