# Modified Reynolds equation for steady flow through a curved pipe

## TL;DR

This paper derives a modified Reynolds equation for steady, low-Reynolds-number flow in curved, narrow pipes, accounting for large curvature and torsion, with validated approximations of velocity and pressure.

## Contribution

It introduces a new modified Reynolds equation for complex curved channels derived from Stokes equations using asymptotic methods.

## Key findings

- Derived a modified Reynolds equation applicable to highly curved channels.
- Provided validated approximations for velocity and pressure fields.
- Compared results with simpler models to justify accuracy.

## Abstract

A modified Reynolds equation governing the steady flow of a fluid with low Reynolds number through a curvilinear, narrow tube, with its derivation from Stokes equations through asymptotic methods is presented. The channel considered may have large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed by artificially imposing appropriate boundary conditions at the inlet and the outlet. A justification for the approximations is provided along with a comparison with a simpler case.