Question

It is estimated that 7 × 106 kg of water pours over the Niagara Falls every second.
If the falls are 50 m high, and if all the energy of the falling water could be
harnessed, what power would be available? (g = 10 N/kg)​

Answer 1

Given:

It is estimated that 7 × 106 kg of water pours over the Niagara Falls every second. If the falls are 50 m high, and if all the energy of the falling water could be harnessed.

To find:

Power generated ?

Calculation:

The stored gravitational potential energy in the water (at the top of the falls) is getting converted to kinetic energy (as the water falls) and hence does the work.

Now , the power generated can be expressed as the ratio of work done to the time taken :

$\rm\therefore \: power = \dfrac{work}{time}$

$\rm\implies\: power = \dfrac{m \times g \times h}{t}$

$\rm\implies\: power = \dfrac{(7 \times {10}^{6} )\times 10\times 50}{1}$

$\rm\implies\: power = 35 \times {10}^{8 } \: watt$

$\rm\implies\: power = 3500 \times {10}^{6 } \: watt$

$\rm\implies\: power = 3500 \: mega \: watt$

So, power generated is 3500 Megawatt.