A ratio between actual volumetric flowrate through the real orifice and volumetric flowrate estimate through the ideal orifice:
| (1) | C_d = \frac{q}{q_{\rm ideal}} |
where
| (2) | q_{\rm ideal}= \epsilon \cdot \frac{\pi d^2}{4} \cdot \sqrt{\frac{2 \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} | orifice narrowing ratio |
d | orifice diameter |
D | pipe diameter |
\epsilon | expansion factor |
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} in the pipe:
| (3) | C_d = C_d(\beta, {\rm Re}) |
where
| (4) | {\rm Re} = \frac{v \cdot D}{\nu} = \frac{4 \, q}{\pi \, D \, \nu} |
where
\nu | kinematic viscosity |
v | cross-sectional average flow velocity in a pipe |
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:
| (5) | 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
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS) / Pipeline Choke @model
[ Orifice Plate Expansion Factor @ 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