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Chemical engineering other topics FAQ

Hydraulic calculations

How to do an orifice calculation by MortenA
Posted: 14 Nov 03

This FAQ is a collection of statements from various mails re. orifices. I have selected them because they look right to me and stays on the subject. The mails may reference questions and remarks not repeated in this FAQ. Mails are separated by "---". Bear in mind that you can generally distinguise between two type os orifices:

   1) Restriction orifices
   2) Flow element

Both of these can then be used for gas and for liquids.



Crane technical paper 410 is an invaluable resource and covers how to calculate the resistance created by an orifice in a piping system.  I highly recommend you get a copy.

A search on google will locate the website where you can order it.

The formula for the resistance of an orifice:

W = 1891*Y*d1^2*C*(dP*rho)^0.5

Y is the expansion factor for a gas.  For a liquid it is equal to 1.0.  You need the book to read off Y.

d1 is the orifice diameter in inches

C is the orifice coefficient which is a function of the beta ratio and Reynold's number.  If the system is in turbulent flow, 0.6 is a reasonable estimate.

dP is the pressure drop in psi

Cockroach (Mechanical) Jul 28, 2003
This problem can be a very complex issue.  Use the AGA Report Number 3 (API 14.3) for industrial standard specifications on orifice measurement, either gas or liquid, single phase.

Otherwise, I would use known textbook references such as Miller to model your situation.  There are programs available on the market, most are no good unless you see the API monogram or equivalent.  I will concede that depending on your level of accuracy, expensive purchased software may be beyond budgetary constrains.

Flow Measurement Engineering Handbook
Miller, Richard W
McGraw Hill, 1996 (Third Edition)
ISBM 0-07-042366-0

This reference is the industry Cadillac my friend, well worth it for the price tag!
Kenneth J Hueston, PEng
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

BRIS (Civil/Environme) Jul 30, 2003
The question was for the correct calculation of flow reduction v orifice diameter.

The orifice calculations will give you the head loss across the orifice for a specified flow. (or the flow for a specified head loss). There is no direct relationship between orifice diameter and flow reduction. The head loss across the orifice will cause a flow reduction in your system but in order to calculate the flow reduction you will need to look at the overall system not just at the orifice. i.e when you reduce the flow you will also reduce the head losses through other fittings and pipes in the system and you have to look at the system as a whole.

For water the basic orifice equation (in SI units)is:

Q = Cd.a.(2.g.Dh)^0.5

Cd = C/(1-C^2(a/a1)^2)^0.5

a = area of the orifice
a1 = area of the pipe
Dh = head loss across the orifice

C is basically the contraction coefficient (the diameter of the vena contracta/ the diameter of the orifice). For turbulent flow (Reynold number above 10,000 it is about 0.62. For viscous flow C may be 0.7.

as D23 notes If you tell us what fluid you are dealing with and provide a basic description of the system you would likely get a more useful response.


athomas236 (Mechanical) Jul 29, 2003
If you want to establish a relationship between orifice size and flow then what you need is a relationship for pressure drop across an orifice not the pressure differential.

Formulae for orifices usually relate the pressure difference that would be measured say near the flanges of the orifice to the flow. What you really need is the the pressure difference with tapping points as far apart as possible as this most closely reflects the permanent pressure loss.

In such a case I would use Miller as Crane 410 tends to give formulae for flange tappings.



stanier (Mechanical) Jul 30, 2003
Try out this on line calculation for orifice plates. http://www.efunda.com/formulae/fluids/calc_orifice_flow...;


BRIS (Civil/Environme) Jul 31, 2003
The orifice plate calculations as noted by stainer are for calculating the flow from pressure tappings not for calculating the overall pressure drop. (See the post from athomas236 above).

dpenz (Mechanical) Jul 31, 2003
Overall pressure loss through an orifice depends on the Beta ratio (orifice diameter compared to pipe diameter).  There is a curve in ASME Fluid Meters.  An equation that fits the curve within 2% is

% pressure loss = 0.958 + 0.022*Beta - 0.934*Beta^2

For example, at Beta = 0.5, % pressure loss = 0.735, overall pressure loss = 0.735 * differential

Your procedure should be to assume a pump head, look up flow on the pump curve, then select an orifice size, calculate differential at that flow rate (using any of the references given above), calculate pressure loss, add to the pump head, look up new (lower) flow, recalculate differential and pressure loss and continue iterating until the solution settles out.

If you don't like the answer, select a larger or smaller orifice size and iterate again.

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