Force = Pressure (lb/sq in.) * Area of bore (sq. in.)
So at peak pressure, the force is:
Force = 51000 * (PI*.25^2)/4 = 2503 lbs. force
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Pressure (psi)= Force (lbs force) / bore area (sq in.)
Pressure = 2503 / ((PI*.5^2)/4)= 12,750 psi
With the top formula are you assuming a 100 gr bullet weight? If that's so since you used the 2503 then you have a 50 cal shooting a 100 gr bullet for that pressure. As you increase bullet weight the pressures go up. You'd be better off comparing something with a reasonable bullet weight. The minimum I'd use would be 240 gr. Your pressures will be higher than you think. Of course this doesn't take into account the differences between plastic (saboted bullets) and a copper jacketed lead bullet or bore conditions. The smoother the barrel the more velocity your pressure will give you. And plastic saboted bullets don't generate the friction of a copper jacketedbullet which would translate to slightly lower back pressure/increased velocity for the same bore. If your comparing the Copper jacketed bullet to a lead conical that doesn't equate right either. The lead will use some of the pressure to swell into the rifling. This is why comparing saboted bullets of equal weight the lead bullet will be somewhat slower. 100-200 FPS depending on bullet weight.
In reality formulas really don't tell you anything but theoreticals. The only way to know for sure is to use a test barrel specifically designed to test pressure. Strain gauges won't even give you accurate data. You can use them as a comparison tool but their use in muzzleloaders is shaky at best.