## Monday, 7 June 2010

### Reynolds Number

The Reynolds Number is a non dimensional parameter defined by the ratio of

dynamic pressure (ρ u2) and

shearing stress (μ u / L)

and can be expressed as

Re = (ρ u2) / (μ u / L)

= ρ u L / μ

= u L / ν (1)

where

Re = Reynolds Number (non-dimensional)

ρ = density (kg/m3, lbm/ft3 )

u = velocity (m/s, ft/s)

μ = dynamic viscosity (Ns/m2, lbm/s ft)

L = characteristic length (m, ft)

ν = kinematic viscosity (m2/s, ft2/s)

Reynolds Number for a Pipe or Duct

For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for a duct or pipe can be expressed as

Re = ρ u dh / μ

= u dh / ν (2)

where

dh = hydraulic diameter (m, ft)

Reynolds Number for a Pipe or Duct in common Imperial Units

The Reynolds number for a pipe or duct can also be expressed in common Imperial units like

Re = 7745.8 u dh / ν (2a)

where

Re = Reynolds Number (non dimensional)

u = velocity (ft/s)

dh = hydraulic diameter (in)

ν = kinematic viscosity (cSt) (1 cSt = 10-6 m2/s )

The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is

laminar when Re < 2300

transient when 2300 < Re < 4000

turbulent when Re > 4000

Example - Calculating Reynolds Number

A Newtonian fluid with a dynamic or absolute viscosity of 0.38 Ns/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s.

The density can be calculated using the specific gravity like

ρ = 0.91 (1000 kg/m3)

= 910 kg/m3

The Reynolds Number can then be calculated using equation (1) like

Re = (910 kg/m3) (2.6 m/s) (25 mm) (10-3 m/mm) / (0.38 Ns/m2)

= 156 (kg m / s2)/N

= 156 ~ Laminar flow

(1 N = 1 kg m / s2)