Water drives a waterwheel (or turbine) of radius 3.5 m. The water enters at a speed v_1 = 7.5 m/s and exits from the waterwheel at a speed v_2 = 4.0 m/s.

Question

a) If 84 kg of water passes through per second, what is the net torque?
b) If the water causes the waterwheel to make one revolution every 5.3 s, how much power is delivered to the wheel?

Answer 1

Force = change in momentum/ change in time
Force = F= 84 kg/s *(7.5 -4)m/s = 294 Newtons
Torque = force*radius =F R = 294*3.5 = 1029 Newton meters

Power = force *distance/time =F*2piR/time = torque *2 pi/time = 2 pi * 1029/5.3 = 1212 watts