Name: Gravitational Potential Energy
Uploaded: 2019-07-19
Duration: 9 min 10 s
Description: The energy possessed by a body because of its position in a gravitational field is known as Gravitational Potential Energy. Let’s learn about it in detail in...

Question

The water falls at the rate of 2000 kg/second from a fall of height 100 m. What is the initial potential energy of water? What is the kinetic energy of water on the surface? If the energy is used to run a turbine of an electric generator whose efficiency is 90%, calculate the amount of power generated.

Accepted Answer

Given,

Mass flow rate of water: $\frac{m}{t} = 2000 {kgs}^{- 1}$

Height from which the water falls: $h = 100 m$

Acceleration due to gravity: $g =10 {ms}^{- 2}$

Efficiency of an electric generator: $η = 90 %$

The potential energy of an object at a certain height: $U = mgh$

$\Rightarrow U = \dot{m} \times g \times h$

$\Rightarrow U = 2000 \times 10 \times 100 = 2 \times 10^{6} {Js}^{- 1}$

The initial potential energy of the water: $U = 2 \times 10^{6} {Js}^{- 1}$

During a water fall, potential energy gets converted into kinetic energy, and at an instant just before reaching the turbine, its kinetic energy becomes maximum. After driving the turbine when the water reaches the bottom of a dam on the surface, its velocity becomes zero because its entire kinetic energy has been converted into mechanical energy by turbine and hence its kinetic energy becomes minimum or zero. Energy is always conserved.

The kinetic energy of water on the surface $KE = 0 J$

During this entire process, the initial potential energy has been converted totally into kinetic energy which then gets converted into mechanical energy in the turbine for electricity generation.

So, the energy available for power generation will be equal to initial potential energy of water.

Thus, the power generated by the turbine will be $P = η \times U$

$\Rightarrow P = \frac{90}{100} \times 2 \times 10^{6} = 1.8 \times 10^{6} {Js}^{- 1} = 1.8 \times 10^{6} W$

Therefore, amount of power generated by the turbine is $P = 1.8 \times 10^{6} W$ .

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