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)

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