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 20 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_t = 1 - can be calculated as

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:

• 1 psi (lb/in²) = 6,894.8 Pa (N/m²) = 6.895×10^-2 bar
• 1 MPa = 10⁶ Pa

• Modulus of Elasticity or Young's Modulus - and Tensile Modulus for common Materials

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

Outside diameter (in)

Wall thickness (in)

Yield strength (psi)

Ultimate (tensile) strength (psi)

Total Design Factor

Barlow's Wall Thickness Calculator

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

Outside diameter (in, mm)

Yield strength (psi, MPa)

Internal pressure (psi, mm)

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

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 = 10³ kPa = 10⁶ Pa