@wikipedia
A ratio between actual volumetric flowrate through the orifice and volumetric flowrate estimate through the ideal orifice:
| LaTeX Math Block |
|---|
|
C_d = \frac{q}{q_{\rm ideal}} |
where
| LaTeX Math Block |
|---|
| anchor | q_ideal |
|---|
| alignment | left |
|---|
|
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
| LaTeX Math Block Reference |
|---|
|
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 :
| LaTeX Math Block |
|---|
|
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 @ model:
| LaTeX Math Block |
|---|
|
C_d = C_{d, \infty}(\beta) + b(\beta) \cdot {\rm Re}^{-n} |
| Device | | | |
|---|
| Nozzle, ISA 1932 | 0.99 − 0.2262 · β4.1 | 1,708 − 8,936 · β + 19,779 · β4.7 | 1.15 |
| Orifice, Corner Taps | 0.5959 + 0.0312 · β2.1 − 0.184 · β6 | 91.71 · β2.5 | 0.75 |
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
