# Laminar Poiseuille Flow Through a Pipe

In this application, AcuSolve is used to simulate the
flow of carbon dioxide (CO_{2}) 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

_{2}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 CO

_{2}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

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. The computation cost of the solution is reduced significantly due to the use of extruded elements in the streamwise direction and the fully established flow profile that is assigned.

## Simulation Settings for Laminar Poiseuille Flow Through a Pipe

SimLab database file: <your working directory>\pipe_laminar\pipe_laminar.slb

Global

- Problem Description
- Flow Type - Steady State
- Turbulence - Laminar

- Auto Solution Strategy
- Relaxation factor -
`0.2`

- Relaxation factor -
- Material Model
- CO2
- Density
`1.808`kg/m3 - Viscosity
`1.46e-5`kg/m-sec

- Density

Model

- CO2
- Volumes
- Fluid
- Element Set
- Material Model - CO2

- Element Set

- Fluid
- Surfaces
- Inflow
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
- Advanced Options
- Integrated Boundary Conditions
- Mass Flux
- Type - Constant
- Constant value -
`-2.6625e-05`kg/sec

- Mass Flux

- Integrated Boundary Conditions

- Outflow
- Simple Boundary Condition - (disabled to allow for periodic conditions to be set)

- Wall
- Simple Boundary Condition
- Type - Wall

- Simple Boundary Condition

- Inflow
- Periodics
- Periodic 1
- Individual Periodic BCs
- Velocity
- Type - Periodic

- Pressure
- Type - Single Unknown Offset

- Velocity

- Individual Periodic BCs

- Periodic 1

## References

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