Calculating Speed and Force in Water Jet Impact | Fluid Mechanics Homework

[pedro97]

Homework Statement

"A jet of water issues from a nozzle, of diameter h_1=0,102 m (and depth b=1 m), at a speed U_1=2,02 m/s. The jet strikes a flat plate of mass M=2,05 kg, as shown in figure, and it breaks into two jets of equal speed and diameter h_2=0,122 m and h_3=0,102 m. Determine the speed at which the water leaves the plate, U. Knowing that α=30° and that the volume in transition is V=5,05 L, find the components F_x and F_y of the total force that should be applied on the plate to maintain it in equilibrium". (Solutions are U=0.9198, F_x=28.48 and F_y= -389.7).

Homework Equations

-Momentum conservation equation
-Fluid mechanics equations

The Attempt at a Solution

To answer the first question, I took the jet as my control volume and I applied the momentum conservation equation on it:
(-ρU_1h_1b)+(ρUh_2b)+(ρUh_3b)=0
So: U=(U_1h_1)/(h_2+h_3)= 0.9198
My doubts concern the second question: I think I should use the rate of change of momentum, but I'm not sure how to continue this...

 

[Chestermiller]

Homework Statement

"A jet of water issues from a nozzle, of diameter h_1=0,102 m (and depth b=1 m), at a speed U_1=2,02 m/s. The jet strikes a flat plate of mass M=2,05 kg, as shown in figure, and it breaks into two jets of equal speed and diameter h_2=0,122 m and h_3=0,102 m. Determine the speed at which the water leaves the plate, U. Knowing that α=30° and that the volume in transition is V=5,05 L, find the components F_x and F_y of the total force that should be applied on the plate to maintain it in equilibrium". (Solutions are U=0.9198, F_x=28.48 and F_y= -389.7).

Homework Equations

-Momentum conservation equation
-Fluid mechanics equations

The Attempt at a Solution

To answer the first question, I took the jet as my control volume and I applied the momentum conservation equation on it:
(-ρU_1h_1b)+(ρUh_2b)+(ρUh_3b)=0
So: U=(U_1h_1)/(h_2+h_3)= 0.9198
My doubts concern the second question: I think I should use the rate of change of momentum, but I'm not sure how to continue this...

Tell us what you've learned about the macroscopic momentum balance equation, and discuss how it might be applied to this problem. Also, tell us why your first equation is not a momentum conservation equation.