## Application of Von-Karman Integral Momentum Equation

**Introduction:** An absolute estimate of flat-plate laminar boundary layer properties for

**Application of method A: **Self-similarity of boundary layer velocity profiles signifies that

Where , the boundary layer thickness, = f(x), the distance from the leading edge the boundary layer thickness, = f(x), the distance from the leading edge

The boundary conditions to be satisfied for a boundary layer over a flat plate are:

At y = 0: u = 0, (since ), ,The last condition is imposed by the B L equation :

since LHS = 0 at y = 0.)

and at : u = uo, (since at

Simplest polynomial form of satisfying these is

Now it is found that this form of velocity profile does indeed correspond quite well with measurements for laminar B.L.s over flat plates: so what follows can represent the behavior of such a laminar B.L.Then, by definition, Displacement Thickness

Similarly, for Momentum Thickness :

Therefore

Substituting in Momentum Equation for zero pressure gradient

Local friction coefficient,