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

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

where

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

and

	pressure drop on the choke,
	choke narrowing ratio
	orifice diameter
	pipe diameter

The deviation from ideal estimation arise from fluid friction with choke elements and possible flow turbulence.

The discharge coefficient is a function of a choke narrowing ratio and Reynolds number :

C_d = C_d(\beta, {\rm Re})

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

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

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

Device
Nozzle, ISA 1932	0.99 − 0.2262 $\cdot$ β^4.1	$1708 - 893 6 \cdot β + 1977 9 \cdot β^{ 4.7 }$	$1.15$
Orifice, Corner Taps	0.5959 + 0.0312 $\cdot$ β^2.1 − 0.184 $\cdot$ β⁶	91.71 $\cdot$ β^2.5	0.75

Reference

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

https://neutrium.net/fluid_flow/discharge-coefficient-for-nozzles-and-orifices/

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 ]

See also

Reference