Streamline flow through curved pipes

TLDR

The study examines flow in curved pipes, focusing on shear stress, gravitational acceleration, hydraulic mean depth, mean velocity, fluid density, and viscosity, noting that most parameters are dimensionless unless otherwise specified. The authors introduce a numerical coefficient C = F d / (8 μ v) to quantify curvature‑induced resistance, along with mean coil diameter D, curvature ratio d / D, and frictional drag intensity F on the pipe wall.

Abstract

C, a numerical coefficient , defined, as F d /8 μv representing the increase of resistance due to curvature, d , diameter of pipe. D, mean diameter of coil. d /D, curvature ratio. F, intensity of frictional drag on wall of pipe, i. e . shear stress at boundary, g , gravitational acceleration, m , hydraulic mean depth, = area/perimeter, v , mean velocity of flow, = volume flowing per unit time/cross sectional area of pipe, ρ , density of fluid, μ viscosity of fluid. All the values given in the paper are dimensionless, except in those cases in which some dimension is specifically stated.