# Poiseuille Flow with a constant external force (gravity)

Hi all,

I am simulating a Poiseuille Flow in a 2D channel.

My system in dimensionless units is the following:

Ref vel = 0.01
Re = 6
Resolution = 100
Lx (channel length) = 2
Ly (channel heigth) = 1

My boundary conditions are the following:
-Periodic on the x axis;
-No-slip condition on the top and the bottom of the channel (y-axis) implemented via the use of addVelocityBoundaryCondition1N (bottom) and addVelocityBoundaryCondition1P (top)

The lattice is initialized at equilibrium with constant density 1.

A force is applied via the Guo External Force BGK Dynamics: therefore, I am aiming to reproduce a parabolic Poiseuille velocity profile.

According to He-Zou (1997), the force is related to the maximum velocity in the profile via the equation:

U[sub]c[/sub] = L[sup]2[/sup] G / 8 nu

where L is the height of the channel (the typical length), nu is the viscosity and G is related to the force via F = rho G

According to the chosen units, L is 1, nu is 1/6 and, via the chosen Guo dynamics, I set an external force with value force = 10[sup]-2[/sup]. If I am not mistaken, as F = rho G, also G is then 10[sup]-2[/sup].

Indeed, I succesfully manage to reproduce the parabolic profile, but my question concerns some numerical factors.
According to my estimations, I would expect Uc to be 0.75 x 10[sup]-2[/sup], but thatâ€™s definitely not the case. Instead, I get really high speeds. When, on the contrary, I set G = 10[sup]-6[/sup], I get Uc = 0.75. Therefore, there is a factor of 10[sup]-6[/sup] in G that I do not retrieve when performing the unit conversions.

Where does this 10[sup]-6[/sup] factor arise? Am I doing something wrong with the unit conversions? Any help is warmly welcome!

Alessio