text: As a measure of flow compressibility, the Mach number can be derived from an appropriate scaling of the continuity equation. The full continuity equation for a general fluid flow is:<math display="block">{\partial \rho\over{\partial t}} + \nabla\cdot(\rho {\bf u}) = 0
  \equiv -{1\over{\rho}}{D\rho\over{Dt}} = \nabla \cdot {\bf u} is the material derivative,  is the density, and  is the flow velocity.  For isentropic pressure-induced density changes,  where  is the speed of sound.  Then the continuity equation may be slightly modified to account for this relation:The next step is to nondimensionalize the variables as such:where  is the characteristic length scale,  is the characteristic velocity scale,  is the reference pressure, and  is the reference density.  Then the nondimensionalized form of the continuity equation may be written as:where the Mach number . In the limit that , the continuity equation reduces to  &mdash; this is the standard requirement for incompressible flow.