A metal plate 064 cm thick and 15 cm square swings about a h

A metal plate 0.64 cm thick and 15 cm square swings about a horizontal edge in the figure below. A horizontal jet of water 1.25 cm ID diameter impinges with its axis perpendicular to and 5 cm below the edge of the hinge and keeps it steadily inclined at 20 degree to the vertical. Find the velocity of the jet if the metal plate has s.g. of 8.

Solution

By momentum theorem, if V is the velocity of jet, the force exerted on the plate is the rate of change in momentum . Assuming the jet is brought to rest, the force is m\'Vcos 20, where V is the jet velocity

mass flux in the jet is pi*(1.25/100)²   /4 * 1000 kg * V cos20 =0.12272*V *cos20 N =.05V N

Moment of this force about O,   = moment of wt of plate about O= mass*9.81*7,5*cos70/100

solving for V get 0.876 m/s

( if momentum of deflected jet to be considered, need to know the deflected velocity and get difference of momentum)