I said canon not mortar.
You are mixing up canon with mortars.
Two different things.
No, neither of us are mixing the cannons and mortars. Follow my link to the Columbiad article. Those big guns were definately cannons, not mortars. They had a range of over six miles, so it is resonable that the shell you found was fired from across the river. Remember that the sights on artillery in those days were just overgrown rifle sights. Indirect fire was not used until the Spanish-American war. It is possible that the half shell you have resulted from it bouncing off its target in the river after smashing whatever it hit.
Try to find the exact diameter of the shell. I'm sure there are archives that provide detailed movements of guns during the war. You have a nice artifact. Try to find out more about it.