Understanding Pressure Vessels

spray cans, rocket propellant tanks, subc pipelines, industrial reactors, and this propane tank. They all have one thing in common. Their main purpose is to contain a fluid that's at a higher pressure than the environment. These are all pressure vessels. Pressurized fluids can exert enormous forces on the walls of the vessels that contain them. In this video, we'll

explore how engineers apply simple mechanics principles to ensure pressure vessels can safely contain their contents without risk of catastrophic failure. Most pressure vessels are either spherical or cylindrical. One of these shapes handles pressure much better than the other, even though it's less commonly used. We'll get to why that is a bit later on. Let's start

by looking at the cylindrical pressure vessel. It contains a fluid at high internal pressure with the outside of the vessel seeing a lower atmospheric pressure from the surrounding environment. What we're interested in is the difference between these two pressures. The gauge pressure P. The net effect of this gauge pressure is to push outwards on the inside surface

of the cylinder causing stresses to develop in two main directions within the vessel wall. in the hoop direction around the circumference of the cylinder from the pressure trying to radially expand the circular cross-section and in the longitudinal direction from the pressure pushing against the ends of the vessel and trying to stretch it

along its length. Being able to quantify these stresses is the key to safely designing pressure vessels. Let's focus on deriving an expression for the hoop stress first. We can do this by considering an arbitrary section of the vessel of length L and cutting it in half to examine the hoop stress within it.