Finding Fan Curve w/ Orifice Plates & Fixed RPM

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To find a fan curve using orifice plates at a fixed RPM, the challenge lies in calculating flow due to the dependency of the coefficient of discharge on the Reynolds number, which is unknown without flow measurement. This creates a paradox where the flow cannot be determined without first knowing the Reynolds number. An alternative method suggested is to use the hydraulic diameter of the orifice at its exit to compute the Reynolds number. Additionally, it's noted that fan curves are typically provided by the manufacturer. Understanding these dynamics is crucial for accurately generating a fan curve.
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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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