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Problem 3.57
[Difficulty: 2]
Given:
Liquid concrete poured between vertical forms as shown
t
0.25 m
⋅
=
H3
m
⋅
=
W5
m
⋅
=
SG
c
2.5
=
(From Table A.1, App. A)
Find:
(a) Resultant force on form
(b) Line of application
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
dp
dy
ρ
g
⋅
=
(Hydrostatic Pressure  y is positive downwards)
F
R
p
c
A
⋅
=
(Hydrostatic Force)
y'
y
c
I
xx
Ay
c
⋅
+
=
(Location of line of action)
x'
x
c
I
xy
c
⋅
+
=
W
= 5 m
H
= 3 m
F
R
t
= 0.25 m
Liquid Concrete
x’
y’
Assumptions:
(1) Static fluid
(2) Incompressible fluid
(3) Atmospheric pressure acts at free surface
and on the outside of the form.
For a rectangular plate:
I
xx
WH
3
⋅
12
=
I
xy
0
=
x
c
2.5 m
⋅
=
y
c
1.5 m
⋅
=
Integrating the hydrostatic pressure equation:
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 Fall '07
 Lear
 Statics, Fluid Mechanics

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