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Reynolds Number Calculations

NOTE: It is true that flow is typically considered "laminar" when the Reynolds Number is less than 2,300.

But.....

for the proposes of the design of separation equipment that utilize inclined plates, a series of baffles or separation media of any kind, a Reynolds Number of less than 500 is the industry norm (less than 300 preferred).

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

  • dynamic pressure (ρ u2) and
  • shearing stress (μ u / L)

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

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)

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)

Online Reynolds Calculator

Below are two links to online Reynolds Number Calculators.

Reynolds Number Calculator

Reynolds Number Calculator