# Barlow's Formula - Calculate Internal, Allowable and Bursting Pressure

Barlow's formula is used to determine

- internal pressure at minimum yield
- ultimate burst pressure
- maximum allowable pressure

### Internal Pressure At Minimum Yield

Barlow's formula can be used to calculate the "*Internal Pressure*" at minimum yield

P_{y}= 2 S_{y}t / d_{o}(1)

where

P_{y}= internal pressure at minimum yield (psig, MPa)

S_{y}= yield strength (psi, MPa)

t = wall thickness (in, mm)

d_{o}= outside diameter (in, mm)

**Note!** - in codes like ASME B31.3 modified versions of the Barlow's formula - like the Boardman formula and the Lame formula - are used to calculate burst and allowable pressures and minimum wall thickness.

#### Example - Internal Pressure at Minimum Yield

The internal pressure for a *8 inch* liquid pipe line with outside diameter *8.625 in* and wall thickness *0.5 in* with yield strength *30000 psi* can be calculated as

*P _{y} = 2 (30000 psi) (0.5 in) / (8.625 in)*

* = 3478 psi*

### Example - Polyethylene PE pipe

The yield strength of a 110 mm polyethylene pipe is *22.1 MPa*. The minimum wall thickness for pressure 2*0 bar (2 MPa)* can be calculated by rearranging eq. 1 to

*t = P _{y} d_{o} / (2 S_{y})*

* = (2 MPa) (110 mm) / (2 (22.1 MPa))*

* = 5 mm *

### Ultimate Burst Pressure

Barlow's formula can be used to calculate the "*Ultimate Burst Pressure"* at ultimate (tensile) strength as

P_{t}= 2 S_{t}t / d_{o}(2)

where

P_{t}= ultimate burst pressure (psig)

S_{t}= ultimate (tensile) strength (psi)

#### Example - Ultimate Burst Pressure

The ultimate pressure for the pipe used in the example above with ultimate (tensile) strength *48000 psi* can be calculated as

*P _{t} = 2 (48000 psi) (0.5 in) / (8.625 in)*

* = 5565 psi*

### Working Pressure or Maximum Allowable Pressure

Working pressure is a term used to describe the maximum allowable pressure a pipe may be subjected to while in-service. Barlow's formula can be used to calculate the maximum allowable pressure by using design factors as

P_{a}= 2 S_{y}F_{d}F_{e}F_{t}t / d_{o}(3)

where

P_{a}= maximum allowable design pressure (psig)

S_{y}= yield strength (psi)F_{d}= design factor

F_{e}= longitudinal joint factor

F_{t}= temperature derating factor

#### Typical Design Factors - F_{d}

- liquid pipelines:
*0.72* - gas pipe lines - class 1:
*0.72* - gas pipe lines - class 2:
*0.60* - gas pipe lines - class 3:
*0.50* - gas pipe lines - class 4:
*0.40*

#### Example - Maximum Allowable Pressure

The "*Maximum Allowable Pressure"* for the liquid pipe line used in the examples above with *F _{d} = 0.72, F_{e} = 1 *and

*F*can be calculated as

_{t}= 1 -*P _{a} = 2 (30000 psi) 0.72 1 1 (0.5 in) / (8.625 in)*

* = 2504 psi*

Barlow's formula is based on ideal conditions and room temperatures.

### Mill Test Pressure

The "*Mill Test Pressure*" refers to the hydrostatic (water) pressure applied to the pipe at the mill to assure the integrity of the pipe body and weld.

*P _{t} = 2 S_{t} t / d_{o} (4)*

*where*

*P _{t} = test pressure (psig)*

*S _{t} = specified yield strength of material - often 60% of yield strength (psi)*

### Wall Thickness

Barlow's formula can be useful to calculate required pipe wall thickness if working pressure, yield strength and outside diameter of pipe is known. Barlow's formula rearranged:

*t _{min} = P_{i} d_{o} / (2 S_{y}) (5)*

*where*

*t _{min} = minimum wall thickness (in)*

*P _{i} = Internal pressure in pipe (psi)*

#### Example - Minimum Wall Thickness

The minimum wall thickness for a pipe with the same outside diameter - in the same material with the same yield strength as in the examples above - and with an internal pressure of *6000 psi* - can be calculated as

*t = (6000 psi) (8.625 in) / (2 (30000 psi)) *

* = 0.863 in*

From table - *8 inch* pipe *Sch 160* with wall thickness *0.906 inches* can be used.

### Material Strength

The strength of a material is determined by the tension test which measure the tension force and the deformation of the test specimen.

- the stress which gives a permanent deformation of 0.2% is called the
**yield strength** - the stress which gives rupture is called the
**ultimate strength or the tensile strength**

Typical strength of some common materials:

Material | Yield Strength (psi) | Ultimate (Tensile) Strength (psi) |
---|---|---|

Stainless Steel, 304 | 30000 | 75000 |

6 Moly, S31254 | 45000 | 98000 |

Duplex, S31803 | 65000 | 90000 |

Nickel, N02200 | 15000 | 55000 |

A53 Seamless and Welded Standard Pipe, Grade A | 30000 | 48000 |

A53 Seamless and Welded Standard Pipe, Grade B | 35000 | 60000 |

*1 psi (lb/in*^{2}) = 6,894.8 Pa (N/m^{2}) = 6.895x10^{-2}bar*1 MPa = 10*^{6}Pa

### Barlow's Pressure Calculator

The Barlow's formula calculator can be used to estimate

- internal pressure at minimum yield
- ultimate burst pressure
- maximum allowable pressure

### Barlow's Wall Thickness Calculator

The Barlow's formula calculator can be used to estimate minimum wall thickness of pipe.

### Example - A53 Seamless and Welded Standard Pipe - Bursting Pressure

Bursting pressure calculated with Barlow's formula (2) for A53 Seamless and Welded Standard Pipe Grade A with ultimate (tensile) strength *48000 psi*. Pipe dimensions - outside diameter and wall thickness according ANSI B36.10.

NPS | Outside Diameter | Bursting Pressure (psi) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Schedule | ||||||||||||||

(in) | (in) | |||||||||||||

10 | 20 | 30 | STD | 40 | 60 | XS | 80 | 100 | 120 | 140 | 160 | XXS | ||

3/8 | 0.675 | 12942 | 12942 | 17920 | 17920 | |||||||||

1/2 | 0.84 | 12457 | 12457 | 16800 | 16800 | 21371 | 33600 | |||||||

3/4 | 1.05 | 10331 | 10331 | 14080 | 14080 | 20023 | 28160 | |||||||

1 | 1.315 | 9710 | 9710 | 13068 | 13068 | 18251 | 26135 | |||||||

1 1/4 | 1.66 | 8096 | 8096 | 11046 | 11046 | 14458 | 22092 | |||||||

1 1/2 | 1.9 | 7326 | 7326 | 10105 | 10105 | 14198 | 20211 | |||||||

2 | 2.375 | 6225 | 6225 | 8812 | 8812 | 13905 | 17624 | |||||||

2 1/2 | 2.875 | 6778 | 6778 | 9216 | 9216 | 12522 | 18432 | |||||||

3 | 3.5 | 5925 | 5925 | 8229 | 8229 | 12014 | 16457 | |||||||

3 1/2 | 4 | 5424 | 5424 | 7632 | 7632 | |||||||||

4 | 4.5 | 5056 | 5056 | 7189 | 7189 | 9344 | 11328 | 14379 | ||||||

5 | 5.563 | 4452 | 4452 | 6471 | 6471 | 8628 | 10786 | 12943 | ||||||

6 | 6.625 | 4057 | 4057 | 6260 | 6260 | 8144 | 10419 | 12520 | ||||||

8 | 8.625 | 2783 | 3083 | 3584 | 3584 | 4519 | 5565 | 5565 | 6611 | 8003 | 9038 | 10084 | 9739 | |

10 | 10.75 | 2233 | 2742 | 3260 | 3260 | 4465 | 4465 | 5305 | 6421 | 7537 | 8930 | 10047 | 8930 | |

12 | 12.75 | 1882 | 2485 | 2824 | 3057 | 4232 | 3765 | 5180 | 6355 | 7529 | 8471 | 9879 | 7529 | |

14 | 14 | 1714 | 2139 | 2571 | 2571 | 3003 | 4073 | 3429 | 5143 | 6432 | 7502 | 8571 | 9641 | |

16 | 16 | 1500 | 1872 | 2250 | 2250 | 3000 | 3936 | 3000 | 5064 | 6186 | 7314 | 8628 | 9564 | |

18 | 18 | 1333 | 1664 | 2336 | 2000 | 2997 | 4000 | 2667 | 5003 | 6165 | 7333 | 8331 | 9499 | |

20 | 20 | 1200 | 1800 | 2400 | 1800 | 2851 | 3898 | 2400 | 4949 | 6149 | 7200 | 8400 | 9451 | |

22 | 22 | 1091 | 1636 | 2182 | 1636 | 3818 | 2182 | 4909 | 6000 | 7091 | 8182 | 9273 | ||

24 | 24 | 1000 | 1500 | 2248 | 1500 | 2752 | 3876 | 2000 | 4876 | 6124 | 7248 | 8248 | 9376 | |

30 | 30 | 998 | 1600 | 2000 | 1200 | 1600 | ||||||||

32 | 32 | 936 | 1500 | 1875 | 1125 | 2064 | ||||||||

34 | 34 | 881 | 1412 | 1765 | 1059 | 1943 | ||||||||

36 | 36 | 832 | 1333 | 1667 | 1000 | 2000 | ||||||||

42 | 42 | 1143 | 1429 | 857 | 1714 | |||||||||

*1 in (inch) = 25.4 mm**1 MPa = 10*^{3}kPa = 10^{6}Pa

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