Question

3. A vane on wheels moves on the 15° incline plane when a stream of water having a nozzle exit velocity of V, is turned 45° by the v reaction force, F, exerted by the incline plane to a vane is 300 N, moving downward paralleled to the inclined plane, determine a nozzle exit veloci that make a vane velocity, Vo, is 5 m/s. ane as indicated in Fig. If the ty of V Let the mass of water on the vane is 2 kg. Mass of vane is 10 kg. Ai 0.02 m2 Note: the CV should be covered the stream water and the vane 10 points Moving

Answer 1

The diagram of vane is redrawn with necessary forces as shown below

I I AS I5 t5 んWC0815

Total weight of water and vane, W = (10+2)*9.81 = 117.72 N

component of weight along y direction = W cos15 = 117.72*cos15 = 113.7088 N

normal reaction force = 300 N

Net upward force = 300 - 113.7088 = 186.2912 N

Upward force due to jet of water = m*(V₁cos45 - 0 ) = $\rho$A₁V₁(V₁cos45 - 0 )

186.2912 = 1000*0.02*cos(45)*V₁²

gives, V₁² = 186.2912/(1000*0.02*cos45) = 13.172777708

Therefore V₁ = 3.6294 m/s