Reynolds number is a dimensionless number that is a ratio of a fluid’s inertia and the viscous effects on the fluid. Equation 1 is used to describe Reynolds number.

**(Eq 1) ** $Re=\frac{ρvD}{μ}$

Re = Reynolds Number

ρ = Density

v = Fluid Velocity

D = Pipe Diameter

μ = Dynamic Viscosity

### Laminar, Translation, & Turbulent Flow

One of the main uses of Reynolds number is to describe the flow of a fluid going through a pipe. Reynolds number can be used to determine whether the fluid’s flow is laminar or turbulent flow. If the Reynolds number is less than 2100 for a round pipe then the flow can be considered laminar, while if the Reynolds number is above 4000 the flow through a round pipe can be considered turbulent. Finally, if the Reynolds number is in between 2100 and 4000 then the flow is transitional, which means part of the flow is laminar while part of it is turbulent.

The reason why it is important to know if a fluids flow is turbulent or laminar is because the fluid will behave differently since the particles for a laminar flow follow a stream line, while fluid particles for a turbulent flow follow their own random paths.