I have built a pneumatic tennis ball lancher (with compressed air). I need to develop theory (i.e. equations and formula) to determine the velocity as the ball leaves the barrel. I have the projectile motion after the ball leaves the barrel down pretty well. I'm having issues acounting for pressure drop among other things. As seen in the attached picture, there is a PVC resevoir with has compressed air. The valve opens by a current from the battery and the air shoots the ball out. Note I need physics forumlas and not a link to a projectile motion calculator site. Thank you.