The formulation of governing equations of fluid dynamics is based on 3 conservation laws (mass, momentum and energy). However, how can I explain that the momentum is conserved, and thus it can be used to derive the momentum equation? Please help.

That momentum is conserved is one of the laws of mechanics. It is rather an axiom and cannot be proved. When friction is present as in viscous fluids, momentum is not conserved in the strict sense of the word but we know how it is going to be destroyed. The rate at which momentum is lost is equal to the rate at which dissipative mechanisms destroy momentum. So in general a quantity is said to be conserved if

rate of change of quantity in a control volume = rate of production/destruction + rate at which it is transported in/out of the control volume

F = m * a where F is the net "external" force on the system

m is the mass of the system of interest

and a = Dv/Dt is the acceleration. (Note: D/Dt is the "material" derivative)

Just another observation (question) regarding momentum,

Angular momentum? How many CFD codes actually conserves (solves for) angular momentum as well as linear momentum? Is it not important that angular momentum be conserved as well?

I know that the equations of angular momentum does not form part of the traditional Navier Stokes equation set, why??

My common sense tells me that we are actually building an additional error into the formulation by disregarding the effects of angular momentum on the flow field? Any comments on this issue?

In fluid mechanics the angular momentum equation is not a separate equation to the momentum equation (in solid mechanics it is).

Tom.

Conservation of angular momentum is already contained in the equations of fluid mechanics. The symmetry of the stress tensor ensures this. I cannot comment whether numerical methods also conserve angular momentum.

If you wish to numerically conserve angular momentum instead of the swirl component you may by rearranging the flux term (but you cannot strictly conserve both). This rearrangement is quite common for RANS codes targeted at swirling jets where the strict conservation of angular momentum is physically more desirable.