Velocity of the jet?

Question

A square plate of uniform thickness 10mm and side length of 150mm hangs from hinges at its top edge. A horizontal jet of diameter 10mm strikes the plate at a point 50mm vertically below the hinge.The plate is deflected and comes to rest at an angle of 30 degree to the vertical. what is the velocity of the jet.

Specific weight of the plate = 75 kN/m^3

Answer 1

Assuming that the jet is a water jet.

The weight of the plate is:

W = 10 x 150 x 150 x 75000/1000^3 = 16.875 kg

The force acting on the plate to keep it at 30 degrees with the vertical is:

50F = 16.875 x 75 x sin30

F = 12.65625 kg

But:

F = pA

Where; p = pressure

A = area of the jet

A =( pi x(10/100)^2)/4 = 0.00007854 sq.m

p = 12.65625/.00007854 = 161144.0031 kg/m^2

but;

h = p/w

Where;

h = the pressure head

w = the density of water equal to 1000kg/m^3

Therefore;

h = 161144.0031/1000 = 161.144 m

But;

v = (2gH)^.5, hence

v = (2x9.81x161.144)^.5 = 56.22851 m/sec