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?
We have to determine the most efficient design, for maximum power generation at hydroelectric power plant.
Step 1 of 3</p>
Law of conservation of linear momentum: If no external force acts on the system, then the final momentum of the system is equal to the initial momentum of the system. Thus momentum is conserved.
Step 2 of 3</p>
Assume that water is falling down onto the turbine blades with momentum of After the water is incident on the turbine blades, consider that the momentum gained by the turbine blades is and the water rebounded with a momentum of .
As no external force acts on the system, therefore by using the law of conservation of momentum, we get the relation between the momentums as,
As the water rebounds from the turbine blade, its momentum after rebound is opposite to the momentum of turbine blade. Hence, the magnitude of the initial momentum of falling water is expressed as
Hence, the magnitude of the momentum gained by turbine blades is,