Im a puxxle solver and wish to include the side tracks as well as the straight line..which may be useful to those asking other questions than yours. One could edit down to minimal essence but its far more work...the long letter that one doesnt have time to make shorter..

Not only did you get your answer but others asking other issues may also get theirs. But thanks for the edit..

I might point out you assumed the pressure was accumulative since the pumps are in series..Could be its merely a reduncancy feature and either pump supplies adequate pressure..If thats not to much information