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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 :

AL2006

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)


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