Consider the vessel. It is filled to a depth of 1 foot of water. Write an integral in terms of y (the distance from the bottom) for the work required to pump all the water to the top of the vessel. Water weights 62.4 lbs/ft(adsbygoogle = window.adsbygoogle || []).push({}); ^{3}.

Relevant Equations

W = ∫F dx

Pressure = density * g * depth

F = Pressure * V

Attempt

P = 62.4 * 9.8 * y = 611.52y

Based on similar triangles, I was able to get a width of (3/2)y. Thus, the volume becomes:

V = 5*(3/2)y*Δy = 7.5yΔy

So the force is F = (611.52y)(7.5y)Δy

I stopped here because I wasn't sure about my work. Any help?

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# Homework Help: How much work is required to pump all of the water to the top?

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