Reynold's number
Reynold's number is a dimensionless number allotted empirically to the circumstances in which the turbulence occurs in fluids flowing through the vessels. It takes into account the diameter of the vessel, the velocity of the flow, and the viscosity and density of the fluid. A convenient number, called as Reynolds number, can be used for approximating the transition between turbulent and laminar flow. The Reynolds number is the ratio of flow rate to viscosity. Reynolds number (Re) is the ratio of inertial forces to viscous forces and can be given by the formula:
Re = ρVD/μ
where V = velocity, D = pipe diameter, ρ = density of the fluid, and μ = fluid viscosity. Laminar Flow is there if R is less than 63 and Turbulent Flow exists if R is greater than 63. It can be defined as a dimensionless number which is significant in the design of a model of any system in which the effect of viscosity is significant in controlling the velocities or the flow pattern of a fluid; equal to the density of a fluid, times a characteristic length, times its velocity, divided by the fluid viscosity. The Reynolds number is important 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 among the fluid inertia and the sheer stress as a result of viscosity. If the Reynolds Number is large, the effect of viscosity is small. A small Reynolds Number gives laminar flow while the high Reynolds Number gives result to the turbulent flow. For a laminar and a turbulent boundary layer both increasing Reynolds Number gives lower skin friction drag. However, due to the higher energy loss in the boundary layer, a turbulent layer has higher skin friction drag always. A high value of Reynold's number signifies that the viscous forces are small and the flow is inviscid.