Chapter 3, Solution 70.
Two parts of a water trough of semicircular crosssection are held together by cables placed along the length of the trough.
The tension
T
in each cable when the trough is full is to be determined.
Assumptions
1
The atmospheric pressure acts on both sides of the trough wall, and thus it can be ignored in calculations for
convenience.
2
The weight of the trough is negligible.
Properties
We take the density of water to be 1000 kg/m
3
throughout.
Analysis
To expose the cable tension, we consider half of the trough whose crosssection is quartercircle. The hydrostatic
forces acting on the vertical and horizontal plane surfaces as well as the weight of the liquid block are:
Horizontal force on vertical surface:
N
3679
m/s
kg
1
N
1
m)
3
m
m)(0.5
2
/
5
.
0
)(
m/s
81
.
9
)(
kg/m
1000
(
)
2
/
(
2
2
3
=
⋅
×
=
=
=
=
=
A
R
g
A
gh
A
P
F
F
C
ave
x
H
ρ
ρ
The vertical force on the horizontal surface is zero, since it coincides with the free surface
of water. The weight of fluid block per 3m length
is
N
5779
m/s
kg
1
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 Spring '08
 Bohl

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