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

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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}

choke narrowing ratio

LaTeX Math Inline
bodyd

orifice diameter

LaTeX Math Inline
bodyD

pipe diameter 

LaTeX Math Inline
body\epsilon

expansion factor


The deviation from ideal estimation 

LaTeX Math Block Reference
anchorq_ideal
 arise from fluid friction with choke elements and possible flow turbulence.

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The most popular engineering correlation covering all ISO 5167 tapping arrangements is given by Discharge coefficient @ model:

LaTeX Math Block
anchor8W4JO
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C_d = C_{d, \infty}(\beta) + b(\beta) \cdot {\rm Re}^{-n}

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Device

LaTeX Math Inline
bodyC_{d, \infty}

LaTeX Math Inline
bodyb

LaTeX Math Inline
bodyn

Nozzle, ISA 19320.99 − 0.2262 · β​4.1​​1,708 − 8,936 · β + 19,779 · β​4.7​​1.15
Orifice, Corner Taps0.5959 + 0.0312 · β​2.1​​ − 0.184 · β​6​​91.71 · β​2.5​​0.75



See also

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

Pipeline Engineering / Pipeline / Choke 


Reference

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Anchor
Stolz
Stolz
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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