Reynold's Number:

Reynold's number is a dimensionless number allotted empirically to the circumstances in which turbulence occurs in fluids flowing through vessels. It takes into account the velocity of the flow, the diameter of the vessel, and the density and viscosity of the fluid. A convenient number, called the Reynolds number, can be used for estimating the transition between laminar and turbulent flow. The Reynolds number, a ratio of flow rate to viscosity. Reynolds number (Re) is the ratio of inertial forces to viscous forces and is given by the formula:

Re = ρVD / μ

where ρ = density of the fluid, V = velocity, D = pipe diameter, and μ = fluid viscosity. Laminar Flow exists if R is less than 63 and Turbulent Flow exists if R is greater than 63. It is defined as a dimensionless number which is significant in the design of a model of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid; equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity. The Reynolds number is significant in the design of a model of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern. It is a number that establishes the proportionality between the fluid inertia and the sheer stress as a result of viscosity. If the Reynolds Number is large, the viscosity effect is small. A low Reynolds Number gives laminar flow while a high Reynolds Number gives turbulent flow. For both a laminar and a turbulent boundary layer increasing Reynolds Number gives lower skin friction drag. However, because of the higher energy loss in the boundary layer, a turbulent layer always has higher skin friction drag. A high value of Reynold's number indicates that viscous forces are small and the flow is essentially inviscid.