Question #190765

a water tank in the shape of a right circular cone has an altitude of 15 feet and a base radius of 10 feet. If the tank is full of water, find the work done in pumping all the water over the top of the tank.

Expert's answer

For the purpose of SI units, I convert the foot to meter first

Altitude=15 feet=4.571meter

Radius at top=10feet=3.04m

Pouring out water is required from 0 to height of 4.571 full height of tank. It requires integration to be done on the given limit

Work = Force x distance

Force=weight density x volume

Force=9.81x density x volume

Force=9.81x1000xvolume

Force=9.81*1000*3.14* x^2*dy

Work=9.81*1000*3.14* x^2*dy(15-y)

Work=9.81*1000*3.14* x^2* (15-y)dy

Slope=m=15/10=1.5

y-0+m(x-0)

y=1.5x

x=y/1.5

x=2/3y=

Thus work is

Work=9.81*1000*3.14* (0.66^2)* (15-y)dy

Work=13690.4(15-y)dy

Work=13690.4(15y-y^2)

Work=13690.4(15*4.571-(4.571)^2))

Work=652634.49Nm

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