@wikipedia
A ratio between actual volumetric flowrate through the real orifice and volumetric flowrate estimate through the ideal orifice:
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C_d = \frac{q}{q_{\rm ideal}} |
where
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q_{\rm ideal}= \epsilon \cdot \frac{\pi d^2}{4} \cdot \sqrt{\frac{2 \cdot \Delta p}{\rho \cdot (1-\beta^4)}} |
and
The deviation from ideal estimation
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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 in the pipe:| LaTeX Math Block |
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C_d = C_d(\beta, {\rm Re}) |
where
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{\rm Re} = \frac{v \cdot D}{\nu} = \frac{4 \, 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:
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C_d = 0.5961 + 0.0261 \cdot \beta^2 - 0.216 \cdot \beta^8 + 0.000521 \cdot \left( \frac{ 10^6 \, \beta }{ {\rm Re}} \right)^{0.7} |
See also
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Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS) / Pipeline Choke @model
[ Orifice Plate Expansion Factor @ model ]
Pipeline Engineering / Pipeline / Choke
Reference
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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
