Determination of Orifice Discharge Coefficient
ISO 5167 provides an equation (given below) for the orifice discharge coefficient, Cd, as a function of β (d/D), Reynolds number (Re), L1 and L2, where L1 is the distance of the upstream pressure tap from the orifice plate and L2 is the distance of the downstream pressure tap from the orifice plate. As shown in the figure above L1 = L2 = 0 for corner taps; L1 = L2 = 1" for flange taps; and L1 = D & L2 = D/2 for D-D/2 taps. The equation for the orifice discharge coefficient is:
Cd - 0.5959 + 0.0312 β2.1 - 0.1840 β8 + 0.0029 β2.5(106/Re)0.75 + 0.0900(L1/D)[β4/(1 - β4)] - 0.0337(L2/D)β3
This equation can be used to find the orifice discharge coefficient for an orifice flow meter with any of the three standard pressure tap configurations, but not for any other arbitrary values of L1 and L2. The introduction of standard pressure tap configurations and the equation for Cd, allows a given orifice flow meter to conveniently use different size orifice openings and cover a wide flow measurement range.
Note that an iterative (trial and error) calculation is needed to get a value for Cd, because the upstream velocity needed for Re isn't known until Cd is known. An Excel spreadsheet works well for the iterative calculation of the orifice discharge coefficient using this equation. For a downloadable Excel template for the use of this equation, see the article, "Excel Templates for Venturi and Orifice Flow Meter Calculations."
A U.S Dept. of the Interior reference with information about ISO 5167 for determining the orifice discharge coefficient is provided below.