Frequently Asked Question

Mass conservation

Mass conservation states that mass cannot be created or destroyed inside a control volume. The local equation balances density accumulation with net mass flux. For constant-density flow it reduces to a divergence-free velocity field; for variable-density flow, density remains inside both the accumulation and flux terms. The same principle provides a direct engineering check on any flow calculation.

ρ is density, t is time, and u is velocity. An integrated control-volume form compares the sum of mass entering and leaving with accumulation.

Worked example

If 0.80 kg/s enters a domain and 0.78 kg/s leaves, the imbalance is 0.02 kg/s. Relative to inlet flow, the imbalance is 0.02/0.80 = 2.5%. If the study requires a one-percent mass balance, the solution is not ready for that conclusion. Check boundary normals, leakage, density variation, source terms, and numerical conservation.

Reporting: state whether imbalance is absolute, normalized by inlet flow, or normalized by a reference flux.

Engineering check

For Conservation Laws and Control-Volume Thinking, report the governing output together with the reference condition, mesh or model assumptions, boundary data, convergence evidence, and sensitivity to the dominant input. Check a conservation balance or limiting case before comparing the result with a requirement. If the output changes materially under a reasonable refinement or input variation, the conclusion should be treated as conditional rather than final.