## fan curve question

If I had a fan sitting in a small duct, and used several different sized orifice plates to create different restrictions, how would I find the fan curve? I run the fan at the same RPM each test.

The problem I run into is using the equation for orifice flow that relates pressure drop, area ratio, density, and coefficient of discharge to find flow. The coefficient of discharge is a function of the Reynold's number, but if the flow is what I'm trying to measure, then I don't know the Reynold's number. As a consequence of that I cannot know the coefficient of discharge, and thus cannot calculate flow for each orifice plate. Sort of like a paradox it seems to me.

Am I missing something here? Is there an alternative method to generating a fan curve?

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 Use the hydraulic diameter of the orifice at its exit to compute the reynolds number.
 A fan curve goes with the fan, its manufacturer should have given it.
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