At a hydroelectric power plant, the water pressure head is...

At a hydroelectric power plant, the water pressure head is at a height of $300 \mathrm{~m}$ and the water flow available is $100 \mathrm{~m}^{3} \mathrm{~s}^{-1}$. If the turbine generator efficiency is $60 \%$, estimate the electric power available from the plant $\left(g=9.8 \mathrm{~ms}^{-2}\right)$.

Key Concepts

Power Calculation

This concept involves the integration of water’s potential energy, flow rate, and system efficiency to estimate the electric power output. The calculation typically uses the formula Power = density × flow rate × gravitational acceleration × height × efficiency, combining all key variables to determine the renewable energy produced.

Gravitational Potential Energy

This concept refers to the energy possessed by a mass due to its position in a gravitational field. In hydroelectric power generation, the water stored at a height has potential energy that is calculated by the product of mass, gravitational acceleration, and height. This energy is what is converted into mechanical energy by the turbine.

Flow Rate

Flow rate is a measure of the volume of water moving through the turbine per unit time, typically expressed in cubic meters per second. It is a critical parameter because it directly determines the mass of water available to convert its potential energy into kinetic energy and ultimately into electrical energy.

Turbine and Generator Efficiency

Efficiency represents the fraction of the water's potential energy that is successfully converted into electrical energy by the turbine and generator system. Due to various losses in the conversion process, only a portion of the available energy is harnessed, making it essential to account for the efficiency percentage in power calculations.

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