A Levels Physics

A turbine at a hydroelectric power station is situated 30 m below the level of the surface of a large
lake. The water passes through the turbine at a rate of 340 m per minute.
The overall efficiency of the turbine and generator system is 90%.
What is the output power of the power station? (The density of water is 1000 kg m-3.)
A 0.15MW
B 1.5MW
C 1.7 MW
D 90 MW


Choice B is correct because:

Density (ρ)  = Mass (m) / Volume (V)

1000 = m / 340

m = 340 000 Kg (Mass of water passing through the turbine per minute)

GPE = (m)(g)(h) 

GPE = ( 340 000 ) ( 9.81 ) ( 30 ) 

GPE = 100062000 J

Power = Δ GPE / Time

Power = 100062000 / 60 [Time is taken in seconds]

Power = 1667700 W

The efficiency of the turbine and generator is 90% therefore output power is 90% of the obtained power.

Output Power = 1667700  x 0.90 = 1.5 MW  

Power | 2013 - O/N - 9702/11 | Q19