Barlow's Formula  Calculate Internal, Allowable and Bursting Pressure
Calculate pipes 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 inservice. 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:
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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