# 5.3.2.1: Non Deformable Control Volume

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

$\label{mass:eq:cvCmCV} \overbrace{\dfrac{d\,\int}{dt}}^{ = 0} \longrightarrow \int_{S_{c.v.}} V_{rn} dA = 0$

or in a more explicit form as

$\label{mass:eq:cvCmCV1} \int_{S_{in}} V_{rn}\, dA = \int_{S_{out}} V_{rn}\,dA = 0$