Question

Suppose a river is 1 m deep, 100 m wide and flows towards falls 100 m tall at a speed of 10 m/s.   If an hydroelectric plant at the bottom of the falls can convert 100 % of the loss of gravitational energy of the water into electrical power, how many households could the plant power? Assume a typical household has 10 hundred watt appliances turned on at any given time.

Answer 1

River is 1 m deep and 100 m wide and flowing with speed 10 m/s.

So, volume speed = 1*100*10 = 1000

​​​​also we know that density of water= 1000  

So, mass speed of water = 1000*1000 kg/s = 10^6 kg/s

Now, waterfall is 100 m tall and gravitational potential energy = mgh

So, rate of gravitational potential energy = (mass speed)gh

= 1000000*9.81*100 J/s = 9.81*10^8 J/s

Now,

As it is given that hydroelectric plant can convert 100% of loss of gravitational energy of water into electrical power.

So, the electrical power= 9.81*10^8 J/s or 9.81*10^8 watts

Also, one household uses 1000 watts

So, number of households = (9.81*10^8)/1000 = 9.81*10^5

So, the required answer = g*100000 = 9.81*10^5 = 981000

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