Question 2

A circular water tank, 3m in diameter, tapers into a cone as shown in the figure below. It

is open to the atmosphere at the top. The tank is used to store water and distribute it to

a local town. It is supplied with water through a horizontal pipe 200 m long and 220 mm

diameter. A pump feeds the pipe and maintains a constant gauge pressure of 150 kPa at the

entry to the pipe. The pipe may be assumed to have a constant friction factor A = 0.02 and

losses other than those due to wall friction may be neglected. The tank discharges water to

the town through an opening at the base of the cone, that has a diameter of 300 mm and a

Cd = 0.68.

Assuming the outflow is closed:

(a) What is the piezometric head maintained by the pump at the inlet to the pipe?

(b) Write an expression for the frictional head loss along the pipe due to a flow rate Q, and

hence find an expression for Q when the water level of the tank is a height h above the

pipe

If the tank is filled to a height of 7 m prior to the outflow being opened:

(c) Find the time taken for the water level to reduce to 2 m, assuming the inflow is maintained

throughout.