Answer to Question #87452 in Mechanics | Relativity for Unknown277793

Question

Q1.A 50 mm diameter stream of water strikes a 0.5 m by 0.5 m square plate which is at an angle of 30 degrees with the stream’s direction. The velocity of the water in the stream is 20 m/s and the jet strikes the door at its centre of gravity. If the plate is hinged at A, by neglecting the friction and self-weight of the plate, determine the normal force P applied at the upper edge of the plate to keep the plate in equilibrium. You may assume that the velocities of the jet remain unchanged after split.

Answer 1

The normal force P:

$$P=F \cos30° (1)$$

Newton’s second law of motion:

$$Δmv=FΔt (2)$$

where Δm is the change of water mass

The change of water mass:

$$Δm=ΔV\times \rho =SvΔt\rho =\frac {\pi d^2}{4} vΔt\rho (3)$$

Put (3) in (2):

$$\frac {\pi d^ 2}{4} vΔt\rho\times v= FΔt (4)$$

We got:

$$F=\frac {\pi d^ 2}{4} v^2 \rho (5)$$

where ρ is the water density

Put (5) in (1):

$$P=\frac {\pi d^ 2}{4} v^2 \rho \cos30° (6)$$

Using (6) we got:

P=68.3 N

Answer:

68.3 N