| Abstract: | SUMMARY Basing their studies on an extended Reynolds principle of similarity, the authors present in this paper a thorough theoretical investigation of the turbulent flow in pipes. Making appropriate assumptions regarding the distribution of the turbulent apparent viscosity over the entire pipe diameter, the well-known discharge formulas, i. e. the resistance laws, of Prandtl-V. Kármán for the hydraulically smooth and the hydraulically rough region, and of Colebrook for the transition region—the accuracy of these being well established by measurements—can be clearly shown to be correct. Thus it is also possible to determine the velocity distribution in the region near the wall for the hydraulically smooth region and the transition region, as well as for the hydraulically rough region. The concept, that the flow with a fully developed roughness effect begins when the laminar boundary layer at the wall disappears can be seen to be in close agreement with the asssumptions made. The limits which were established for the hydraulically rough region and the transition region correspond well with the curve plotted by PRANDTL and the boundary curve of Rouse. |
