In a hydroelectric power station, the water is flowing at 2 ms -1 in the river, which is 100 m wide and 5 m deep. The maximum power output from the river is

Question

In a hydroelectric power station, the water is flowing at 2 ms -1 in the river, which is 100 m wide and 5 m deep. The maximum power output from the river is (A) 1.5 MW (B) 2 MW (C) 2.5 MW (D) 3 MW

Tardigrade Admin · Accepted Answer

Given, area of river, A=100 m × 5 m =500 m 2 Density of water, ρ=103 kg / m 3 and v=2 ms -1 ∴ Mass of water flowing per second, m=A ρ v =500 × 103 × 2=106 kg / s Power of power station, P= Kinetic energy of water flowing per second =(1/2) m v2=(1/2) × 106 × 22 =2 × 106 W =2 MW

Q. In a hydroelectric power station, the water is flowing at 2ms−1 in the river, which is 100m wide and 5m deep. The maximum power output from the river is

1.5 MW

2 MW

2.5 MW

3 MW

Given, area of river, A=100m×5m =500m2 Density of water, ρ=103kg/m3 and v=2ms−1 ∴ Mass of water flowing per second, m=Aρv =500×103×2=106kg/s Power of power station, P= Kinetic energy of water flowing per second =21​mv2=21​×106×22 =2×106W=2MW

Q. In a hydroelectric power station, the water is flowing at $2 m s^{- 1}$ in the river, which is $100 m$ wide and $5 m$ deep. The maximum power output from the river is