Fluid mechanics problem. In the picture below we have a sphere (consider it massless) acting as a valve in a water tank. At the bottom, theres a hole (which magnitude is determined by the angle theta. I am asked to calculate the total vertical force acting on the sphere. And after that, when theta is (3Pi/4) what must the height h be so that the water doesn't flow through the hole. I can calculate the pressure on any point of the sphere but how do I calculate this vertical force? Is it archimedes i have to use? Thanks for your help.