An electric pump is used to moved 1,000,000 kg of water during the day from a la

Question

An electric pump is used to moved 1,000,000 kg of water during the day from a lake at an elevation of 1000 meters to another lake used for storage at an elevation of 2000 meters. The water is then allowed to flow downhill during the night through a turbine connected to an electrical generator in order to create electricity. Assume the overall efficiency of the pump is 80% and the overall efficiency of the generator is 70%.

a) How much energy is required to pump the water uphill?

b) What is the potential energy of the stored water?

c) What is the net (overall) efficiency of the water movement process?

d) Would this process be useful for producing electrical energy at night using water storage? Why?

Explanation / Answer

Here ,

m = 1 *10^6 Kg

h1 = 1000 m

h2 = 2000 m

a) energy required to pump the water uphill = m * g * (h2 - h1)/efficiency

energy required to pump the water uphill = 1 *10^6 * 9.8 * (2000 - 1000)/0.70

energy required to pump the water uphill = 1.4 *10^10 J

the energy required to pump the water uphill is 1.4 *10^10 J

b)

potential energy of stored water = m * g * h2

potential energy of stored water = 1 *10^6 * 2000 * 9.8

potential energy of stored water = 1.96 *10^10 J

c)

net efficiency of water movement = 0.70 * 1.96 *10^10/(1.4 *10^10)

net efficiency of water movement = 0.98 =98 %

d)

No , this will Not be userful for producing electricity as the energy used is more than energy used

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