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Problem 3.58
[Difficulty: 4]
Given:
Window, in shape of isosceles triangle and hinged at the top is located in
the vertical wall of a form that contains concrete.
a
0.4 m
⋅
=
b
0.3 m
⋅
=
c
0.25 m
⋅
=
SG
c
2.5
=
(From Table A.1, App. A)
Find:
The minimum force applied at D needed to keep the window closed.
Plot the results over the range of concrete depth between 0 and a.
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dh
ρ
g
⋅
=
(Hydrostatic Pressure  h is positive downwards)
F
R
A
p
⌠
⎮
⎮
⌡
d
=
(Hydrostatic Force on door)
y' F
R
⋅
A
yp
⋅
⌠
⎮
⎮
⌡
d
=
(First moment of force)
Σ
M0
=
(Rotational equilibrium)
d
dA
h
a
w
b
D
Assumptions:
(1) Static fluid
(2) Incompressible fluid
(3) Atmospheric pressure acts at free surface and on the
outside of the window.
Integrating the pressure equation yields:
p
ρ
g
⋅
hd
−
()
⋅
=
for h > d
p0
=
for h < d
where
dac
−
=
d
0.15 m
⋅
=
Summing moments around the hinge:
F
D
−
a
⋅
A
hp
⋅
⌠
⎮
⎮
⌡
d
+
0
=
F
D
dF = pdA
h
a
F
D
1
a
A
⋅
⌠
⎮
⎮
⌡
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 Fall '07
 Lear
 Fluid Mechanics

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