A small water tower has a cylindrical chamber $3m$ in diameter and $4m$ tall. The bottom of the cylinder is $15m$ above the ground. Water is pumped from an underground reservoir into the chamber, via a pipe that enters through the bottom of the chamber. The surface of the reservoir is $5m$ below the ground. Assume that the tower, reservoir, and pipes are adiabatic, and that all water is at a uniform temperature, and a uniform density of $1000\frac{g}{c}{m}^3.$

A$.$ When the water tower is completely empty, what is the minimum pump work required to move $1kg$ of water into the tower?

B$.$ When the water tower is almost full, what is the minimum pump work required to move $1kg$ of water into the tower?

C$.$ A home has a second floor faucet is $3m$ above the ground. The ground in the area is level, and there is nothing powering the water except the force of gravity. When the faucet it turned on$,$ what is the maximum velocity the water can have?