Homogeneous pressure decay in multi-chamber vacuum system with finite conductance

We derived the geometrical parameters on the tube connections that homogenize the pressure drop in a multi-chamber vacuum system, where each chamber has a distinct volume and all are connected to the same vacuum pump. We start deriving the pressure drop in a single chamber for a tube with finite conductance. Next, we derive a solution that provides the radius and length for each tube connection between the chambers and the pump that homogenize the pressure drop in all chambers.