# Vacuum Pump in a Pipe System

I am trying to fit a vacuum pump at one end of a pipe system and a cylindrical container with a size that has minimal clearance with the inner pipe wall would be inserted at the inlet to the pipe system.

The purpose of the vacuum pump is to create a pressure difference so that the lower pressure region at the vacuum pump would cause the higher atmospheric pressure to force its way to the low pressure region and the force would be used to push or move the cylindrical container in the pipe system.

My aim is to calculate the acceleration, velocity and displacement of the container in the pipe at any instant.

I wonder if it is fine to calculate the force acting on the container due to the pressure difference by using the equation P = F / A where P is the pressure difference between the atmospheric pressure and the low pressure region at the vacuum pump, A is the area of the container and F is the force acting on the container.

I was thinking of applying the principle of impulse to the container to calculate the effect of force acting on the container with respect to time. However, I notice that the vacuum pump would reduce the pressure gradually and would only reach the final vacuum pressure after the evacuation time. Please advice on how to calculate the force due to the pressure difference at the instant the pump is switched on until the final vacuum pressure.

Thanks

Charles