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

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

where

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

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
$\begin{array}{l}{\rm Re}\end{array}$	Reynolds number

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

(3)	$\begin{array}{l}\displaystyle C_d = \frac{d_D}{d} + 0.3167 \cdot \left( \frac{d}{d_D} \right)^{0.6} + 0.025 \cdot \big [ \log {\rm Re} - 4 \big ]\end{array}$

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See also