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,