Steady pressure driven two‐phase stratified laminar flow through a pipe

The two phase pressure driven flow in a circular pipe in which the interface occupies an arbitrary horizontal position has, as shown by earlier authors, an explicit analytical solution in which the velocities are expressed as Fourier integrals. Here this is used to express the volumetric fluxes of each fluid as one‐variable integrals whose values can be easily computed. The results agree with those obtained by Gemmell and Epstein by numerical integration of the differential equations.