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In multiphase flow the Darcy friction factor can be calculated as Darcy friction factor Single-phase @model with specific approximation of Reynolds number:

$\begin{array}{l}\displaystyle {\rm Re} = \frac{\rho_L \, v_L^2 \, d_L^2 + \rho_g \, v_g^2 \, d_g^2}{\mu_L \, v_L \, d_L + \mu_g \, v_g \, d_g}\end{array}$

where

Derivation

Reynolds number represent the ration of intertial forces to viscous forces:

$\begin{array}{l}\displaystyle {\rm Re} = \frac{\rm Intertial \ Forces}{\rm Viscocus \ Forces}\end{array}$

Reference

L. E. Ortiz-Vidala, N. Mureithib, and O. M. H. Rodrigueza ,TWO-PHASE FRICTION FACTOR IN GAS-LIQUID PIPE FLOW, Engenharia Térmica (Thermal Engineering), Vol. 13, No. 2, December 2014, p. 81-88

Shannak, B. A., 2008, Frictional Pressure Drop of Gas Liquid Two-Phase Flow in Pipes, Nuclear Engineering and Design, Vol. 238, pp. 3277-3284.

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Darcy friction factor Multiphase @model

Reference