Frequently Asked Question

Compressibility and waves

Compressibility matters when density changes influence continuity, momentum, energy, or wave propagation. Mach number compares flow speed with acoustic speed, while temperature and pressure are coupled through thermodynamic closure. Shocks and expansions create strong gradients and require conservation-consistent treatment. Static and total quantities must never be mixed without stating the reference frame and thermodynamic definition.

M is Mach number, U is speed, a is acoustic speed, γ is heat-capacity ratio, R is the specific gas constant, and T is absolute temperature.

Worked example

At U = 340 m/s and a = 340 m/s, M = 1.0. A temperature change alters acoustic speed and therefore the local Mach number even if velocity is unchanged. Use absolute temperature and properties consistent with the gas composition.

Check: compare total-pressure loss, static-pressure recovery, shock position, and energy conservation using consistent planes.

Engineering check

For Reynolds, Mach, Prandtl, and Peclet Numbers, 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.

Engineering note

For Reynolds, Mach, Prandtl, and Peclet Numbers, state the intended use, input range, dominant mechanism, units, boundary conditions, acceptance criterion, and evidence owner. Use an independent balance, limiting case, repeat measurement, or sensitivity check to challenge the result. Document the configuration and uncertainty so another engineer can reproduce the reasoning and determine whether the result remains valid after a design, material, boundary, or process change.