In 1904 Prandtl showed that the effects of viscosity at a high Reynolds number could be represented by approximating the Navier–Stokes equations with the celebrated boundary-layer equations, which for two-dimensional steady flow reduce to:

Here,

and

are the coordinates parallel and perpendicular to the body surface, respectively.

For a semi-infinite wedge with an angle of taper

, one can prove that far from the wedge the potential flow is given by

, where

or

, and

is a scale factor.

The above boundary-layer equations admit a self-similar solution such that the velocity profiles at different distances

can be made congruent with suitable scale factors for

and

. This reduces the boundary-layer equations to

*one ordinary differential equation.*Let us introduce a function

such that:

where

.

Then, we have from continuity equation:

.

The boundary-layer equations can be written as follows:

with

and

The above equation can be solved for a user-set value of parameter

when

and

using the shooting technique. The limiting case

is flow over a flat plate (Blasius problem). Using the following definitions of

and

, one can obtain the particle trajectories (streamlines) for different starting points. This Demonstration plots such trajectories and also shows the growth of the boundary-layer

(red curve) in a separate plot for any value of the wedge angle. The evolution of the

-velocity component and its congruent properties with the growth of the boundary layer is also shown.