Zero pressure outlet condition

Hello all. I am trying to model flow through a pipe with a bulb in the middle of it, and have run into some problems. Below is a picture of the situation. At the inlet (on the left), there is a time-dependent mass flow rate. At the outlet (on the right), I want to specify a zero-pressure outlet condition (i.e. the fluid to be at zero absolute pressure). While setting boundary conditions, I noticed that SolidWorks doesn't allow zero-values for pressures. I tried two separate cases, since I wasn't sure which pressure to set to "zero". First, I ran a simulation with the static pressure equal to 1e-12 Pa, and then I ran a simulation with the total pressure equal to 1e-12 Pa. I have some questions based on the results.

1) In both cases, I noticed that the simulation results consistently have a negative pressure at the outlet (as seen by the legend in the picture below), which I set to be at 1e-12 Pa in my boundary condition. Why is my boundary condition not satisfied?

2) During the calculation, I also get negative pressure warnings which are still present by the time the calculations have finished. As far as I understand, this should not happen. Why does this happen, and how can I fix it?

3) If I want the fluid's pressure to be zero at the outlet, should I set the static or total pressure to near-zero?

Help is appreciated. Thanks.

SolidworksFlow Simulation