Blasius Solution for the Flat Plate (No Pressure Gradient)

In incompressible flow, the self-similar solution due to Blasius is based on the idea that the u-velocity profile is of the form

where, as seen before, S(x) ~ , and n = Уф. If one introduces the stream

function ф(х, y) = US(x)F(n), the governing equation for F(n) is:

FF” + 2 F= 0 (8.79)

The boundary conditions are as follows

• at n = 0: F = F’ = 0,

• as n F’ ^ 1.

The numerical solution of Blasius yields the results

Note that Co/ = 2Cf (l) = 26(l)/1.