What is the Mach number?

• A. The ratio of inertial to gravitational forces
• B. The ratio of dynamic pressure to static pressure
• C. The ratio of viscosity to density
• D. The ratio of fluid velocity to the speed of sound

Answer: (D)

The main idea being tested is how fast the flow is compared with the speed at which pressure disturbances travel in the same fluid. This is captured by the Mach number, defined as the fluid velocity divided by the speed of sound in the medium (M = V / a). Because the speed of sound depends on temperature and gas properties, Mach tells you how important compressibility effects are in the flow. If the velocity is much less than the speed of sound, density changes are negligible and you can treat the flow as incompressible. When the velocity approaches or exceeds the speed of sound, pressure waves can’t propagate upstream quickly enough, leading to significant density changes and phenomena like shocks. This is why Mach numbers around 1 mark sonic flow and higher numbers indicate supersonic behavior. The other ratios describe different physical ideas (for example, inertial effects relative to gravity describe a different flow regime, and simply dynamic versus static pressure isn’t the same as the speed-based comparison), so the ratio of flow speed to speed of sound is the one that directly measures compressibility effects.