The work required to pump the water out of the spout.
The work is calculated by using the formula W=∫abf(x)dx
From the given figure, let the distance above the bottom of tank be x
Let the horizontal slice of water having thickness ∆x lying at a distance x
Let the width of the slice lying at distance x be w,
By similar triangles,
This slice has a volume 10(2x)∆x ft3
The weight of the slice is about (62.5)20x∆x
and the water must be lifted (6-x) m by the pump.
Therefore, work needed is about 62.56-x20x∆x ft-lb.
andtherefore, the total work required is
The work required to pump the water out of the spout is ≈45000 ft-lb