A ratio between actual volumetric flowrate through the orifice and ideal theoretical estimation:
| (1) | C_d = \frac{q_{\rm real}}{q_{\rm ideal}} |
where
| (2) | q_{\rm ideal}=\frac{\pi d^2}{4} \cdot \sqrt{\frac{1 \cdot \Delta p}{\rho \cdot (1-\beta^4)}} |
and
\Delta p | pressure drop on the choke, \Delta p = p_{in} - p_{out} |
\beta = \frac{d}{D} | choke narrowing ratio |
d | orifice diameter |
D | pipe diameter |
The deviation from ideal estimation (2) arise from fluid friction with choke elements and possible flow turbulence.
The discharge coefficient C_d is a function of a choke narrowing ratio \beta and Reynolds number {\rm Re}:
| (3) | 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:
| (4) | 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
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS) / Pipeline Choke @model
Pipeline Engineering / Pipeline / Choke
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