Blasius Solution for the Flat Plate (No Pressure Gradient)

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

S(x) 5.0

x Rex

(8.80)

S*(x) 1.7203 x *fRTx

(8.81)

6(x) 0.664 x Rex

(8.82)

0.664

Cf(x) = vw;

(8.83)

1.328

Df VR*

(8.84)

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

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