[Jimro]

Fastest possible in theory is the speed of gunpowder expansion minus the energy required to overcome inertia minus loss to friction. The problem becomes that in reality, as bore size decreases friction increases (why you have to pump harder to get the same amount of water through a smaller pipe than a larger pipe), so you are left with trying to find the right compromise of bore diameter to chamber volume.

Because chamber volume...as it increases you can put more powder in it, but in order to not destroy the firearm it must burn slower, so in order to harness more of the potential energy the barrel must be made longer....

So to get more velocity, engineers try tricks like discarding sabots to get the decreased friction and energy transfer of a large bore, but with a projectile mass of a smaller bore. Or they try to use a squeeze bore where the projectile starts out one diameter, and is then reduced in diameter to get an increase in velocity like going from a big hose to a small hose (same volume into a decreased diameter pipe equals more velocity).

In practice, WWII era squeeze bore anti tank guns got into the 4,600 fps range, and as already stated the 120mm smoothbore cannon can get up to 5,700 fps.

At this point tank gun designers (unless they are German then it is Panzer kanone designers) aren't trying for more velocity, but more mass. Rheinmetall is working on a 130mm gun and the US military flirted with a 140mm gun, the Russians seem to be sticking to the 125mm bore for now. And essentially everyone has abandoned the squeeze bore concept for the time being.

Jimro