Conservation of mass is one of the first checks in a flow calculation. For steady incompressible flow through a single inlet and outlet with no leakage, the volumetric flow rate is the same at both sections.
Key idea
Q = A × Ū, where Q is volumetric flow rate, A is cross-sectional area, and Ū is the cross-sectional mean normal velocity.
Understand the idea
Velocity can vary across the section. Multiplying area by the centreline velocity generally gives the wrong flow rate. The mean velocity represents the area average of the component normal to the section.
Engineering example
If water flows at a mean speed of 0.5 metres per second through a cross-section of 0.002 square metres, the volumetric flow rate is 0.001 cubic metres per second: one litre per second. If the area halves while the same incompressible flow rate passes through, the mean speed doubles.
Checkpoint
If the outlet area is one quarter of the inlet area, how does the mean speed change?
Under the stated steady incompressible assumptions, it becomes four times as large. The product of area and mean velocity remains constant.
A practical check
In a computational result, compare the inlet and outlet mass flow rates and report the imbalance with a clear normalization. A small residual alone does not establish conservation or overall accuracy.