Fully developed turbulent pipe flow

Abstract

Incompressible pipe flows are fully developed if the velocities are independent of the axial coordinate. The theory of turbulent pipe flows at high Reynolds numbers leads to analytical expressions for the velocity profile and the friction factor, which contain free constants. One of the latter is the well-known Krmn constant. The free constants can be determined from the best available experimental data. Final formulae for the velocity distribution and the friction factor are derived. Further effects on these laws are also considered, such as wall roughness and low Reynolds number effects. © Springer-Verlag Berlin Heidelberg 2005.