Generating stations 23

 Question = A hydroelectric power station is supplied from a reservoir having an area 50 km² and a head of 50 m . if overall efficiency of plant is 60% ,  find the rate of which the water level will fall ? , when the station is generated 30,000 kilowatt .

Solution = Area of reservoir = 50km² or , 50 ×10⁶ m² ,  • H = 50 m. • η plant = 60% , or , 0.6 , • Water level fall = ? , Power generated = 30,000 kW , 

» let , 

» 1 hour or, 3600 sec.. = x metre fall Water , 

» in 1 sec.. = x ÷ 3600 fall Water , 

» average discharge/sec . = ( Area of reservoir ×x ) ÷ 3600 , 

» or , 

» 50 km²  or , 50 × 10⁶ = ( 50 × 10⁶ × x ) /3600 , = 1.388 × 10⁴ x m³  , 

» weight of water available/sec.  =W = 1.388 ×10⁴ x m³ × 1000 × 9.81 , N 

» 13.624 × 10⁷ x N , 

» average Power produced = W × H × η plan , = 13.624x × 10⁷ × 50 m  × 0.6 , = 408.749x ×10⁷ Watt , or , 408.749x × 10⁴ kW , 

» but , kW produced = 30,000 kW , 

» So , 408.749x × 10⁴ kw = 30,000 kw , 

» x = ( 30,000 kw ) ÷ ( 408.749 × 10⁴ kw ) = 0.007339 m/hour , or, ×1000 = mm , = 7.33 mm/hour ,  ( Water level fall ) answer ✓