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

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 Stolz:

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