GATE ME 2018 Set 1 — Question 52
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Fluid Mechanics → Fluid Kinematics & Dynamics → Control Volume Analysis
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Question
A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. The total flow rate through the sprinkler is litre/sec and the cross-sectional area of each exit nozzle is cm. Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).
Correct answer
9.5 to 10.5
Solution
Given:
Total flow rate, L/s m/s
Flow through each arm, m/s
Nozzle area, cm m
Relative velocity of water, m/s
Radii, cm m, cm mFor a frictionless hinge at steady state, the net torque is zero. Assuming clockwise rotation :
Arm 2 (20 cm) moves opposite to its jet direction:
Arm 1 (10 cm) moves in the same direction as its jet: Torque balance:
rad/sThe steady state angular speed is 10.00 rad/s.
Total flow rate, L/s m/s
Flow through each arm, m/s
Nozzle area, cm m
Relative velocity of water, m/s
Radii, cm m, cm mFor a frictionless hinge at steady state, the net torque is zero. Assuming clockwise rotation :
Arm 2 (20 cm) moves opposite to its jet direction:
Arm 1 (10 cm) moves in the same direction as its jet: Torque balance:
rad/sThe steady state angular speed is 10.00 rad/s.
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