Let us consider the law of conservation of mass as applied to the control volume.

Figure 12.1

During a time interval , let the mass enter the control volume and the mass leave the control volume. Let represent the mass inside the control volume at time t, and represent the mass inside the control volume at time (t+dt). The law of conse rvation of mass gives:

	(12.1)
	(12.2)

Here the LHS gives the change in mass within the CV during the interval , while RHS gives the net mass flow into the CV during the time . Dividing both sides of the equation by , we get

(12.3)

In the limiting case as , we obtain

(12.4)

The LHS gives rate of accumulation of mass inside the CV and the RHS has respective terms giving rate of mass entering the CV and rate of mass leaving the CV.

If the CV has many inlet and exit ports, the equation becomes

(12.5)