# 5.3.2.1: Non Deformable Control Volume

- Page ID
- 702

For this case the volume is constant therefore the mass is constant, and hence the mass change of the control volume is zero. Hence, the net flow (in and out) is zero. This condition can be written mathematically as

\[

\label{mass:eq:cvCmCV}

\overbrace{\dfrac{d\,\int}{dt}}^{ = 0} \longrightarrow

\int_{S_{c.v.}} V_{rn} dA = 0 \tag{13}

\]

or in a more explicit form as

Steady State Continuity

\[

\label{mass:eq:cvCmCV1}

\int_{S_{in}} V_{rn}\, dA = \int_{S_{out}} V_{rn}\,dA = 0 \tag{14}

\]

Notice that the density does not play a role in this equation since it is canceled out. Physically, the meaning is that volume flow rate in and the volume flow rate out have to equal.

### Contributors

Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.