If the head of a hydroelectric power plant is doubled, what is the effect on its peak power producing capability?

When the head of a hydroelectric power plant is doubled, the peak power output significantly increases due to the relationship between the potential energy of the water and the height from which it falls. The power produced by a hydroelectric plant can be expressed with the equation:

[ P = \eta \times \rho \times g \times h \times Q ]

where:

• ( P ) is the power output,
• ( \eta ) is the efficiency of the system,
• ( \rho ) is the density of water,
• ( g ) is the acceleration due to gravity,
• ( h ) is the height (head) of the water,
• ( Q ) is the flow rate of the water.

In this equation, the height (head) ( h ) is a crucial variable. If the head is doubled, the potential energy available for conversion to electrical energy effectively increases. Specifically, the power output is directly proportional to the height of the water column.

When you double the head, assuming that the flow rate remains constant and that there are no changes in efficiency or the density of the water, the new power output would be calculated as:

[ P' = \eta \times \rho \