transferring unit in the case of inlet and outlet pressure

Hi every body
consider a flow in channel. channel width is H. boundary condition is inlet pressure=Pi and outlet pressure Po.
Note that reynolds is unknown because we dont have any charactristic velocity.
if we consider charactristic length= H then delta_x=1/N(number of nodes). but my question is that How can I found delta_t to transfer unit from lattice to physical unit and vice versa???:((
If one BC was velocity it can be solved easily. For example if inlet=Ui we have:
taking U_charactristic-in-lattice=0.1 and U_charactristic= Ui ::::>> delta_t=U_charactristic-in-latticedelta_x
=========>>>> U=U_charactristic
U_lattice(that we obtain it from solveing LBM)delta_x/delta_t=Ui0.1*delta_x/delta_t
As you see when velocity is known the unit transfer is easy but when we have pressure in inlet and outlet how we can transfer units???:(((((
thanks for your answer

nu_phys = (1/3)(tau-0.5)(dx^2/dt)

Assuming you know your physical viscosity, and lattice spacing, then you can use the equation to calculate timestep.

Dear brucedjones
thank you very very much
but there is some problem
consider I use your proposed equation. if I consider e.g tau=1 then dt can be found. but how I can transfer pressure in real to lattice. you know that pressure dimension is:
kg/(m s^2)
now what about kg???
I really am confused. I read the notes of latt:
Choice of units in lattice Boltzmann simulations
Jonas Latt
but my problems remain:((((
thanks a lot

All the unit conversion factors are a combination of dx, dt and rho0, where,

rho_phys = rho_lb*rho0

Since we use rho_lb ~ 1, rho0 is simply the base density of your fluid.

Looking at the units of these factors we have,

dx = m, dt = s, rho0 = kg/m3,

And you need a conversion from dimless to kg/(m s^2), which would be,


Applying dimensional analysis on that you get,

(kg/m3)*(m2/dt2) = kg/m s2