The Barlow formula is a simplification of Lame's formula for thin walled pipes/ cylinders. The book by AP Moser (Buried Pipe Design) gives the derivation and arrives at S = PD/2t where D is infact the average diameter. This makes sense if you consider that there is a stress profile across the pipe wall with highest stress at the inside edge. So the average stress occurs in the material at the centre (ie. Do - t). The above book has a couple of good sketches illustrating this. Outer diameter is however quoted in the Barlow equation in some contexts - for example in ASME 31.8. This is apparently a simplification (infact nominal outside diameter is used which is actually a bit smaller than the real outer diameter). If using the formula to calculate wall thickness the answer will be slightly conservative but then you will generally look up a standard wall thickness (eg. from the table in ANSI B36.10) so you will likely arrive at the same answer anyway.
Pressure =Force/Area
You use the information that you do have, and a formula that relates it to theradius or diameter of the circle. As an example: The circumference is very helpfulif you know it.
pi = circumference / diameter
Euler published the formula, which relates complex exponentials to trigonometric functions in 1748. See related link.
A mathematical formula, such as Speed = Distance / Time for example.
Pressure =Force/Area
You use the information that you do have, and a formula that relates it to theradius or diameter of the circle. As an example: The circumference is very helpfulif you know it.
What in the community relates to air pressure?
pi = circumference / diameter
PSI
Pi (3.14159265358.....)
The bore of a gun relates to the diameter of the hole in the barrel - and in turn the diameter of the bullet the gun can fire.
E = mc2
w=mg
power = work/time
1 atm (standard atmospheric pressure) is 101,325 kPa.
The Ideal Gas Law, equation PV = nRT relates the pressure to the constant R, where P is pressure, V is volume, n is number of moles, and T is temperature. Boyle's Law provides a relationship between the volume of a gas and its pressure where temperature is constant. The equation is PV = k where P is the pressure of the gas, V is the volume of the gas, and k is a constant. Charles' law states that the volume of a given mass of a gas, at constant pressure, is directly proportional to its temperature. V1/T1 = V2/T2