where \(\rho_g\) is the gas density and \(\rho_l\) is the liquid density.
Consider a two-phase flow of water and air in a pipe of diameter \(D\) and length \(L\) . The flow is characterized by a void fraction \(\alpha\) , which is the fraction of the pipe cross-sectional area occupied by the gas phase. advanced fluid mechanics problems and solutions
u ( r ) = 4 μ 1 d x d p ( R 2 − r 2 ) where \(\rho_g\) is the gas density and \(\rho_l\)
where \(\rho_m\) is the mixture density, \(f\) is the friction factor, and \(V_m\) is the mixture velocity. \(f\) is the friction factor
δ = R e L ⁄ 5 0.37 L