Impact of a jet of water

Mar 2018
1
0
Hi, I would like some help with the following problem:
"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. Kowing 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).

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 tried to apply again the momentum equation now on the whole system, but I think this is not the right way to solve it...
Thank you in advance for the help.
 

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Jun 2016
1,289
616
England
To get the force, you need the rate of change of momentum.

You say
the volume in transition is V=5,05 L
Do you mean 5.05 liters per second?

remember 1 litre of water masses 1 kg.
 
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