# Laminar Poiseuille Flow Through a Pipe

In this application, AcuSolve is used to simulate the flow of carbon dioxide (CO2) entering a pipe with a fixed velocity. AcuSolve results are compared with analytical results using the Hagen-Poiseuille approach as described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with constant flow velocity.

## Problem Description

The problem consists of CO2 flowing through a circular pipe 0.0025 m in diameter and 0.01 m long, as shown in the following image, which is not drawn to scale. The CO2 enters the pipe with an average inlet velocity of 3.0 m/s. The flow field develops as a result of the viscous shearing on the fluid at the pipe wall.

## AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. The pressure decreases along the length of the pipe.
The analytical pressure drop between the inlet and the outlet is presented with the corresponding AcuSolve result in the following table.
Table 1.
Analytical pressure drop (Pa) AcuSolve pressure drop (Pa) Percent deviation from analytical
Inlet to outlet pressure drop 2.242 2.245 0.099

## Summary

The AcuSolve solution compares well with analytical results for laminar flow through a pipe. In this application, the pressure drop along the length of the pipe is caused by the viscous shearing near the pipe wall. The AcuSolve steady state solution compares well with the analytical solution, with less than 0.1 percent error.

## Simulation Settings for Laminar Poiseuille Flow Through a Pipe

AcuConsole database file: <your working directory>\pipe_laminar\pipe_laminar.acs

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Laminar
• Auto Solution Strategy
• Relaxation factor - 0.2
• Material Model
• CO2
• Density 1.808 kg/m3
• Viscosity 1.46e-5 kg/m-sec

Model

• Volumes
• Fluid
• Element Set
• Material Model - CO2
• Surfaces
• Inflow
• Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
• Integrated Boundary Conditions
• Mass Flux
• Type - Constant
• Constant value - -2.6625e-05 kg/sec
• Outflow
• Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
• Wall
• Simple Boundary Condition
• Type - Wall
• Periodics
• Periodic 1
• Individual Periodic BCs
• Velocity
• Type - Periodic
• Pressure
• Type - Single Unknown Offset

## References

F. M. White. "Viscous Fluid Flow". Section 3-2.1. McGraw-Hill Book Co., Inc.. New York. 1991.