[MAMAD]

Dear all
I have a simple question but i am a little confused!
I solved a simple internal flow of a converging nozzle and now i want to compute the force on the body. I calculate it in two ways
1- i used a control volume outside of nozzle (using pressure and momentum at inlet & outlet)
2- i used a CV inside the nozzle (Integrating pressure on walls)
But i got different answers i dont know why???
PLEASE help me !!!

[LuckyTran]

This is a common mistake in CV analysis when trying to apply concepts learned from 1D control volumes in constant area ducts to non-constant area problems.

The only way to compute the force is to do a control volume analysis on the entire system, inlets & outlets & walls. You cannot do a control volume on only the inlet & outlet (those are only control surfaces). Likewise your control volume cannot only include the walls and not the inlet and outlet (still a control surface).

[MAMAD]

Dear Lucky Tran
Thanks for your response but i didn't get the point
what do you mean about non constant area? do you mean the 1D boundary assumption?
when i use the CV outside the nozzle, there is nothing on the nozzle acting except at control surfaces. we did this in fluid mechanics and there was nothing on walls!
i see the example in almost all fluid mechanic books!
what should i do? should i take into account pressure on body and momentum at in/outlet?

thank again!

[LuckyTran]

Sorry I got confused, thought you were trying to calculate thrust.

Integrating only the pressure only gives the pressure force and doesn't give you the viscous force. You need to include the wall shear stress also when you do the integration. Maybe that's the problem?

[MAMAD]

Dear LuckyTran

Viscose terms are not so big!!!
the flow is supersonic
i attached a figure which i mean about CV inside the nozzle.

Now if i use CV outside (think the dashed line is nozzle and the line is CV) there is no pressure on walls except ambient pressure which we can neglect it on the entire CV.

Thank you