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@wikipedia


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

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{\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}

where

LaTeX Math Inline
body\rho_L

liquid density

LaTeX Math Inline
body\rho_g

gas density

LaTeX Math Inline
bodyv_L

liquid velocity

LaTeX Math Inline
bodyv_g

gas velocity









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titleDerivation


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

LaTeX Math Block
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{\rm Re} = \frac{\rm Intertial \ Forces}{\rm Viscocus \ Forces}





See also


Physics / Fluid Dynamics / Pipe Flow Dynamics / Darcy–Weisbach equation / Darcy friction factor 



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., doi.org/10.1016/j.nucengdes.2008.08.015