A ratio between actual volumetric flowrate through the orifice and volumetric flowrate estimate through the ideal orifice:

(1)	$\begin{array}{l}\displaystyle C_d = \frac{q}{q_{\rm ideal}}\end{array}$

where

(2)	$\begin{array}{l}\displaystyle q_{\rm ideal}= \epsilon \cdot \frac{\pi d^2}{4} \cdot \sqrt{\frac{2 \cdot \Delta p}{\rho \cdot (1-\beta^4)}}\end{array}$

and

$\begin{array}{l}\Delta p\end{array}$	pressure drop on the choke, $\begin{array}{l}\Delta p = p_{in} - p_{out}\end{array}$
$\begin{array}{l}\beta = \frac{d}{D}\end{array}$	choke narrowing ratio
$\begin{array}{l}d\end{array}$	orifice diameter
$\begin{array}{l}D\end{array}$	pipe diameter
$\begin{array}{l}\epsilon\end{array}$	expansion factor

The deviation from ideal estimation (2) arise from fluid friction with choke elements and possible flow turbulence.

The discharge coefficient $\begin{array}{l}C_d\end{array}$ is a function of a choke narrowing ratio $\begin{array}{l}\beta\end{array}$ and Reynolds number $\begin{array}{l}{\rm Re}\end{array}$ :

(3)	$\begin{array}{l}\displaystyle C_d = C_d(\beta, {\rm Re})\end{array}$

It can be estimated for popular choke types or tabulated in laboratory.

The most popular engineering correlation covering various tapping arrangements is given by ISO5167:

(4)	$\begin{array}{l}\displaystyle C_d = C_{d, \infty}(\beta) + b(\beta) \cdot {\rm Re}^{-n}\end{array}$

Device	$\begin{array}{l}C_{d, \infty}\end{array}$	$\begin{array}{l}b\end{array}$	$\begin{array}{l}n\end{array}$
Nozzle, ISA 1932	0.99 − 0.2262 $\cdot$ β^4.1	$1, 708 - 8, 93 6 \cdot β + 1 9, 77 9 \cdot β^{ 4.7 }$	$1.15$
Orifice, Corner Taps	0.5959 + 0.0312 $\cdot$ β^2.1 − 0.184 $\cdot$ β⁸	91.71 $\cdot$ β^2.5	0.75

Reference

ISO5167 – Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full

M J Reader-Harris and J A Sattary, THE ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION - THE EQUATION FOR ISO 5167-1, National Engineering Laboratory, East Kilbride, Glasgow, 1996

J E Gallacher, ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION, Shell Pipe Line Corporatio, Paper 5.1, NORTH SEA FLOW MEASUREMENT WORKSHOP, 23-25 October 1990

Stolz,J.,"A Universal Equation for the Calculation of Discharge Coefficient of Orifice Plates";, Proc. Flomeko 1978- Flow Measurement of Fluids,H. H. Dijstelbergenand E. A.Spencer(Eds), North-HollandPublishingCo.,Amsterdam(1978), pp 519-534

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Orifice Plate Discharge coefficient @ model

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