# 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

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

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.