@wikipedia

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

C_d = \frac{q_{\rm real}}{q_{\rm ideal}}

where

q_{\rm ideal}= \epsilon \cdot \frac{\pi d^2}{4} \cdot \sqrt{\frac{12 \cdot \Delta p}{\rho \cdot (1-\beta^4)}}

and

The deviation from ideal estimation 

The discharge coefficient 

C_d = \frac{d_D}{d} + 0.3167C_d(\beta, {\rm Re})

where

{\rm Re} = \frac{v \cdot \left(D}{\nu} = \frac{d4 \, q}{\pi \, D \, \nu}

where

It can be estimated for popular choke types or tabulated in laboratory.

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

C_d = 0.5961 + 0.0261 \cdot \beta^2 - 0.216 \cdot \beta^8d_D} \right)^{0.6} + 0.025000521 \cdot \big [ \logleft( \frac{ 10^6 \, \beta }{ {\rm Re} -} 4 \big ]\right)^{0.7}

See also

...

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

[ Orifice Plate Expansion Factor @ model ]

Pipeline Engineering / Pipeline / Choke

Reference

...

ISO5167 – Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full

M J Reader-Harris and J A Sattary, THE ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION - THE EQUATION FOR ISO 5167-1,  National Engineering Laboratory, East Kilbride, Glasgow, 1996

J E Gallacher, ORIFICE PLATE DISCHARGE COEFFICIENT EQUATION, Shell Pipe Line Corporatio, Paper 5.1, NORTH SEA FLOW MEASUREMENT WORKSHOP,  23-25 October 1990

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

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 ]