Complicating matters further, bore friction is not constant throughout. It peaks when the pressure peaks because that is when acceleration peaks and the g forces try to squash the bullet, bulging it slightly outward outward against the bore surface. . This is why, absent a narrowing taper or extra roughness further down it's length, a bore's heaviest metal fouling occurs where the bottom of the bullet's bearing surface is in the bore when the pressure peaks.
An interesting example is the 22 Long Rifle. Depending on the load, the powder burns out when the bullet is in the range of about 16 to 19 inches into its tour of the tube. At that point velocity ceases to change much. Friction and the dropping pressure as it goes down a longer tube seem to roughly neutralize one another. This has an interesting consequence. Because the expansion ratio is so high, variations in chamber size don't tend to have a significant effect on 22 RF velocities. Coupled with the relative stability of the velocity after 19" of travel, most any 22 RF rifle with a barrel that long or longer will shoot match ammunition to Irving 50 fps of the velocity published on the box. This provides the shooter with a convenient way to confirm his chronograph is working as it should.
An interesting example is the 22 Long Rifle. Depending on the load, the powder burns out when the bullet is in the range of about 16 to 19 inches into its tour of the tube. At that point velocity ceases to change much. Friction and the dropping pressure as it goes down a longer tube seem to roughly neutralize one another. This has an interesting consequence. Because the expansion ratio is so high, variations in chamber size don't tend to have a significant effect on 22 RF velocities. Coupled with the relative stability of the velocity after 19" of travel, most any 22 RF rifle with a barrel that long or longer will shoot match ammunition to Irving 50 fps of the velocity published on the box. This provides the shooter with a convenient way to confirm his chronograph is working as it should.