REYNOLDS NUMBER

REYNOLDS NUMBER

In fluid mechanics, the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.
Reynolds numbers frequently used to characterize different flow regimes, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce random eddies, vortices and other flow instabilities. Reynolds numbers can be greatly varied depending on the temperature of fluids, viscosity, and also the elevation at which the experiment is conducted.

The Reynolds Number is a non dimensional parameter can be given as
Re = ρ VL/µ = VL/υ = QL/υ A

where:
• V is the mean fluid velocity (SI units: m/s)
• L is a characteristic length, (traveled length of fluid) (m)
• μ is the dynamic viscosity of the fluid (Pa•s or N•s/m² or kg/m•s)
• ν is the kinematic viscosity (ν = μ / ρ) (m²/s)
• ρ is the density of the fluid (kg/m³)
• Q is the volumetric flow rate (m³/s)
• A is the pipe cross-sectional area (m²)
Experimental observations determine the type of flow, laminar flow occurs when Re < 2300 and turbulent flow occurs when Re D > 4000. In the interval between 2300 and 4000, laminar and turbulent flows are possible ('transition' flows), depending on other factors, such as pipe roughness and flow uniformity).
APPLICATIONS:
• It is used to determine the type of flow.
• The physical stability of suspensions depends on the rate of settling of particles. For this study, rate of sedimentation of particles Stokes’ law is used. Hence type of flow (whether laminar or turbulent) is important.
• The rate of heat transfer in liquids also depends on the flow, whether laminar or turbulent.
REFERENCES:
http://en.wikipedia.org/wiki/Reynolds_number
Text book of pharmaceutical engineering by C.V.S. Subbramanyam