The "pressure" in the manuals is the peak pressure that happens during the whole process of burning the propellant and pushing the bullet out the muzzle. This happens in the first few inches that the bullet travels.
Some powders burn more quickly than others. With a slower burning powder, the peak will happen when the bullet is farther down the barrel.
The basic gas pressure laws relate pressure, volume, and temperature. If you have a larger volume, it takes more gas to fill it to a given pressure (such as 60,000 psi), and there is more potential energy stored in the compressed gas.
Remember also, the pressure behind the bullet varies with time. It builds rapidly, then "tails off" as the bullet moves. That is why the bullet picks up most of its energy in the first few inches, and relatively less in the parts of the barrel closer to the muzzle. The final muzzle velocity is the effect of this varying pressure vs. time.
The whole business boils down to coupling the potential energy out of the compressed gas without exceeding the peak PSI that would be dangerous to the barrel and receiver.
A powder that burns very quickly will have a realtively high peak pressure, but cannot maintain it as the bullet moves off.
A slower burning powder will maintain the pressure mear max for a longer time, so the bullet may end up going faster for a slower powder with a lower peak pressure.
Or, "what denton said!"
Don
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Gerard Schultz
GS Custom Bullets