GATE 2018 ME (ME1) – Question 52
The sprinkler shown rotates horizontally about a frictionless hinge. Total water flow is 1 litre/s, shared equally by two arms with outlet areas 1 cm² each. Arm lengths are 10 and 20 cm as shown. Steady angular speed, to two decimals, is ______ rad/s.
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Correct answer: 9.50 to 10.50
Explanation
Each relative jet speed is $(Q/2)/A=0.0005/0.0001=5$ m/s. Both outlets point the same way in plan, with signed moment arms −0.1 and +0.2 m. Zero net angular-momentum flux gives $\omega(0.1^2+0.2^2)+5(-0.1+0.2)=0$. Thus ω = −10 rad/s, or magnitude 10.00 rad/s clockwise.