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For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:
The walls of pressure vessels generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are longitudinal stress, circumferential (hoop) stress and radial stress. The radial stress for a thick-walled cylinder is equal and opposite to the gauge pressure on the inside surface, and zero on the outside ...
where is hoop stress, or stress in the circumferential direction, is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the sphere, and t is thickness of the sphere wall. A vessel can be considered "thin-walled" if the diameter is at least 10 times (sometimes cited as 20 times) greater than the wall ...
Barlow's formula (called "Kesselformel" [1] in German) relates the internal pressure that a pipe [2] can withstand to its dimensions and the strength of its material.. This approximate formula is named after Peter Barlow, an English mathematician.
Autofrettage is a work-hardening process in which a pressure vessel (thick walled) is subjected to enormous pressure, causing internal portions of the part to yield plastically, resulting in internal compressive residual stresses once the pressure is released. The goal of autofrettage is to increase the pressure-carrying capacity of the final ...
Pipes and pressure vessels subject to external overpressure, caused for example by steam cooling within the pipe and condensing into water with subsequent massive pressure drop, risk buckling due to compressive hoop stresses. Design rules for calculation of the required wall thickness or reinforcement rings are given in various piping and ...
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is the cylinder stress or "hoop stress". For the thin-walled assumption to be valid the vessel must have a wall thickness of no more than about one-tenth (often cited as one twentieth) of its radius. The cylinder stress , in turn, is the average force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in ...