There is typically a governing standard for the particular vessel; eg: ASME Boiler and Pressure Vessel Code, API, BS 5500, etc. The particular Code will specify the allowable stress for the material based on temperature and other factors. A formula is given for the Code-required thickness based on the internal pressure, diameter, welding or forging joint efficiency, allowable stress, etc. The same formula can be inverted to find the pressure that corresponds to a given thickness. The MAWP would then be that pressure less any static head acting on the component.
That is a pretty simplistic answer as for circumferential stress in a cylinder or in a head. It can get more complicated than that once other Code criteria is considered for cone-cylinder junction reinforcing, nozzle reinforcing, etc.
For a complete vessel you would calculate the MAWP for each component. The smallest value of MAWP would govern for the vessel.
For example, in ASME Section VIII Division the required thickness for a cylinder (based on circumferential stress) is given:
t = P*IR/(S*E-0.60*P)
But if 't' is known then the maximum pressure is found as:
P = S*E*t/(IR+0.60*t)
You have to subtract the static liquid pressure from this maximum pressure to get the MAWP.
pr5200,
TomBarsh gave you really good advice for vessels (since this is the "boiler and pressure vessel forum", that was probably a good way to go), but since your handle shows up as "petroleum" I'd like to add that for piping outside of a facility the calculation is dominated by location factors (e.g., population density) that are described very well in ASME B31.8.
Remember also that the MAWP may also be taken as the design pressure if MAWP calculations are not provided or required. Establishing a MAWP is not always "free" as you can run into problems when considering other loads on a component that is already max'd out.
codeeng: That is a very good point. With modern computer software it's easy to calculate and report the MAWP. But fabricators who want to minimize confusion and questions from their customers might consider running calculations for design pressure only. Then again, a wise vessel owner will likely want to know what the vessel MAWP is for possible future rerating or tweaking of the process and won't want the vessel MAWP limited by some rinky dink component(s) that may be costly to replace. ...just points out the conflicting needs of the various constituencies.
Thank everyone for their quick response. If I'm reading this correctly, the only time MAWP should vary from the design thickness is when different shell/head thickness' are used during fabrication, excluding other limiting factors, such as nozzles, loadings, etc.
pr5200: In practice the theoretical MAWP will likely be greater than the design pressure since the required thickness will be some oddball number running out to a number of decimal places, whereas the manufactured thicknesses will likely be rounded off to standard material thicknesses (say, like, tr=0.8093456" versus a nominal thickness of 13/16" or 7/8"). This isn't a bad thing since the excess thickness in the shell can be used for reinforcement of nozzles and other discontinuities.
But as mentioned above there is no Code requirement (ASME, at least) to calculate the MAWP. In ASME Code the design pressure may be used in lieu of the MAWP for purposes of calculations, name plate, etc. Doing so simplifies a lot of issues but at the expense of greater flexibility for process design.
The MAWP would also be different from the design pressure depending on the defined CA (corrosion allowance or other extra thickness), if you take this on acount there is a "new and cold" MAWP and a "corroded" MAWP.
I mention the corrosion allowance since in general the corrosion allowance is an extra thickness that the designer defines depending on a relative criteria. So, it can be said that the easiest way to increase a MAWP is changing your mind about the CA value. (Of course, it is suposed that the CA should be defined on a correct basis).
Also, emphazising what Tombarsh said if there is a weaker component in the vessel, for example, a lower class flange, a thin neck, certain type of weld, etc., the MAWP would be the pressure that this component would resist.
