For example we have to simulate flow in simple cylinder. We have its length (L), diameter (2R), input and output pressure (pInput, pOutput).
Make an assumption that this flow is a Poiseuille flow, we can calculate velocity depending on the parameter r (length from the axis of the cylinder) according to the Poiseuille equation:
v = (pInput-pOutput) * (R^2 - r^2) / (4kinematicViscosityL)
and which value of physical velocity I should take into account in equation:
dt_ph = u_lb * dx_ph / u_ph (later I need it to calculate tau and nu_lb)
dt_ph - delta t physical
dx_ph - delta x physical
u_lb - velocity in lb units
it’s a matter of choice. your reference velocity can be the average or the maximum value on the poiseuille profile. reference quantities are introduced so that we’re able to compare the same thing in different units. which means: you can take either value as a reference, but you must adopt the same choice in all units. and, you must adopt the same choice as your colleagues if you want to compare your simulation with theirs and you’d like to say things like “i have the same reynolds number”.
So, for example
I want to simulate blood flow and I know that this flow will be a Poiseuille flow.
And I think that if i get uMax to calculate all lb quanties and next I get uAverage to calculate all lb quanties
I will receive different results because for example tau will be different
So how to do If we want to be as close to real process as possible?
tau may vary, but the reynolds number will be the same. and in an incompressible flow, the reynolds number is the only independent parameter. this is why you can put a model airplane into a wind tunnel and get the same flow as for the real airplane, although none of the reference quantities (length, velocity, and sometimes viscosity) is the same. the reynolds number is the same, and this is what matters.