Velocity distribution of a plug flow of a periodic structure in a cylindrical tube

The problem of determining the velocities in the plug regime of the flow of a gas–liquid mixture in a closed cylindrical tube is considered. The discrete structure of the plug flow is periodic of elementary cell. For the derivation of the transcendental equation the Abeles formula is used. The values of velocities in each cell is obtained. With increasing their number, the velocities increase and in the limit, tend to the speed of sound in homogeneous gas–liquid mixture.