Volumetric Flow Rate
The conservation of mass equation can be simplified if the fluid is incompressible and the control volume size is fixed.
First, if the density of the fluid is constant (doesn’t change with time or position) the density term can be brought outside of the integrals and the Conservation of Mass equation can be written as
Cancelling the density results in the equation
Second, if in addition to the density being constant, the control volume size is constant, then the Conservation of Mass Equation becomes
This equation states that the net volumetric flow rate is equal to zero.
Definition of volumetric flow rate, assumptions associated with volumetric flow rate, how to apply the conservation of mass and volumetric flow rate.