We consider an incompressible viscous fluid flowing through a cylindrical pipe with rough wall. Motivated by the applications, we assume the periodicity of the roughness in the longitudinal direction and that the flow is governed by the prescribed pressure drop between pipe’s ends. The goal of the paper is to investigate the effects of the corrugated boundary on the fluid flow by taking into account the effects of inertia as well. Starting from the Navier–Stokes system and employing the average boundary roughness as the small parameter, we propose a higher-order correction of the standard Hagen–Poiseuille velocity via boundary layer analysis. Using the obtained result we propose the new formula for the Darcy–Weisbach friction coefficient.

我们考虑一种不可压缩的粘性流体，流经具有粗糙壁的圆柱管。根据应用的动机，我们假设在纵向方向上粗糙度是周期性的，并且流量是由管道两端之间的规定压降控制的。本文的目的是通过考虑惯性的影响来研究波纹边界对流体流动的影响。从Navier–Stokes系统开始，并以平均边界粗糙度作为较小参数，我们通过边界层分析提出了对哈根–泊瓦标准速度的高阶校正。利用获得的结果，我们提出了达西-魏斯巴赫摩擦系数的新公式。