I'm currently working on the development of a chock-absorber based on liquid cristal technology, and i would like to know how i could determine the reynolds number in a square duct where flows a Liquid cristal? This should allow me to say if the flow is theoretically turbulent or laminar in that duct.

(1). Re = ( U * L )/ znu; where U is the average velocity (derived from the mass flow/(density*area) ), L is the duct width, znu is the kinematic viscosity (viscosity/density).

if the duct is non-circular it is standard to use the hydraulic diameter for your length scale where the hydraulic diameter you can find the definition of hydraulic diameter in any basic fluids book