A dam holds a reservoir of water that drives a turbine power

A dam holds a reservoir of water that drives a turbine powered generator to provide hydroelectric power. Water flows from a pipe in the bottom of the dam 220ft below the top of the water through the turbine at a rate of 1650 lbm/s and then empties out of the turbine outlet pipe (3 in schedule 40) into the river below. How much horse power can the turbine theoretically produce? Also draw the schematic diagram.

Solution

Solution :

We know that turbine generates power in the dam because of the potential energy ad it is given by

P = (M*g*h)/33000

M= 1650 lbm/s = 99000 lbm/min

g= 32.2 ft/s²

h= 220 ft

P = 99000*32.2*220 / 33000

P= 21252 HP

This is the power that the turbine can produce theoretically.