Barlow's formula relates the internal pressure that a pipe

Pipe (material)

A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases , slurries, powders, masses of small solids...

 can withstand to its dimensions and the strength of its material

Strength of materials

In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...

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where

P = pressure (typically, pounds per square inch)

S = allowable stress

Yield (engineering)

The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed...

 (typically, pounds per square inch, yield or tensile depending upon application)

t = wall thickness (typically, inches)

D = outside diameter (typically, inches)

This formula figures prominently in the design of autoclaves

Autoclave (industrial)

Industrial autoclaves are pressure vessels used to process parts and materials which require exposure to elevated pressure and temperature. The manufacture of high-performance components from advanced composites often requires autoclave processing....

 and other pressure vessel

Pressure vessel

A pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.The pressure differential is dangerous and many fatal accidents have occurred in the history of their development and operation. Consequently, their design,...

s.

The formula is named after Peter Barlow, an English mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

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The design of a complex pressure containment system involves much more than the application of Barlow's formula. For almost all pressure vessel

Pressure vessel

A pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.The pressure differential is dangerous and many fatal accidents have occurred in the history of their development and operation. Consequently, their design,...

s, the ASME code stipulates the requirements for design and testing.