An open cylindrical tank of area 100 m2 and height 2m empties to the atmosphere through a long horizontal pipe connected at the bottom. The pipe has a length of 20 m and an inside diameter of 25 mm. If the tank is initially filled with an incompressible Newtonian liquid, please:

(a) Express the average fluid velocity v(t), in the unit of m/sec, in the pipe as a function of water level (h(t)). Assume a friction factor, fF, of 0.005 in the horizontal pipe and entry and exit friction losses could be ignored.

(b) Start with mass conservation and use the v(t) obtained in (a), express h(t) as a function of time and calculate the time required to lower the water level in the tank from 2 m to 0.5 m above the open end of the pipe.