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LaTeX Math Block
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{\rm Re} =\frac{ \sum_\alpha \rho_\alpha \, u_\alpha \, A_\alpha}
{\sum_\alpha \mu_\alpha \, \sqrt{A_\alpha} } =\frac{ \dot m}
{\sum_\alpha m\mu_\alpha \, \sqrt{A_\alpha}
{} } = \frac{\dot m}{\sqrt{A}} \cdot \frac{1}{ \sum_\alpha \mu_\alpha \, \sqrt{As_\alpha} }


2-phase Gas-Liquid  flow

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LaTeX Math Block
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{\rm Re} = \frac{\rho_L \, u_L^2 \, A_L + \rho_g \, u_g^2 \, A_g}{\mu_L \, u_L \, \sqrt{A_L} + \mu_g \, u_g \, \sqrt{A_g}}

where

LaTeX Math Inline
body\rho_L

liquid density

LaTeX Math Inline
body\rho_g

gas density

LaTeX Math Inline
bodyu_L

liquid velocity

LaTeX Math Inline
bodyu_g

gas velocity

LaTeX Math Inline
bodyA_L

cross-sectional area occupied by liquid 

LaTeX Math Inline
bodyA_g

cross-sectional area occupied by gas 

LaTeX Math Inline
body\mu_L

liquid viscosity

LaTeX Math Inline
body\mu_g

gas viscosity



See also

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

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