Answer to Question #280227 in Physics for John

Question

Water from a dam falls on a turbine 30 m below at the rate of 60 m³/min. After

leaving the turbine wheel the water has a velocity of 9 m/s. What is the maximum

efficiency of the turbine? What is the maximum power developed?

Answer 1

The maximum efficiency of the turbine

$\eta=\frac{W}{W_{total}}=\frac{\rho Qtgh-\rho Qtv^2/2}{\rho Qtgh}=1-\frac{v^2}{2gh}=1-\frac{9^2}{2\cdot9.8\cdot30}=0.86$

The maximum power developed

$P=\eta \rho Qt gh/t=\eta \rho Q gh=0.86\cdot1000\cdot1\cdot9.8\cdot30=252\ 840\ (W)$