Flow meter models

This page documents the equations implemented in the Orifice equipment for computing flow through differential pressure meters. All variables are in SI units.

Orifice plate

The discharge coefficient $C$ is calculated with the Reader–Harris/Gallagher correlation as implemented in ISO 5167:

\[C = 0.5961 + 0.0261\beta^2 - 0.216\beta^8 + 0.000521\left(\frac{10^6\beta}{Re_D}\right)^{0.7} +(0.0188 + 0.0063A)\beta^{3.5}\left(\frac{10^6}{Re_D}\right)^{0.3} +(0.043 + 0.080e^{-10L_1}-0.123e^{-7L_1})(1-0.11A)\frac{\beta^4}{1-\beta^4} -0.031(M_2' -0.8M_2'^{1.1})\beta^{1.3}\]

The expansibility factor is \(\epsilon = 1 - (0.351 +0.256\beta^4 +0.93\beta^8)\left[1-\left(\frac{P_2}{P_1}\right)^{1/\kappa}\right]\)

The mass flow rate is obtained iteratively from \(m = \left(\tfrac{\pi D^2\beta^2}{4}\right) C \epsilon \frac{\sqrt{2\rho(P_1-P_2)}}{\sqrt{1-\beta^4}}.\)