A jet of water impinges on a vane and is deflected at 45 degress. The volume flo

Question

A jet of water impinges on a vane and is deflected at 45 degress. The volume flow rate is Q=0.13 m^3/s and the nozzle velocity is v= 35 m/s. What force must be exerted on the illustrated vane if it is to move directly away from the jet at a constant speed of u= 10m/s?

A jet of water impinges on a vane and is deflected at 45 degrees. The volume flow rate is Q=0.13 m^3/s and the nozzle velocity is v= 35 m/s. What force must be exerted on the illustrated vane if it is to move directly away from the jet at a constant speed of u= 10m/s?

Explanation / Answer

initial velocity of jet = 35 m/s;

angle of the vane = 45 deg ;

velocity of jet in the x direction after impinging on thr vane = u/cos 45;

Vx = 14.14 m/s

similarly Vy = u/cos 45 = 14.14 m/s;

Q' = 0.13 .^3/s;

mass flow rate m' = d.Q' = 1000 *0.13 = 130 kg/s;

Fx = m' * (Vx - v);

Fx = 130 * (14.14 -35);

Fx = -2711.8 N;

F y = m' * ( Vy -v) ;

Fy = 130 * 14.14;

Fy = 1832.2N;

Total force F = sqrt [Fx^2 + Fy^2[;

F = 3276.10 N

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