Question

Water flows over Victoria Falls, which is 128 m high, at an average rate of 1.39 × 106 kg/s. The acceleration of gravity is 9.81 m/s 2 . If half the potential energy of this water were converted into electric energy, how much power would be produced by these falls? Answer in units of MW.

Answer 1

Potential energy of water is $PE=mgh$

Power is the rate at which the work is done , $P=\frac{mgh}{t}=\frac{m}{t}gh$

Given that, Height from where water falls is $h=128\,m$

Rate at water falls in time $t$ is $\frac{m}{t}=1.39*10^6\,kg/s$

Half of the potential energy is converted into electric energy,

Power produced by water falls is  $\frac{P}{2}=\frac{m}{t}\frac{gh}{2}=1.39*10^6*\frac{9.81*128}{2}=872.7*10^6\,W=872.6\,MW$