I tried to understand of some formulas in ISA Standard "Flow Equations for Sizing Control Valves": http://integrated.cc/cse/ISA_750101_SPBd.pdf

ISA standard likes to give formulas without giving reasons. For example, following formula is about expansion factor Y (page 22, Eq.32) :

$$ Y = 1- \frac{x}{3F_{\gamma}x_T} $$

I've spent a lot of time trying to figure above formula out, but without success. I would be very grateful if someone could give a derivation, or you could point me to a literature.

  • 1
    $\begingroup$ Dimensional analysis is one possibility see BReynolds and Buckingham. Or it may derive from experimental work. $\endgroup$
    – Solar Mike
    Apr 19, 2023 at 5:00
  • $\begingroup$ I don't think so. $\endgroup$
    – John
    Apr 19, 2023 at 5:52
  • $\begingroup$ So with valves, or what can be assumed to be orifices, how do you get the coefficient of discharge? As you "don't think so" ?? I remember "proving" those coefficients by experiment as labs at uni... $\endgroup$
    – Solar Mike
    Apr 19, 2023 at 6:50
  • $\begingroup$ Dear Mike, You may be right, I find Buckingham's old paper, maybe it has answer. Thank you! $\endgroup$
    – John
    Apr 19, 2023 at 7:08


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