In multiphase flow the Darcy friction factor can be calculated as Darcy friction factor Single-phase @model with specific approximation of Reynolds number:
| (1) | {\rm Re} = \frac{ \sum_\alpha \rho_\alpha \, u_\alpha^2 \, A_\alpha} {\sum_\alpha \mu_\alpha \, u_\alpha \, \sqrt{A_\alpha} } = \frac{ \sum_\alpha \rho_\alpha \, q_\alpha^2 / A_\alpha} {\sum_\alpha \mu_\alpha \, q_\alpha / \sqrt{A_\alpha} } = \frac{1}{\sqrt{A}} \cdot \frac{ \sum_\alpha \rho_\alpha \, q_\alpha^2 / s_\alpha} {\sum_\alpha \mu_\alpha \, q_\alpha / \sqrt{s_\alpha} } |
where
\rho_L | liquid density | \rho_g | gas density |
u_L | liquid velocity | u_g | gas velocity |
A_L | cross-sectional area occupied by liquid | A_g | cross-sectional area occupied by gas |
\mu_L | liquid viscosity | \mu_g | gas viscosity |
Homogeneous fluid flow
| (2) | {\rm Re} =\frac{ \sum_\alpha \rho_\alpha \, u_\alpha \, A_\alpha} {\sum_\alpha \mu_\alpha \, \sqrt{A_\alpha} } =\frac{ \dot m} {\sum_\alpha \mu_\alpha \, \sqrt{A_\alpha} } = \frac{\dot m}{\sqrt{A}} \cdot \frac{1}{ \sum_\alpha \mu_\alpha \, \sqrt{s_\alpha} } |
2-phase Gas-Liquid flow
| {\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
\rho_L | liquid density | \rho_g | gas density |
u_L | liquid velocity | u_g | gas velocity |
A_L | cross-sectional area occupied by liquid | A_g | cross-sectional area occupied by gas |
\mu_L | liquid viscosity | \mu_g | gas viscosity |
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