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) = 6.895x10^-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

• Load Calculator!

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)

• Load Calculator!

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.

• 1 in (inch) = 25.4 mm
• 1 MPa = 10³ kPa = 10⁶ Pa