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Problem 3.70
[Difficulty: 2]
Given:
Geometry of dam
Find:
Vertical force on dam
Assumptions:
(1) water is static and incompressible
(2) since we are asked for the force of the water, all pressures will be written as gage
Solution:
Basic equation:
dp
dh
ρ
g
⋅
=
For incompressible fluid
p
ρ
g
⋅
h
⋅
=
where p is gage pressure and h is measured downwards from the free surface
The force on each horizontal section (depth d and width w) is
Fp
A
⋅
=
ρ
g
⋅
h
⋅
d
⋅
w
⋅
=
(Note that d and w will change in terms of x and y for each section of the dam!)
Hence the total force is (allowing for the fact that some faces experience an upwards (negative) force)
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 Fall '07
 Lear
 Fluid Mechanics

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