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ICSE Class 10 Answered

A hydroelectric power station takes its water from a lake whose water level is at a hight of 50m above the turbine, Assuming an overall efficiency of 40 %, calculate the mass of water which must follow through the turbine each second to produce power output of 1MW.   Pls solve this question clearly step by step so that i can understand  
Asked by krcraju1973 | 19 May, 2019, 01:03: PM
answered-by-expert Expert Answer
Efficiency = 40% 
Work done = 40% x Potential energy 
 
P.E = mgh 
 
m = ? 
g ≈10 m/s2 
h = 50 m 
 
Thus,
 
useful work done = 40 % x (m x 10 x 50)
= (40/100) x (500 x m)
= 200 x m 
 
We know, 
Power = Work done/ time 
t = 1 s 
→1 MW = 200 x mass of water flowing per second 
 
1 MW = 1 x 106 W
 
Thus,
1 x 106 W = 200 x m 
 
m = 106 / 200
m = 5000 kg 
 
Thus, 5000 kg mass of water must flow through turbine per second to produce a power output of 1MW. 
Answered by Shiwani Sawant | 19 May, 2019, 02:46: PM

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