Question

A water jet with a diameter of 70 mm is deflected by 60⁰ at the velocity of 36 m/s
at the beginning of the blade as shown in figure below. Calculate the magnitude
of the force generated by water on the blade when the velocity of water jet
leaving the blade is 30 m/s due to friction.

Answer 1

According to the momentum equation

$F_x=v_1(-\rho v_1A_1)+v_2\cos60°(\rho v_2A_2)=$

$=36\cdot (-1000\cdot36\cdot3.14\cdot0.07^2)+30\cdot\cos60°\cdot(1000\cdot30\cdot3.14\cdot0.07^2)=$

$=-13017(N)$

$F_y=-v_2\sin60°(\rho v_2A_2)=-30\cdot\sin60°(1000\cdot30\cdot3.14\cdot0.07^2)=-11992(N)$

$F=\sqrt{F_x^2+F_y^2}=\sqrt{13017^2+11992^2}=17699(N)$