Hydraulic resistance of plane channels and annulus with different roughness on opposite walls

Abstract

A new method for prediction of hydraulic resistance for a turbulent flow in plane channels and annulus is proposed. In spite of the importance of this issue, only very few publications devoted to the investigation into hydrodynamics in these channels are available, and there are no methods for predicting hydraulic resistance of a flow in these channels at all. The flow in channels with different roughness on the walls is described using the Prandtl semiempirical theory of a turbulent boundary layer. The flow in a channel cross-section is divided into two noninteracting layers of different thickness flowing along the walls with different roughness. The basic balance correlations are derived for a plane channel. To match the velocity profiles of both layers at the interface point, a logarithmic velocity profile is used. This yields a closed system of equations for predicting hydraulic resistance in plane channels with a given different roughness on opposite walls. It is demonstrated that the obtained correlation may be used for predicting hydraulic resistance in annulus as well. Experiments were carried out with a water flow in an annulus. Each annuli consisted of a pipe having a smooth wall into which a rod with artificial roughness on the surface was inserted coaxially. Two types of roughness were investigated: trapezoid and threadlike ones. Comparison of the predictions with the experimental data confirmed the validity of the proposed method. It can be used in designing flowpaths of various power installations.