[fabio21]

Hi, I've found two different versions of NS equations and I would enjoy some explanations.
The doubts are related to the diffusive term.

I've found both:

\nu * \nabla^2 u ;
1/Re * \nabla ^2 u ;

I tend to think that the 1st one is more correct, even though some academic notes refer to the 2nd one and I can't figure out why.

Can you please give me some help?

[mprinkey]

The first is assuming dimensional quantities for velocity, length, and time. The second is the dimensionless form that assumes dimensionless velocity, length, etc. based on some characteristic length and time scales. Dimensional analysis is usually taught in first semester fluids, heat transfer, and thermodynamics texts. It is central to flow characterization, especially for experimental work and for tabulation of practical engineering data and model creation. It is not a difficult thing to master.

[fabio21]

Thank you for such a fast and precise reply.
Now I've got it.

May be I've done quite a superficial analysis of the problem, also mislead by the fact that neither any nondimensional hypothesis was stated nor a coherent mathematical notation was used in the notes.

[LuckyTran]

Originally Posted by fabio21

also mislead by the fact that neither any nondimensional hypothesis was stated nor a coherent mathematical notation was used in the notes.

Don't blame the notes. It is common to believe that someone else reading it takes it in the same context. For example, when you wrote....

Originally Posted by fabio21

\nu * \nabla^2 u ;
1/Re * \nabla ^2 u ;

You did not say what nu nabla u or nabla^2 or Re is. They could mean anything. You were just as misleading yet it somehow still made sense to someone.