Question

HYDROSTATIC FORCE

A vertical dam has a semicircular gate as shown in the figure below. Find the hydrostatic force against the gate. (Round your answer to the nearest wholenumber.)
1 N

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Answer #1

the figure is missing but i know the problem from before.
here is what you need to do:
Force on the thin slice between y and y+dy is
dF = (pressure)(area) = (H-y)ρg (dy)(2w)

But the half-width w is √(r2 -y2). so

F = (Int from 0 to r) [2(H-y)ρg √(r2 -y2)dy]
= (Int from 0 to r) [2Hρg √(r2 -y2)dy] - (Integral from 0 to r) [2ρg√(r2 - y2)ydy]
= 2Hρgπ - 2ρg(8/3)

Now substitute H = 10, ρ=density of water in kg/m3(look it up), g = 9.8 and evaluate. The answer will be in N.
please,rate! thank you.

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