The Drag Coefficient and the Navier-Stokes Fractional Equation

Abstract

The purpose of this work is to relate the Navier-Stokes fractional equation with the formulae for the drag coefficient, as are those of the Kármán-Schönherr, Prandtl-Kármán, and Nikuradse. The thickness of the boundary layer induces a multifractal description and a generalization of Blasius experimental result for the friction factor; whereas the dimensions are obtained by the approximations of Blasius and Falkner-Skan of the pressure gradient. The number associated with the multifractal characteristics are adjusted, and formulae, under study, are inferred. They are represented as a bi-multifractal, which provides an analytical way to find a critical Reynold’s number, which draws the Kármán-Schönherr formula as appropriate to limit the right of the viscous sublayer. The frictional force is generalized to represent the fractional derivative as a multifractal whose resolution is the reciprocal of the Reynolds number and of appropriate dimension. Thus, the transformation of the moldable wall shapes is described as the result of the action of the frictional force on them.