The power output from an hydro-electric power plant depends on

Question

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Option C: Discharge, head and system efficiency

Explanation & Concepts:
The electrical power output of a hydroelectric power plant is directly proportional to the rate of water flow (discharge), the height from which the water falls (head), and the overall efficiency of the conversion system. This relationship is derived from the conversion of potential energy into kinetic energy and then into electrical energy.

Working Principle: Water stored at a height possesses potential energy given by $P.E. = mgh$. As water flows down through a penstock, this energy is converted into kinetic energy which rotates a turbine coupled to a generator. The power $P$ is given by $P = \eta \rho g Q H$, where $\eta$ is efficiency, $\rho$ is water density, $g$ is gravity, $Q$ is discharge, and $H$ is the net head.

Key Formulas: $P = \eta \rho g Q H$ — Theoretical power output formula; $H = H_g - h_f$ — Effective head considering frictional losses

Key Points: Discharge ($Q$) is measured in $m^3/s$.; Net head ($H$) is the gross head minus losses due to friction in the penstock.; System efficiency ($\eta$) accounts for turbine, generator, and transmission losses.; The power output is independent of the type of dam itself; the dam's primary purpose is head creation and water storage.

Advantages: Renewable and sustainable energy source; Low operating and maintenance costs; Provides quick start capability for grid stability

Disadvantages: High initial capital investment; Environmental impact on local ecosystems; Dependent on hydrological conditions

Applications: Base load power generation; Peak load leveling in electrical grids; Pumped storage for energy management

Additional Info: The power output formula $P = \eta \rho g Q H$ clearly shows that $P \propto Q$ and $P \propto H$.. Option A and B are incorrect because the 'type of dam' is a structural feature, not a variable in the instantaneous power output calculation. Option D is incorrect for similar reasons.

Answer: C is correct — The power output is a function of the water discharge rate, the effective head, and the overall plant efficiency.

Exam Tip: In competitive exams, remember that structural components like dams or spillways are for energy storage, while dynamic variables like Q and H determine instantaneous electrical output.

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Option A: Type of dam, type of catchment area and discharge

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Option B: Type of dam, head and system efficiency

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Option D: Type of turbine, type of dam and type of catchment area

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