I am befuddled over how to calculate the force acting on a surface point of a deformed balloon (filled with water or air). I have drawn a picture to help illustrate. I have written a small program in c++ that uses the Runge-Kutta algorithm to simulate simple physics systems, like networks of interconnected springs connecting point masses, in 2 dimensions. My simulation does not incorporate gravity. I want to be able to simulate things like multiple balloons of varying internal pressures packed together in a 2d box. Or a squeezed water balloon that is instantly released and rises back into it's natural circular shape. 1.) Does it even make sense to attempt to simulate an object with internal pressure (balloon) in 2 dimensions, or are 3 dimensions absolutely required? Assume that I can calculate the internal area of each balloon, the internal pressure, distance from the balloon's center, and all other necessary variables. 2.) How do I calculate the force exerted on the surface points pointed to by red arrows in the picture? 3.) Does the force exerted on the surface points originate from the center of pressure of the balloon? Is this center calculated like calculating the centroid of a solid polygon?