Restrictive Orifice

[HardyPatel]

If i want to calculate the flow through a restrictive orifice, i have to check whether the flow is choked flow or not (Please Comments). I found equations for liquid and vapor from crane's Technical Paper 410 for not choked flow.
For liquid:
W = 1891*c*d^2*(dp*rho)^0.5

For Vapor:
W = 1891*Y*c*d^2*(dp*rho)^0.5

From Technical paper 410, you have to use graph for calculating value of c (Discharge coefficient for both) and Y (Expansion Factor only for vapor case). I need equations or explicit correlation to calculate the value of c and Y.

Questions:
1. Can anyone tell me where i can found those Explicit Equations to avoid iteration method?

2. I know the equation for Choked flow (thread124-139392) but how can i calculate that my system has choked flow or not.

3. The equation for choked flow and the equation for not-choked flow are different? or are you agree if i use crane's equation with dp choked instead of actual dp when i have choked flow condition.

4. Where can i search for all other references for calculation of flowrate thorugh restrictive orifice as i would like to understand it and if possible i would like to make a workbook of it for further use.

 

[mbeychok]

HardyPatel:

Read this online article:

http://www.air-dispersion.com/msource.html

and select "Gas Discharge From Pressure Source".

(1) It has the equations for both choked flow and non-choked flow
(2) It includes a discussion of how to determine whether or not the flow will be choked.
(3) It has a number of Internet references that confirm and validate the equations.


Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[CJKruger]

HardyPatel,

Firstly, before you do the calc, decide what your approach will be. You have 2 options:

(a) Calc Y and C based on permanent pressure drop.
(b) Calc Y and C based on flange pressure drop and then multiple dP with pressure recovery ratio.

Assuming you are following (a), then the answers to your questions are:

1) You have to use Y1 and C (or K) for pipe taps. These equations are available in many references (I use Miller and Spink).

2) Use the equation given by Milton. Two issues though:
- It assumes beta < 0.2. If that is not the case, you have to use the equation in Perry.
- A thin plate orifice NEVER chokes.

3) Yes, but you have to limit the dP in both the main equation and in Y1.

4) Miller, Spink, Perry, Crane, etc. Or send me 50 bucks and I will send you my write-up

CKruger

 

[sailoday28]

CJKruger (Petroleum)
- A thin plate orifice NEVER chokes.
To my knowledge only for air and steam. My Crane TP 410 1979 has a reference number10-- R.G. Cunningham Orifice Meters with supercritical flow ASME Paper No 50-A-45.
Cunningham substiates what you have stated.
However, Crane does not give any background other than a refernce. I believe earlier editions of
TP 410 did address supercritical flow. Do you or any other engineers have a copy of the ASME paper?

Regards.

 

[CJKruger]

sailoday28,

As stated, a thin plate orifice does not choke, and it applies to both gases and liquids (flashing).

I still use the equations from Cunningham for gas flow.

Flashing liquid flow will choke if the nozzle length is more than 4 inches. For zero length the flow approaches the liquid only flow equations.

CKruger

 

[djack77494]

I'm confused by the statement that "a thin plate does not choke". Are you saying that as the downstream pressure falls that you do not reach a limiting pressure where further decreases do not increase the flowrate? If you do reach this limit, then you have attained "choked flow" as I understand its meaning. If you do not, then I would like to know why not, since that would contradict what I thought I knew.
Thanks,
Doug

 

[CJKruger]

doug, Yes, for a thin plate orifice gas flow continues to increase with decreasing downstream pressure.

Physically it happens because the vena contracta is downstream of the orifice and increases its diameter at very low outlet pressures.

The Y factor does however changes slope at a certain point, with the overall result that an assumption of gas choke flow is only wrong by 10-20 % if I remember correctly (please check before using it).

The error is more significant for flashing liquid choke flow, which also does not occur in a thin plate orifice.

 

[djack77494]

Thanks for the explanation CJ.

 

[mechprocess]

API 520 Appendix E

Emperical expressions for Y sonic, Ksonic

I tried to cut and past my calculation for this but it wouldn't take.

I made a program for this.

 

[sailoday28]

CJKruger (Petroleum)Do you have any references for gases other than air or steam. I'm interested in noting how the Cd etc. varies.

Regards

 

[CJKruger]

sailoday28, no sorry I don't. I use Cunningham for all gas flows.

The C (or K) value would not changed, as it is defined from liquid flow. The change is built into the Gas Expansion (Y1) factor.

CKruger