Scaling the Hydraulic Efficiency of a Drag-Reducing Agent

The purpose of this article is to deduce the dependence of the hydraulic efficiency of drag-reducing agent on real objects on the hydraulic efficiency of drag-reducing agent in bench or laboratory conditions for two cases: smooth and rough pipeline wall. The method used in this article is a mathematical analysis of the dependenciesof the efficiency of drag-reducing agent in pipelines of different diameters with different roughness of the pipeline wall.This article analyzes the dependencies for calculating the coefficient of hydraulic resistance during flow in pipelines of various diameters. The dependence of the hydraulic efficiency of the drag-reducing agent on the diameterof the pipeline is analyzed. In the course of transformations, including using the Lambert function, an explicit dependence of the hydraulic efficiency of drag-reducing agent under conditions of different diameters for smooth pipes and an implicit dependence for rough pipes was revealed.