REYNOLDS NUMBER AND FRICTION FACTORS

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 < 2100, for critical flow Re is between 2100 and 4000, while turbulent flow prevails for Re > 4000.

The Darcy friction factor is a Reynold number-dependent factor used in the calculation of the pressure loss due to pipe roughness. Friction factor is commonly calculated 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 R_e=VD/ν

     
   Fanning friction factor ƒ_f=ƒ_d/4
   Transmission factor F =2/√ƒ_d
where
     R_e = Reynolds Number
     V = average flow velocity
     ν = kinetic viscosity, centistokes
     D = pipe inside diameter
     ε = absolute internal pipe roughness
     ƒ = friction factor
     ƒ_d = Darcy friction factor
     ƒ_f = Fanning friction factor
     F = Transmission factor