Reynolds number and friction factors

[Freeman]

Flow Through Circular Pipe

The Reynolds Number (Re), is a dimensionless parameter for characterizing fluid flow. It is the criterion used to determine whether flow is Laminar, Critical (transitional) or Turbulent. Usually for laminar flow Re <> 4000.

The Darcy friction factor is a Reynold number-dependent factor used in the computation of the pressure loss due to pipe roughness. Friction factor is commonly computed via the implicit Colebrook-White equation and more recently by explicit equations by Churchill, and by Swamee & Jain. Colebrook-White and the Swamee-Jain equations were designed for the turbulent flow regime, but will be used here also for the critical regime. Churchill's equation spans the entire range from laminar to turbulent. The Fanning factor and the Transmission factor are derivatives of the Darcy friction factor. The relevant equations are given below:

Reynolds Number Re=VD/ν

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Fanning friction factor ƒf=ƒd/4
Transmission factor F =2/√ƒd

where

Re = Reynolds Number
V = average flow velocity
ν = kinetic viscosity, centistokes
D = pipe inside diameter
ε = absolute internal pipe roughness
ƒ = friction factor
ƒd = Darcy friction factor
ƒf = Fanning friction factor
F = Transmission factor

[hegazyadel]

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