A ratio between compressible fluid volumetric flowrate and incompressible fluid volumetric flowrate through the ideal orifice:
(1) | \epsilon = \frac{q_{\rm compressible}}{q_{\rm incompressible}} |
where
(2) | q_{\rm incompressible} = \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 |
For incompressible fluids (water and most types of oil) the expansion factor is \epsilon = 1.
For compressible fluids (condensate, steam and gases) the expansion factor is \epsilon < 1.
The most popular engineering correlation covering various tapping arrangements is given by ISO5167:
\epsilon = 1 - (0.41 + 0.35 \, \beta^4) \cdot \frac{\Delta p}{\kappa \cdot p_{out}} |
where
\Delta p | pressure drop on the orifice |
p_{out} | discharge pressure |
\beta = \frac{d}{D} | orifice narrowing ratio |
\kappa | Adiabatic Index (isentropic expansion factor) |
isentropic exponen
See also
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS) / Pipeline Choke @model
[ Orifice Plate Discharge Coefficient ]