Conservation of mass in a pipe

The distributed nature of long pipes has implications for how the conservation principles apply. We will begin by developing the equation for the conservation of mass. 

All variables are functions of both time and distance. Hence at any time, t, the values at the reference distance x are  

By geometry, the mass flow into the pipe element is  

The mass of the pipe element is the volume divided by the specific volume  

We may now invoke the principle of the conservation of mass as applied to the pipe element, as given by equation (3.28)  

---