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LaTeX Math Block
anchorq_ideal
alignmentleft
q_{\rm incompressible} =  \frac{\pi d^2}{4} \cdot \sqrt{\frac{2 \cdot \Delta p}{\rho \cdot (1-\beta^4)}}

and

LaTeX Math Inline
body\Delta p

pressure drop on the choke

LaTeX Math Inline
body\Delta p = p_{in} - p_{out}

LaTeX Math Inline
body\beta = \frac{d}{D}

chokeorifice narrowing ratio

LaTeX Math Inline
bodyd

orifice diameter

LaTeX Math Inline
bodyD

pipe diameter 


For incompressible fluids  and slightly compressible fluid (water and most types of oil) the expansion factor is 

LaTeX Math Inline
body\epsilon = 1
.

For compressible fluids Strongly Compressible Fluid (condensate, steam and gases) the expansion factor is 

LaTeX Math Inline
body\epsilon < 1
.

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

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

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LaTeX Math Block
anchor\epsilon
alignmentleft
\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]

where

LaTeX Math Inline
body--uriencoded--p_%7Bin%7D

intake pressure

LaTeX Math Inline
bodyp_{out}

discharge pressure

LaTeX Math Inline
body\beta = \frac{d}{D}

orifice narrowing ratio

LaTeX Math Inline
body\kappa

Isentropic exponent (κ), in express analysis can be taken as 1.3


See also

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Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS) / Pipeline Choke @model

Orifice Plate Discharge Coefficient ]Pipeline Engineering / Pipeline / Choke

Pipeline Engineering / Pipeline / Choke