sree555:
There is no equation, formula or relationship that will calculate the "maximum flow allowed" in a pipe.
For a given fluid, given pipe diameter, given pipe length and given flow, there is a specific pressure drop. Then it becomes a matter of:
(1) Can your system tolerate that pressure drop? If not, then you need a larger diameter.
(2) Also, will the linear velocity of the fluid in that given pipe diameter lead to erosion ot some other undesirable effect? If so, then you need a larger diameter.
As a very broad generality, these linear fluid velocities are usually found to be acceptable: about 7 feet per second for liquids and about 40-70 feet per second for gases.
Milton Beychok
(Contact me at www.air-dispersion.com)
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