The motion of liquid filling a pipeline is impeded when the gas ahead of it cannot escape. Entrapped gas will lead to a significant pressure build-up in front of the liquid column, which slows down the column and eventually bounces it back. The pressure and temperature in the gas may become dangerously high, and for example, lead to fires and explosions caused by auto-ignition. This paper considers the case where the trapped gas can escape through a vent. One new element is that the pressure head of the liquid supply reservoir is fluctuating instead of staying constant. The obtained analytical and numerical solutions are utilized in parameter variation studies that give deeper insight in the system's behavior.