The resisting torque associated with the sprinkler rotating with a constant speed of 100 rev/min is approximately 102.88 Nm.
The resisting torque associated with the sprinkler rotating with a constant speed of 100 rev/min can be calculated using the following steps:
Calculate the flow rate of water through each nozzle:
Since 30% of the incoming water enters each nozzle, the flow rate through each nozzle is:
Nozzle flow rate = (30/100) * 3000 ml/s = 900 ml/s
Calculate the velocity of water leaving each nozzle:
Convert the nozzle diameter to radius: Nozzle radius = 20 mm / 2 = 10 mm = 0.01 m
Convert the flow rate to volume flow rate: Nozzle volume flow rate = 900 ml/s / 1000 ml/L = 0.9 L/s
Calculate the velocity: Nozzle velocity = Volume flow rate / Nozzle area = 0.9 L/s / π * (0.01 m)^2 ≈ 28.65 m/s
Calculate the tangential momentum of water leaving each nozzle:
Tangential velocity = Angular velocity * radius = 2 * π * 100 rev/min * 300 mm * (1 m/1000 mm) ≈ 188.5 m/s
Tangential momentum per unit mass = Tangential velocity * Angular momentum = 188.5 m/s * 0.9 kg/s ≈ 169.65 kg·m/s
Tangential momentum of each nozzle = Tangential momentum per unit mass * Mass flow rate = 169.65 kg·m/s * 0.9 kg/s ≈ 152.7 kg·m/s
Calculate the resisting torque:
The resisting torque due to each nozzle is equal and opposite to the torque generated by the water leaving the nozzle:
Torque = Force * Moment arm = (Mass flow rate * Tangential velocity) * Radius
Torque per nozzle = 0.9 kg/s * 188.5 m/s * 0.3 m ≈ 51.44 Nm
The total resisting torque is the sum of the torques from both nozzles:
Total resisting torque = 2 * 51.44 Nm ≈ 102.88 Nm
Therefore, the resisting torque associated with the sprinkler rotating with a constant speed of 100 rev/min is approximately 102.88 Nm.
The probable question can be: (30%)-Water enters a rotating lawn sprinkler through its base at the steady rate of 3000 ml/s as sketched in Fig. The exit diameter of each of the two nozzles is 20 mm and the flow leaving each nozzle is in the tangential direction. The radius from the axis of rotation to the centerline of each nozzle is 300 mm. Determine the resisting torque associated with the sprinkler rotating with a constant speed of 100 rev/min. 300 mm -300 mm w = 100 rev/min с Tip moving direction Water flow direction