Solving the Force Due to Pipe Bend Problem: Conservation of Momentum Approach

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The discussion revolves around calculating the horizontal component of force at a flanged joint in a pipe bend, focusing on the conservation of momentum approach. The user initially struggles with applying the momentum flux equation, considering the flow's steady state and the relationship between velocities and areas. They question whether to use pressure at A1 or A2 due to the discharge to atmosphere. Ultimately, the user resolves their confusion by recognizing the need to differentiate between the resultant vector and the component of velocity in their calculations. The problem highlights the importance of correctly applying fluid dynamics principles in practical scenarios.
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I have question that I'm sure has been asked before. Maybe if you could point me to a thread that'd be great.

The water flows steady discharging to atmosphere. I need to find the horizontal componant of force in the flanged joint & find if it's in tension or compression.

I think I have a Conservation of Momentum problem that I can't figure what I'm doing wrong. I have attached the problem. I figured that due to uniform, steady flow Q=constant so that V1A1=V2A2. So with that I plugged into the momentum flux equation.

=density of water((v2^2)(A2)(cos30)-(V1^2)(A1))+(Pressure)(A2)

If it discharges to atmosphere then I thought maybe it's Pressure(gage)(A1) instead of A2? I think I'm all over the place with this one.



Thanks for any assistance clearing the fog
 

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Sorry, reattached.
 

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Never mind I figured it out. Thanks anyway. I was using for my V2 the resultant vector for both V's. One is the magnitude in the dot product the other V is the vector found by the Vcos(30).
 
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