in a compressed air system P1V1 = P2V2 I don't know what your ^.71 is for.
PV can is energy, when you cancel the units you end up with in-lbs which can be converted into joules, BTUs or whatever
PV (or stored energy) for the Scuba tank and HPA tank =
(pressure scuba tank * volume of scuba tank) + (Pressure HPA + Volume HPA)
you keep the PV for the scuba and the PV for the HPA separate because they are not joined together yet to form one air system. This accounts for the pressure (energy) left in the HPA tank before the refill.
when you hook the two tanks together and open the value you get:
PV = unknown pressure * (volume of scuba tank + volume of HPA tank)
knowing that PV = PV (and ignoring heat issues)
so the new pressure = ((Pscuba * Vscuba) + (Phpa * Vhpa)) /(Vscuba + Vhpa)
when this was discussed back in 2004 or so I put together this spreadsheet.
this assumes a 68 cuin HPA tank and that a scuba tank is 650 cuin
and the HPA tank is refilled once it reachs 1000 psi.
and ignores the loss from heat and the volume of air lost when disconnecting