Note that typical current practice is to select a pressure for CAESAR analysis along the entire line that matches the highest pressure and highest temperature (and in the case of cryogenic systems, lowest temperature) seen anywhere in the line.

So if you have a hydrostatic head at the bottom of the pipe, plus static pressure, you have a design pressure with which to select a wall thickness or piping specification. That pressure then in turn gets fed into stress analysis, and is applied to the entire line in most cases.

In most cases, this is conservative, but when you have thin-walled bends, pressure differentials may result in differing elbow stiffnesses and SIFs and therefore inaccurate results.