[m.gos]

I need some help in understanding some of the governing equations of computational fluid dynamics. I already have some books to read, others are on their way, yet I still find it difficult because I learn much better on examples rather than pure theory. I was hoping someone could 'read out' for me the equations below in a semi-mathematician semi-fluid-dynamicist manner, if you know what I mean.
I know local derivatives, substantial derivatives (total derivative with respect to time), but when it comes to reading equations with understanding I get confused.
First set of equations refers to mass transfer (continuity equation) and is as follows:
http://img855.imageshack.us/i/chds.png/
Second set of equations refers to RENS (Raynolds-averaged Navier-Stokes) k-e turbulance model, so a bit more complicated, but all I really need are the firs two equations - I am sure with that I can do the rest myself:
http://img846.imageshack.us/i/nitf.png/

To give an axample I will give it a try with the 2nd equation from the second set:
The equation is a partial differential form of the continuity (mass conservation) equation. It states that for the considered element of fluid the sum of the time rate of change of density at the fixed point in space (local derivative) and the time rate of change of (mass flow?) equals zero. Does it make sense? Can someone do a similar thing with other 3 equations?

Cheers


Thank you in advance,
Mat