The Reynolds number and the Womersley number are the only two physical parameters necessary to solve an incompressible fluid flow problem.  The Reynolds number is given by:
The terms of the equation itself represent the following:
When the Reynolds number is large, it shows that the flow is dominated by convective inertial effects; When the Reynolds Number is small, it shows that the flow is dominated by shear effects.
The Womersley number is given by:
which is simply the square-root of the Stokes Number; the terms of the equation itself represent the following:
When the Womersley number is large (around 10 or greater), it shows that the flow is dominated by oscillatory inertial forces and that the velocity profile is flat. When the Womersley parameter is low, viscous forces tend to
dominate the flow, velocity profiles are parabolic in shape, and the center-line velocity oscillates in phase with the driving pressure gradient.
Starting with Navier–Stokes equation for Cartesian flow:
The terms of the equation itself represent the following:
Ignoring gravitational forces and dividing the equation by density () yields:
where  is the kinematic viscosity. Since both the Reynolds and Womersley numbers are dimensionless, Navier-Stokes must be represented as a dimensionless expression as well. Choosing , , and  as a characteristic velocity, frequency, and length respectively yields dimensionless variables: 
Dimensionless Length Term (same for y and z):, 
Dimensionless Velocity Term (same for v and w): , 
Dimensionless Pressure Term: ,
Dimensionless Time Term: .
Dividing the Navier-Stokes equation by   (Convective Inertial Force term) gives:
With the addition of the dimensionless continuity equation (seen below) in any incompressible fluid flow problem the Reynolds and Womersley numbers are the only two physical parameters that are in the two equations: