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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

Py = 2 Sy t / do                                     (1)

where

Py = internal pressure at minimum yield (psig, MPa)

Sy = yield strength (psi, MPa)

t = wall thickness (in, mm)

do = 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

Py = 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 20 bar (2 MPa) can be calculated by rearranging eq. 1 to

t = Py do / (2 Sy)

= (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

Pt = 2 St t / do                                 (2)

where

Pt = ultimate burst pressure (psig)

St = 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

Pt = 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

Pa = 2 Sy Fd Fe Ft t / do                                   (3)

where

Pa = maximum allowable design pressure (psig)

Sy = yield strength (psi)

Fd = design factor
Fe = longitudinal joint factor
Ft = temperature derating factor

Typical Design Factors - Fd

• 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 Fd = 0.72, Fe = 1 and Ft = 1 - can be calculated as

Pa = 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.

Pt = 2 St t / do                                      (4)

where

Pt = test pressure (psig)

St = 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:

tmin = Pi do / (2 Sy)                                    (5)

where

tmin = minimum wall thickness (in)

Pi = 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 table8 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:

Ultimate and Yield Strength
MaterialYield 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/in2) = 6,894.8 Pa (N/m2) = 6.895x10-2 bar
• 1 MPa = 106 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.

A53 Seamless and Welded Standard Pipe - Bursting Pressure
NPSOutside DiameterBursting Pressure (psi)
Schedule
(in)(in)

102030STD4060XS80100120140160XXS
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 = 103 kPa = 106 Pa

Related Topics

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