An unsymmetrical sprinker shown in the top view of the setup has frictionless shaft and equal fluid flows through each nozzle with a velocity of 10m/sec relative to nozzle, its angular speed of rotati

Question

An unsymmetrical sprinker shown in the top view of the setup has frictionless shaft and equal fluid flows through each nozzle with a velocity of 10m/sec relative to nozzle, its angular speed of rotation is

TestHub · Accepted Answer

Equal flow through each nozzle: A v 1 ​ = A v 2 ​ ; frictionless shaft: τ n e t ​ = 0 ρ A v 1 2 ​ r 1 ​ = ρ A v 2 2 ​ r 2 ​ ⇒ v 1 ​ r 1 ​ = v 2 ​ r 2 ​ Ground-frame nozzle speeds: v 1 ​ = 10 + 0.5 ω , v 2 ​ = 10 − ω ( 10 + 0.5 ω ) ( 0.5 ) = ( 10 − ω ) ( 1 ) 2.5 ω = 10 ⇒ ω = 4 rad/s

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