Question

I have a serious problem with fluid mechanics; the context im using is 'Transport Phenomena 2nd ed.' by Bird.

I'm in confuse when to use just 'pressure' or 'modified pressure': some cylinderical problems use pressure, some others use modified pressure, and either in spherical problems.

Can anybody explain the difference of two concepts and when to use them??

Answer 1

When system being studied is also subjected to body forces like gravity or centrifugal force in a rotating cylinder problem then modified pressure term is used.

There may be problems where it is asked to neglect effect of gravity as happens in some derivations of Couette Flow example for motion of a fluid between two parallel plates. In such cases only pressure gradient is used for solving problem.

However, if you are asked to take effect of gravity, then analyze whether this gravity will have effect in fluid flow direction. An example is fluid flow between two parallel cylinders. In such case effective gradient is defined in terms of P+?g. In this example if you are next asked to neglect gravity, then effective gradient shall only be in terms of P (i.e. equal to pressure).