Indicating the meaning of the symbols used write mathematical expressions for raynold number? how does its value determine the nature of flow of a fulid ? show that raynold number is a pure number having no dimensions

Dear student, Reynold's Number Formula The Reynold's number is used to describe fluid flow. Flow can be laminar, turbulent, or between these two states (a transient flow). It is found by dividing the fluid's inertial force by its viscous force. The Reynold's number is unitless. Low Reynold's numbers indicate laminar flow, meaning it is smooth and constant. High Reynold's numbers indicate turbulent flow, meaning it is chaotic. Values in between indicate transient flow, meaning the flow changes with time. The Reynold's number can be used for a number of fluid flow situations, as well as objects moving through fluids. R = ( ρvL)/μ R = Reynold's number (unitless) ρ = the density of the fluid (kg/m3) v = the velocity of the fluid (m/s) L = the "characteristic length"or diameter of the fluid flow (m) μ = the viscosity of the fluid For a circular pipe, the characteristic length is the diameter of the pipe. The boundaries between the types of flow are: Laminar flow when R < 2300 Transient flow when 2300 < R < 4000 Turbulent flow when R > 4000. For dimensional proof part, please post that in different thread we will provide you the answer. Regards