The equations governing the one-dimensional flow in vertical pipes of compressible bubbles immersed in fluid are derived. Mass and momentum conservation for each phase are invoked in order to obtain those equations. The effect of the multitude of bubbles on the drag coefficient for a single bubble was modeled with a single parameter. A single value of that parameter was found to fit various different flow conditions. In the case of gas bubbles in liquid, the bubbles' inertia can be neglected. The equations are numerically solved for that particular case and the effects of various initial conditions are observed and discussed.