Comparison of the Exact and Approximate Values of Certain Parameters in Laminar Boundary Layer Flow Using Some Velocity Profiles

Abstract

We apply second, third, fourth, fifth and sixth order velocity profiles to discuss laminar boundary layer flow over a flat plate. Inclusion of these velocity profiles in Von Karman-Pohlhausen (1921) momentum integral equation enables us to determine the approximate values of the parameters namely, (i)  boundary layer thickness, (ii) displacement thickness, (iii) momentum thickness, (iv) thickness ratio, (v) skin friction coefficient, (vi) drag coefficient and (vii) the shear rate relation on the plate. Comparison of the approximate values with the exact Blasius (1908) values leads to the determination of the percentage error for each of the above parameters for the different velocity profiles. From the sixth order velocity profile we can predict that higher order velocity profiles will yield greater percentage errors and hence worse and worse results for these parameters except displacement thickness.