A ratio between compressible fluid volumetric flowrate and incompressible fluid volumetric flowrate through the ideal orifice:

(1)	$\begin{array}{l}\displaystyle \epsilon = \frac{q_{\rm compressible}}{q_{\rm incompressible}}\end{array}$

where

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

and

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

For incompressible fluids and slightly compressible fluid (water and most types of oil) the expansion factor is $\begin{array}{l}\epsilon = 1\end{array}$ .

For Strongly Compressible Fluid (condensate, steam and gases) the expansion factor is $\begin{array}{l}\epsilon < 1\end{array}$ .

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

(3)	$\begin{array}{l}\displaystyle \epsilon = 1 - (0.351 + 0.256 \, \beta^4+ 0.93 \, \beta^8) \cdot \left[ 1 - \left( \frac{p_{out}}{p_{in}} \right)^{1/\kappa} \, \right]\end{array}$

where

$\begin{array}{l}p_{in}\end{array}$	intake pressure
$\begin{array}{l}p_{out}\end{array}$	discharge pressure
$\begin{array}{l}\beta = \frac{d}{D}\end{array}$	orifice narrowing ratio
$\begin{array}{l}\kappa\end{array}$	Isentropic exponent (κ), in express analysis can be taken as ~ 1.3

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See also