The use of conservative form depicts that the advective flux rate of  out of a control volume at the interface  is exactly equal to flux rate of I to the next control volume and so on.
The meaning of calling Eq. (10.1) as “conservative form” is now clearly understood. However, the conservative form of advective part is of prime importance for modeling fluid flow and is often referred to as week conservative form. For the incompressible flow in Cartesian coordinate this form is:
If all the terms in the flow equation are recast in the form of first-order derivative in  and  the equations are said to be in strong “conservative form”.
We shall write the strong conservation form of Navier-Stokes equation in Cartesian coordinate system:
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