Reply To: Porta's Derivation of Lempor Theory
I hope I’ve understood your question correctly, let me know if I’ve missed the point.
My take on this is that it case of “horses for courses”
Conservation of momentum is one of the fundamental laws of physics. To change the momentum of a body it is necessary to apply a force to it. Every force has an equal and opposite reaction, so the body to which the reaction force applies will experience an equal and opposite change in momentum. The total momentum of the system remains constant.
So if you are mixing fluids with different velocities, the overall momentum will remain constant. however the kinetic energy of the mixture will be less that the combined KE of the constituent parts. Therefore it makes sense to use the momentum equation.
If a fluid passes through a nozzle of diffuser, the walls of the nozzle/diffuser will apply a force to the fluid and the momentum of the fluid will change. However, if the nozzle/diffuser is reasonably efficient, the energy of the fluid will remain reasonable constant, based on Bernoulli’s equation, and in this case it makes more sense to use conservation of energy.