1987 f-150 ford pickup.discharging problem.replaced the alternator and it still discharges.new alternator has been check and is working

If the battery is being drained while the engine is running it can only be because the charging system isn't charging or isn't charging enough.

When everything is working correctly the alternator supplies all the current the vehicle needs with a comfortable surplus that keeps the battery charge level topped up.

If the charging system is working correctly and the battery is becoming discharged while driving - the discharge fault would be so huge the result would be smoke and fire. As that isn't the case the obvious conclusion must be a charging system that is defective.

check body ground straps

Not sure I follow the story. The alternator is charging 100amps but the gauge shows less than 14 volts ? Is the alternator output at least 13.5 volts and is that getting to the battery ?

Lead acid batteries don't like being discharged flat, and it could now be damaged and unable to hold a charge. It does sound as though the voltage regulator part of the alternator is allowing discharge to ground when it should not. You would seem to have a good warranty claim on the battery given they did check the alternator and pronounce it OK.

Is the battery now flat again? Has the alternator drive belt broken? Has the alternator output been checked?

Note that if the new battery has been totally discharged by a lack of alternator charging then it's probably ruined and may need another replacement.

Ensure the alternator fuse is not blown, stopping the rotor from being excited, it cannot produce power then. if the battery discharges overnight when the vehicle is off then the vehicle checked for a parasitic draw draining the battery. If the problem occurs while it is running then have all the cables checked for voltage drop or shorts, etc. Also the alternator even though new could be at fault, would have to be checked to be sure though same can go for battery but it is much less likely.

Check alternator for charge,somebody was boost and fray diode inside alternator,start car when car is runing remove positive cable if car stop you need new alternator

has anyone thought about the regulator, i think that its built into the alt, replace it and then see if the prob continues, you can get a pass on the alt test and still have a bunk regulator

Check all wiring connections to alternator and battery to insure all are good, if ok it will most likely need an alternator.