I'd like to help, but this looks suspiciously like it could be an exam question. Is it? Or is it a homework question? I guess either way, the following is not an "out-of-bounds" hint.
Think of weighting the momentum balance equation by using the velocity field as a weight function, and integrate over a volume, similar to how one can develop the FE method by using an arbitrary weighting function made of linearly independent basis functions. Additionally, use the divergence theorem to get the boundary integrals into the solution.
Ideas, yes.
I'd like to help, but this looks suspiciously like it could be an exam question. Is it? Or is it a homework question? I guess either way, the following is not an "out-of-bounds" hint.
Think of weighting the momentum balance equation by using the velocity field as a weight function, and integrate over a volume, similar to how one can develop the FE method by using an arbitrary weighting function made of linearly independent basis functions. Additionally, use the divergence theorem to get the boundary integrals into the solution.
Matt Lewis
Los Alamos, New Mexico
In reply to Ideas, yes. by Matt Lewis
Dear Matt, No, is
Dear Matt,
No, is not an exam question, its a homework question which I struggling. I am very thankful for your help, I hope it will help.
When in doubt
As my graduate advisor said, "When in doubt, use the divergence theorem" :) -Nachiket
Enjoying great moments
You probably are not using the definition of kinetic energy...
Forget the right side ... and derive the kinetic energy and use that statement you gave to you.
When you do that, magic happens: balance of mass, incompressibility and Divergence Theorem.
Take care of definitions and all tools that math offer.
I think "GURTIN, M.E. - An Introduction to Continuum Mechanics " a excellent book.
Rodrigo