3. At Bhakra Nangal Dam, water falls from a height of 225 meters to turn turbines. If the efficiency of energy conversion is 85\% and the flow rate is 1500 cubic meters per second, approximately how much electrical power is generated? (Assume density of water = 1000 kg/m$^3$, g = 9.8 m/s$^2$)
Key Concept: Hydroelectric power generation, Energy conversion
c) 2.81 GW
[Solution Description]
First calculate potential energy per second: P.E. = mgh, where m is mass flow rate.
Mass flow rate = density × volume flow rate = 1000 kg/m$^3$ × 1500 m$^3$/s = 1,500,000 kg/s
Potential energy/s = mgh = 1,500,000 × 9.8 × 225 = 3,307,500,000 J/s or Watts
Electrical power output = Input power × efficiency = 3,307,500,000 × 0.85 = 2,811,375,000 W ≈ 2.81 GW
Your Answer is correct.
c) 2.81 GW
[Solution Description]
First calculate potential energy per second: P.E. = mgh, where m is mass flow rate.
Mass flow rate = density × volume flow rate = 1000 kg/m$^3$ × 1500 m$^3$/s = 1,500,000 kg/s
Potential energy/s = mgh = 1,500,000 × 9.8 × 225 = 3,307,500,000 J/s or Watts
Electrical power output = Input power × efficiency = 3,307,500,000 × 0.85 = 2,811,375,000 W ≈ 2.81 GW