not sure if this helps, but here ya go. info from bill wilson...

We have only built pistols with 11.3" bbls and mine gives 2320fps with the 130gr HotCore and still shoots sub-inch, it's my "car gun" for traveling.

We did a velocity test with the same bbl gradually cutting it from 20" down to 12.5"

BARREL LENGTH EFFECT ON VELOCITY
300 HAMR

125 SIERRA SBT PH 20" bbl 2534 FPS
125 SIERRA SBT PH 18" bbl 2498 FPS (-36)
125 SIERRA SBT PH 16.25" bbl 2486 FPS (-12)
125 SIERRA SBT PH 14.5" bbl 2441 FPS (-45)
125 SIERRA SBT PH 12.5" bbl 2367 FPS (-74)
TOTAL VELOCITY LOSS FROM 20 TO 12.5 167 FPS

130 SPEER FNHC 20" bbl 2485 FPS
130 SPEER FNHC 18" bbl 2460 FPS (-25)
130 SPEER FNHC 16.25" bbl 2438 FPS (-22)
130 SPEER FNHC 14.5" bbl 2412 FPS (-26)
130 SPEER FNHC 12.5" bbl 2346 FPS (-66)
TOTAL VELOCITY LOSS FROM 20 TO 12.5 139 FPS

150 SPEER FNHC 20" bbl 2202 FPS
150 SPEER FNHC 18" bbl 2194 FPS (-8)
150 SPEER FNHC 16.25" bbl 2171 FPS (-23)
150 SPEER FNHC 14.5" bbl 2146 FPS (-24)
150 SPEER FNHC 12.5" bbl 2105 FPS (-41)
TOTAL VELOCITY LOSS FROM 20 TO 12.5 97 FPS

ALL TESTING WAS DONE WITH THE SAME BARREL PROGRESSIVELY SHORTENED FOR NO BARREL TO BARREL VARIATION AND ALL AMMO FOR EACH LOAD FROM THE SAME LOT. ALSO ALL SHOOTING WAS DONE DURING A 5 HOUR PERIOD ON THE SAME DAY USING A LABRADAR TO MINIMIZE THE EFFECT OF ATMOSPHERIC CONDITIONS. ALL CHRONOGRAPH STRINGS WERE 10 SHOTS WITH THE HIGH AND LOW SHOT REMOVED FOR AN AVERAGE OF THE REMAINING 8 SHOTS.

AS YOU CAN SEE AS THE BULLET WEIGHT WENT UP BARREL LENGTH HAD LESS EFFECT ON VELOCITY. AVERAGING THE 16.25 TO 20 NUMBERS IT WORKS OUT TO 10.5 FPS PER INCH.

not sure how they addressed the gas tube length as the barrell was progressively shortened.

anyway, i'll also contribute this...