Question

Assume a hydro power plant with 85% efficiency and 30m head. It is measured that 60 kg of water passes through the turbine in 1 s. What is the output electrical power of this power plant?

a) less than 1 kW
b) between 1 kW and 10 kW
c) more than 10 kW

Please show calculations!

Answer 1

The potential energy of each kg of water, before it falls, is

(M G H) = (1kg) (9.8 m/s²) x (30 m) = 294 joules

The potential energy lost by 60 kg of water pouring through is

(60 x 294) = 17,640 joules

The power output of the plant is

(17,640 joules/sec) x (85%) = 14,994 watts
= almost but not quite 15 kW.

(If you used 10 for gravity, it would come out to 15.3 kW)