Question

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce a power output of 1 MW. (Take g = 10 m s^-2).

April 24, 2024

Answer

Power (P) = 1 MW = 10⁶ W

Time (t) = 1 s

Efficiency = 40%

Work done = 40% of potential energy

⇒ Work done = 0.40 × mgh

= 0.40 × m × 10 × 50

= 200 m

Power = $work\over time$

⇒ 10⁶= $200 m\over 1$

⇒ m = $10^6\over 200$

⇒ m = 5000

Hence, Mass of water which must flow through the turbine = 5000Kg

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