# Barlow's formula

Barlow's formula relates the internal pressure that a pipe[1] can withstand to its dimensions and the strength of its material.

${\displaystyle P={\frac {2St}{D}}}$

where

P = pressure
S = allowable stress
t = wall thickness
D = outside diameter

This formula figures prominently in the design of autoclaves and other pressure vessels.

The formula is named after Peter Barlow, an English mathematician.

## Other formulations

The design of a complex pressure containment system involves much more than the application of Barlow's formula. For pressure vessels, design codes such as the ASME code stipulate the requirements for design and testing.[citation needed]

The formula is also common in the pipeline industry to verify that pipe used for gathering, transmission, and distribution lines can safely withstand operating pressures. The design factor is multiplied by the resulting pressure which gives the maximum operating pressure (MAOP) for the pipeline. This design factor is dependent on class locations which are defined in DOT Part 192. There are four class locations corresponding to four design factors:[citation needed]

• Class 1: An offshore area or any class location unit that has 10 or fewer buildings intended for human occupancy. The Class 1 design factor is 0.72.
• Class 2: any class location that has more than 10 but fewer than 46 buildings intended for human occupancy; design factor 0.60.
• Class 3: any location that has more than 46 or more buildings intended for human occupancy or any area where the pipeline lies within 100 yards (91 meters) of a building or a small, well-defined outdoor area (such as a playground, recreation area, outdoor theater, or place of public assembly) that is occupied by 20 or more persons at least five days a week for 10 weeks in any 12-month period—weeks need not be consecutive. design factor 0.50.
• Class 4: any class location unit where buildings with four or more stories above the ground are prevalent; design factor 0.40.