I am currently designing a HEPA filtered air system for a beverage filling machine.  The goal is to complete an air change every 2 minutes within a 6.5 cubic foot compartment (not sealed and at atmospheric pressure).  The SCFM would thus be 3.25

This is to be accomplished using a 1" inner diameter compressed air line (120PSI) passing through a 0-150 PSI regulator and then exhausting into the top of the fill compartment with open vents on the sides and bottom.

My question is how do I determine what pressure setting I restrict my regulator to in order to achieve my 3.25 SCFM?

(I can measure the length of the piping from the regulator to the fill compartment if necessary as well as the temperature).

You need a regulator you can set at a discharge flow of 3.25 scfm with an outlet pressure of 14.696 psia.

You know the 120 psig inlet pressure, the outlet pressure and the flow.  Flow across the regulator is Q = Cv (P1^2-P2^2), solve for Cv and set the regulator so that the Cv is the same.  Find the Cv vs Position curve for the regulator and see what %Open gives you the Cv you need.

I'm just curious and not familiar with control valve dp flow characteristics- is your statement of
Q = Cv (P1^2-P2^2), a control valve characteristic?

You have a lot of choices.  The one I prefer is use a regulator to drop the pressure to about 65 psig.  Then use PSV calculations to size a choke nipple to give you your desired flow rate.

This does result in critical flow through the choke nipple, but so what?  In spite of what has been said above, critical flow is a very precisely understood thing.  With a known orifice and a known upstream pressure and temperature, critical flow has exactly one mass flow rate regardless of downstream pressure (until downstream pressure increases enough to stop the critical flow).

With a properly sized hole (around 0.056 inches) you will get exactly the flow rate you want without excessive noise or a lot of complexity.  Just set a cheep Big Joe regulator to 65 psig and drill a hole in a pipe-sized billet and you'll have it.  There is nothing magic about the 65 psig.  I would play with the upstream pressure until I got to a hole size that matched a standard drill size (e.g. at 13 psig you would get your flow rate with a 1/8 hole).  Big Joe regulators are regularly used to cut pressure from over 100 psig to under 20 psig for burners without problems.

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