a water tank is in the form of a right circular cylinder with 20 ft and radius 6 ft. if the tank is half full of water, find the work required to pump all of its water over the rim?

Question

a water tank is in the form of a right circular cylinder  with 20 ft and radius 6 ft. if the tank is half full of water, find the work required to pump all of its water over the rim?

nikvist · Answer

$$R=6 ft , H=20 ft$$
$$A=mg(H-h_{cm})$$
m is whole water mass $$m=\rho\frac{\pi r^2H}{2}$$
$$h_{cm}$$ is center of mass position $$h_{cm}=\frac{H}{4}$$
Now you will get $$A=\rho\frac{\pi r^2H}{2}g(H-H/4)=\frac{3\pi\rho gr^2H^2}{8}$$