Actually, all of you are going down the wrong rabbit trail. Orifice measurement is typical in the oil and gas sector, in particular, pipeline measurement.
There are several good programs available on the market. Before spending a lot of really good doe, I would suggest a book by Miller, Measurement Handbook. This book is an industry reference. a benchmark as so to speak, to orifice plate measurement computations for pipeline, hydrocarbon and related industries. My suspicion is that it will lend itself well to water applications.
In general, you are running an ANSI Class 150 application which suggests that a beta ratio of 0.65 would give you near a 100 inch of water differential pressure across the orifice plate. This would suggest 0.705 inches is erroneous under the American Gas Association Report Number 4, which is equivalent to API 14.3, as a throat diameter for the orifice plate. On the other hand, buddy wants a dP equal to 180 psi to 55 psi when the fire hydrant is full bore. This is yet a bigger issue.
I would suggest using a Venture Nozzle and not and Orifice Plate due to structural mechanical issues associated with energy transfer to the equipment. In conventional Bernoulli Obstruction Theory, why would you want to restrict flow to dP= 180 psi in a throat design anyways? Number one, you're going to bend the orifice plate, number two, coefficient losses exceed expected dP losses, number three you need bolts bigger than Anna Nicole Smith's legs to keep the flanging together!
And from where I sit, that's getting rather ulgy!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada