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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:
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 surface. The circumferential stress and longitudinal stresses are ...
For example, consider a thin-walled cylinder subjected to an axial compressive load uniformly distributed along its rim, and filled with a pressurized fluid. The internal pressure will generate a reactive hoop stress on the wall, a normal tensile stress directed perpendicular to the cylinder axis and tangential to its surface. The cylinder can ...
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.
This is a special case of a torus for a = 0 (see below), as well as of a thick-walled cylindrical tube with open ends, with r 1 = r 2 and h = 0 Thin, solid disk of radius r and mass m. = = = This is a special case of the solid cylinder, with h = 0.
For a solid cylinder it is , for a thin-walled empty cylinder it is approximately , and for a thick-walled empty cylinder with constant density it is (+). [ 7 ] For a given flywheel design, the kinetic energy is proportional to the ratio of the hoop stress to the material density and to the mass.
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 ...