Question

At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

Short answer

The design of the turbine blades should be such that the water rebounds.

Step-by-step solution

Change in momentum and power generation

The impulse is more if the object rebounds after the collision.

Let\(\Delta {P_1}\)be thechange in momentum of the water when it comes to rest against the turbine blades and \(\Delta {P_2}\) be the change in momentum of the water when it rebounds against the turbine blades.

The change in momentum in the rebound case will be greater as the final momentum of the water comes to rest after the collision becomes zero. The maximum power is directly proportional to the change in momentum. Therefore, for the maximum power generation,

\(\Delta {P_2} > \Delta {P_1}\)

Relation between the rotation of the axle and momentum change

When the water rebounds, the change in momentum is more. Using the momentum conservation principle and work-energy theorem, you can get the axel to spin faster when the change in momentum is greater.

As the axle runs faster, it will generate more power and transfer the same to the generator, considering some mechanical losses. So, the design of the turbine blades should be such that the water rebounds.