What is Reynolds Number (Re)?
In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it is used to identify different flow regimes, such as laminar or turbulent flow.
It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flowrates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
It is named after Osborne Reynolds (1842–1912), who proposed it in 1883. Typically it is given as follows:
where:
L = Length
μ = dynamic fluid viscosity
ν = kinematic fluid viscosity
ρ = fluid density
The difference between laminar and turbulent flow:
The transition between laminar and turbulent flow is often indicated by a critical Reynolds number which depends on the exact flow configuration and must be determine through experimentation. It is important for engineers to never design for this transition period, and therefore engineers will generally stay away form about the 2000 to 3000 range to ensure that the flow is either laminar or turbulent (for a circular pipe Retransition is around 2300).
How to determine Reynolds number:
One way to determine Reynolds number is to use Moody's Diagram. Pressure drops seen for fully-developed flow of fluids through pipes can be predicted using the Moody diagram which plots the friction factor(f) against Reynolds number (Re) and relative roughness (ε / D). The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases.
Figure 1: Moody Diagram (Click to Enlarge)