Answer to Question #1465 in Mechanics | Relativity for Mia

Question

The water flow through the turbine of a hydropower plant is
660 m^3/min, and the vertical height from the tail water level to the intake water level is 14 m. The efficiency of the power plant is 86 %, which means that the power plant converts 86 percent of the change in the potential energy of the water into electrical energy. How much power does the hydropower plant deliver to the grid? (g= 9.8 m/s)

Answer 1

Firstly, we should find the water mass fow through the turbine per second:
m/t = 1000[kg/m³]*660 [m³/min]/60[sec] = 11000 [kg/s]

The power of the waterflow would be
W = 0.86mgH/t = 0.86 * 11000 [kg/s] * 9.8 [m/s²] * 14 [m] = 1297912 W = 1.30 MW