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66. Problem 15.23P (HRW) Water stands at a depth D behind the vertical upstream face of a dam. Let W be the width of the dam. We have to find (a) the resultant horizontal force exerted on the dam by the gauge pressure of the water and (b) the net torque owing to that gauge pressure about a line O parallel to the width of the dam. (c) The moment arm of the resultant horizontal force about the line through O.
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Solution: Click For PDF Version Width of the dam is W m. Gauge pressure at depth D-h
from the water level at the top of the dam is
Let us consider a strip
The force on the dam due to gauge pressure of water will be
Torque about a line through O, parallel to the width of the dam, will be
Moment arm, L, of the resultant horizontal force about the line through O will, therefore, be given by the relation
We have worked out the expressions for F and
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of width
W for computing the force on the dam due to water at depth D-h
from the water level at the top of the dam. Area of this strip is W
is 
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,
which give