Finite Volume model of 1D fully-developed pipe flow

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Overview

This page has links to MATLAB code and documentation for the finite volume solution to the one-dimensional equation for fully-developed flow in a round pipe

$$\frac{\mu}{r}\frac{\partial}{\partial r}\left(r\frac{\partial u}{\partial r}\right) - \frac{\partial p}{\partial x} = 0$$

where $u$ is the axial velocity, $p$ is the pressure, $\mu$ is the viscosity and $r$ is the radial coordinate. This is a simple and well-known flow with the exact solution

$$u(r) = u_\mathrm{max} \left[ 1 - \left(\frac{r}{R}\right)^2\right] \qquad u_\mathrm{max} = \frac{R^2}{4\mu}\left( -\frac{\partial p}{\partial x} \right)$$

where $R$ is the pipe radius.

The utility of this code archive is that it shows how to derive the finite-volume model in radial coordinates. The model code also gives an example of how mesh refinement improves the accuracy of the numerical model.

Downloads

• Code archive for solving the equation for fully-developed laminar flow in a round pipe.
• Documentation for the finite volume applied to fully-developed laminar flow in a round pipe.

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