Question about gas orifice meter coefficients

Does anyone know where to get a detailed table or simple computation program to accurately compute the coefficient of discharge for orifice gas meters? (The coefficient is a function of the meter tube inner diameter and the diameter of the orifice.) I have a Sonney gas calculator (sort of like a circular slide rule) and on the back there is a table of coefficients, but it is not very accurate.

My production program figures gas volumes for me based on pressure, differential, and temperature, but it is only as accurate as the coefficient I enter into it. There are several things I should be able to calculate by adding/subtracting various gas meter readings, but my calculations keep fluctuating strangely and I believe estimated coefficients are the culprit.

Also, if a physicist happens to know the actual formula, I could just plug it into Excel and make my own little ‘calculator.’