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Sagot :
Answer: the drawdown of the lake in centimeters is 3.02 cm
Explanation:
Given data;
Power of motor = 1000 W
efficiency M = 50% = 0.5
so Effective power = 1000 × 0.5 = 500 W
time t = 2 hrs = 2 × 60 × 60 = 7200 secs
so
Energy = p × t = 500 × 7200 = 3,600,000 J
Now Energy required to pump water to height h = mgh (J)
3,600,000 J = mgh
m = 3,600,000 / gh
given that; h is 2.43 and we know that g is 9.81, we substitute
m = 3,600,000 / (9.81 × 2.43)
m = 3,600,000 / 23.8383
m = 151017.48 kg
Now we know that, Volume = Mass / Density [density of water]
so, Volume = 151017.48 / 1000
Volume = 151.01748 kg/m³
given that surface area = 5000 m²
Drawdown = 151.01748 / 5000
Drawdown = 0.3020 m
we convert to centimeter
Drawdown = 0.3020 m × 100
Drawdown = 3.02 cm
Therefore the drawdown of the lake in centimeters is 3.02 cm
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