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6.6 Anqular Momentum Equation (cont.) . Ex. 6.A6: y 50 m/s Determine the power p

ID: 2086530 • Letter: 6

Question

6.6 Anqular Momentum Equation (cont.) . Ex. 6.A6: y 50 m/s Determine the power produced by the sprinkler-like turbine shown in the sketch below. The turbine rotates in a horizontal plane about point O with a steady angular speed of 500 rpm. Water enters the turbine from a vertical pipe that is coaxial with the axis of rotation. Water exits the turbine through two identical nozzles, each of which has a section area of 10 cm2 The exit speed of the water is 50 m/s relative to the ?-50ms nozzle. Water density is 1000 kg/m3, and pressure at the exit of each nozzle is atmospheric. 90° 0.5 m ? 500 rpm Fluid Mechanics-- Chapter 6 30

Explanation / Answer

Total mass flow out of control volume dm/dt = rho*A*V_rel

= 1000*(2*10*10^-4)*50

= 100 kg/s

Tangential velocity V_tang = 2*pi*r*N/60

= 2*3.14*0.5*500 / 60

= 26.17 m/s

Torque T = r*V_tang*(dm/dt)

= 0.5*26.17*100

= 1308.33 Nm

Power- = 2*pi*N*T/60

= 2*3.14*500*1308.33/60

= 68469.44 W

= 68.47 kW