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The Reynolds Number is a nondimensional 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)
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)
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 (nondimensional)
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
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 x 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)
The calculator below can be used if the density and the absolute (dynamic) viscosity of a fluid is known.
The default values are based on an air at 60oF, 2 atm and density 0.146 lbm/ft3, flowing 20 ft/s between two metal sheets with characteristic length 0.5 ft. Dynamic (absolute) viscosity is 1.22 10-5 lbm/s ft.
The calculator below can be used when the kinematic viscosity of a fluid is known. The default values are for water at 60oC with a kinematic viscosity of 1.13 10-6 m2/s in a schedule 40 steel pipe. The characteristic length (hydraulic diameter) of the pipe is 0.102 m.
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