Problem 3.47
[Difficulty: 2]
Given:
Door of constant width, located in plane vertical wall of water tank is
hinged along upper edge.
D
p
s
L
h
y
x
F
pdA
Hinge
b
1 m
⋅
=
D
1 m
⋅
=
L
1.5 m
⋅
=
Atmospheric pressure acts on outer surface of door; force F is applied
at lower edge to keep door closed.
Find:
(a) Force F, if
(b) Force F, if
p
s
p
atm
=
p
sg
0.5 atm
⋅
=
Plot F/Fo over tange of ps/patm (Fo is force determined in (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)
Σ
M
z
0
=
(Rotational Equilibrium)
Assumptions:
(1) Static fluid
(2) Constant density
(3) Door is in equilibrium
Taking moments about the hinge:
F
−
L
⋅
A
y p
⋅
⌠
⎮
⎮
⌡
d
+
0
=
dA
b dy
⋅
=
Solving for the force:
F
1
L
0
L
y
b y
⋅
p
⋅
⌠
⎮
⌡
d
⋅
=
1
(
)
We will obtain a general expression for F
and then simplify for parts (a) and (b).
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 Fall '07
 Lear
 Fluid Mechanics

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