Velocity of a projectile launched from expanding gasses

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I'm looking for a way to determine the velocity a projectile can reach from expanding gasses (explosion or deflagration). I'm sure there are a lot of variables in here, but for reference, we can work with the 12 pounder Napoleonic cannon. The powder burning is 2.5 pounds of black powder made up of 75% potassium nitrate, 15% softwood charcoal (carbon for our purposes), and 10% sulfur. The projectile will be a 12 pound iron sphere, with a diameter of 4.52 inches. The barrel will be 4.62 inches in diameter, and will be 66 inches long. For the surrounding atmosphere we can assume STP. Are there any other variables or aspects of the question I should mention?
 

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