Lecture 11: Control mass, control volume, mass-, momentum-, kinetic energy balance
Let us give physical interpretation to the above three forms of the theorem.
The first term is the rate of change in the property contained in the CV, which is fixed in the flow field. This term also describes if the property is under steady state or not, or if there is any accumulation of the property, N in the CV.
The 2nd term represents the material rate of change of the property and may be seen as the rate of generation of the property. Note that if because mass of the fluid particles initially marked in CV cannot change, nor it can be generated or destroyed, as the particles move in the flow field.
The 3rd term represents the net rate of change in the property because of the flow of the fluid in and out of the CV through CS. is the rate of volumetric flux in and out of dA, a differential area on CS. is the rate of mass flux. is the rate of the property-flux in and out of the differential areais the rate of the total property over the entire CV.
Take a simple CV in the flow field, shown by the dotted line.
(Fig. 11b)
It is easier to show that the last term
In such case, the fluid enters and leaves the CS only through and . The remaining surface of CS is impervious to the mass.
because mass of the fluid particles initially marked in CV cannot change, nor it can be generated or destroyed, as the particles move in the flow field.
and 
. The remaining surface of CS is impervious to the mass. 
