Calculation of Orifice Meter Coefficient Using ISO 5167
The meter coefficient for an orifice flow meter varies more widely with operating conditions than that of a flow nozzle or venturi meter. For an orifice meter with one of the three ISO standard pressure tap configurations (corner taps, flange taps, or D-D/2 taps) ISO 5167 provides an equation for the orifice coefficient, C, in terms of the pressure tap locations, L1 and L2; the diameter ratio, β; the pipe diameter, D1; and the pipe Reynolds number, Re. See the article, "Use ISO 5167 to Find the Orifice Discharge Coefficient for an Orifice Flow Meter," for more details about ISO 5167, the standard pressure tap configurations, and the following equation for calculating the orifice coefficient in terms of the diameter ratio, β, the pipe Reynolds number, Re, the pipe diameter, D, and pressure tap location parameters, L1 and L2:
C = 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
The Excel formulas for calculation of the orifice coefficient are shown in the image at the left. The image at the right shows an example set of calculations using this Excel template. The calculations in the example and in the downloadable Excel templates are for "flange taps," which have L1 = L2 = 1". See the the article referenced above for more details on other pressure tap configurations.
Note that this is an iterative calculation. The Reynolds number is needed to calculate the orifice coefficient, C, but the velocity in the pipe (needed for the Reynolds number) can't be determined until C is known. The iterative approach that works well with this Excel template is to initially assume a value for the Reynolds number. A value of Re = 105 is typically a good starting point. With the assumed value for Re and values for the other input parameters shown, the orifice coefficient can be calculated and then Q and V can be calculated. The calculated value of pipe velocity, V, is then used to calculate the Reynolds number (Re = D1Vρ/μ). If the calculated value is different from the assumed value for Re, then use the calculated Re as the new assumed value and repeat the calculation. This procedure converges quite rapidly. Usually one or two iterations is all that is needed.
Download this Excel template in U.S. units.
Download this Excel template in S.I. units.