Question

Water is falling on the blades of a turbine at a rate of $3000\,kg$ $minute^{- 1}.$ The height of the falls is $200\,m.$ The power given to the turbine is (Assume $g=10\,m\,s^{- 2}$ )

• A. $200\,kW$
• B. $100\,kW$
• C. $10\,kW$
• D. $1\,kW$

Answer 1

Answer: (B)

Power $=\frac{\text{ work done }}{\text{ time }}$
But work done is equal to the potential energy of the falling water.
Power $=\frac{m g h}{t}$
But $\frac{m}{t}=3000\,kg$ minute $\_{}^{- 1}=\frac{3000}{60}\,kgs^{- 1}$
Power $=\frac{3000}{60}\,\times 10\times 200=100\,kW$