Question

A town is exploring the option of generating hydroelectric power from a stream. What is the maximum available power in a waterfall that has a flow rate of 200 kg/s dropping over a 15 m change in height?

Answer 1

To answer this we calculate the potential energy of 200kg of water at 15m height. We know that this amount of energy is available every second and power is energy expressed per unit time (often per second).

Ep = mass x gravity x height
Ep = 200kg x 9.8 x 15 = 29,400 Joules or 29.4 mega joules (MJ)

Energy = Power x Time so Power = Energy / Time
1 Watt of power equals 1 Joule of energy per second
So we don't actually need to do a conversion, the waterfall is providing 29.4MJ of energy per second, which equates to 29.4 kilowatts (kW) of available power.

Answer 2

The power is equal to energy transferred per unit time.
So, here power will be due to potential energy of the water kept at a certain height. And water is flowing down at the given flow rate.

The flow rate of water is 200kg/s
And the height given is : 15m

So, we calculate the potential energy as: mgh
Where m is the mass,
g is acc due to gravity = 9.8m/s
h is the height

So, potential energy = 200kg*9.8*15
= 29,400 J

Therefore, the maximum power generated is 29400 J/sec = 29400 Watts