Alarge lawn sprinkler with four identical arms is to be converted into a turbine to generate electric power by attaching a generator to its rotating head. water enters the sprinkler from the base along the axis ofrotation at a rate of 15 kg/s and leaves the nozzles in the tangential direction at a velocity of 50 m/s relative to the rotating nozzle. the sprinkler rotates at a rate of 400 rpm in a horizontal plane. the normal distance between the axis of rotation and the center of each nozzle is 30 cm. estimate the electric power produced.

28.22 kW

Explanation:

Angular velocity of nozzles

where is angular velocity, n is rotations per second

= 41.8879 rad/s

Tangential velocity of nozzle

=0.3m* 41.8879 rad/s =12.56637 m/s

Where r is normal distance between the axis of rotation and the centre of each nozzle, =50-12.56637=37.43363 m/s

Where is average absolute velocity, [/ex]V_{jet, r}[/tex] is velocity relative to the rotating nozzle

Angular momentum equation is expressed as

}

=4*0.3*15*37.43363=673.8053 Nm

Energy generated, Q

=28.22429kW

Therefore, electric power produced is 28.22kW