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

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

For compressible fluids (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:

&11 =1-(0.41+0.35~ )-.

isentropic exponent

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See also