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herman74 (Chemical) (OP)
17 Dec 07 5:06

I have an orifice on a sea water discharge line in order to reduce the pressure to the one present in a downstream common discharge.
Since the pressure drop and the flow rate are quite high (3 bar; 12500 m3/h), our supplier have provided us a DN 1400 orifice, 40 mm thickness, with 253 holes with diameter of 20 mm.

I want to verify this choice (also for personal culture), so I searched our library and goggled the net but I was not able to find a formula that could permit to find the pressure drop of a multi hole orifice as a function of:

-) diameter of the single hole
-) number of the holes
-) thickness of the orifice (length of the hole)

Can anyone help me on this topic.

Thanks in advance

rcooper (Mechanical)
17 Dec 07 7:11
For an approximate answer,

Headloss h=k(v^2)/(2g) where v is the velocity through the holes, k is a variable which is a function of the orifice shape and g is the gravitational acceleration.

so in your case, the flow rate (q) is 3.47m3/s

Area = PI*(0.02^2)/4*253 = 0.0794m2

Velocity = q/A = 3.47/0.0794 = 43.66m/s

headloss is 2.6*(43.66)^2/2/g = 252m or about 25 bar?????

I seem to be a factor of 10 out.  How does that sound to other people?

I guess that with the length of the hole being greater than the diameter, that may alter my choice of k, but surely not that much?
katmar (Chemical)
17 Dec 07 7:42
I agree with rcooper that there is a serious error here.  A velocity of 43.66 m/s through an orifice is extreme for water and will lead to a very high pressure drop.  My pressure drop calculation is very close to rcooper's, assuming a thin orifice.

However, I believe a better way to approach it - although not totally rigorous - would be to take 1/253 of the flow (i.e. 49.4 m3/h) and calculate for just one orifice.  In this way it is possible to take the fact that the orifice thickness is double its diameter into account.  The method I use for this calc is from William B Hooper (He of 2K fame) published in Chemical Engineering, November 7 1988, pgs 89-92.

Using the Hooper procedure, and pretending that we have a 100 mm pipe with a single orifice and a flow of 49.4 m3/h I get a pressure drop of approx 15 bar.

If you want to get a pressure drop of 3 bar the flow would have to be about 22 m3/h per hole, giving you 568 holes instead of the 253 specified.


Katmar Software
Engineering & Risk Analysis Software

herman74 (Chemical) (OP)
17 Dec 07 9:07
First of all thanks for for yours quick replies and second sorry because I miss to give you an information. During a first verification of these orifices we found that the maximum allowable flow through the orifice, in our process configuration, was very low. So we ask our supplier to check this issue and they reply us that the holes diameter was wrong and that we have to enlarge them to 35 mm.

We have checked this orifices conjecturing that only one hole is present with a surface equal to the sum of all the 253 holes and then using the formula given by the CRANE's book:

Volumetric Flow = C * Area * SQRT(2 * g * head loss)

My question is if there is better formula than the Crane's one.
-) How important is the fact that there are 253 small holes instead of a bigger one
-) How important is the length of the hole

I think that a difference have to exist otherwise our supplier would have provided us a single hole orifice.


rcooper (Mechanical)
17 Dec 07 9:50
The Crane equation is the same as the equation I gave, just the C is a re-hashed version of my k.

I haven't read the Crane manual (keep trying to get a copy).  With any luck there is a graph in there showing how C varies with the diameter and length of the orifice, and possibly the Reynolds number of the flow through the orifice (if this is the case check exactly what the characteristic length is, and use it).  Do the calculation for 1/253 of the flow through a single 35mm orifice, using the actual dimensions of the orifice to obtain the value of C.  That is the head loss across each individual orifice and the head loss across the plate as a whole.

Incidentally, 35mm orifices seems to give you an answer closer to the required 3 bar(about 2.7 bar by my rough and ready method).
Latexman (Chemical)
17 Dec 07 11:27
Van Winkle et al provided a correlation for "perforated plates" which is documented on page 5-37 in my Perry's Chemical Engineers' Handbook (6th Ed.).  Whether the holes are sharp edged (drilled) or slightly rounded (punched) makes a significant difference.

Good luck,

rcooper (Mechanical)
17 Dec 07 12:16
"Whether the holes are sharp edged (drilled) or slightly rounded (punched) makes a significant difference"

As does whether they de-burr the drilled holes or not.

When ever I have used orifice plates I have ensured they are easily interchangeable and that I have pressure gauges upstream and downstream.  This has let me get close with my first effort and then I trim with my second effort.  This is generally needed because of other uncertainties in the pipe, such as roughness or the effect of two bends closely following each other.
herman74 (Chemical) (OP)
17 Dec 07 12:54
I'm not able to find the graph that Latexman tell, but I have the seventh edition and in the section 5 there is "Heat & Mass transfer" In the part 6 there is "Fluid & Particle Dynamics" and at 6-21 there is somethings about the orifice, but nothing about this graph. However I read that the length of the orifice can improve the pressure recovery, but nothing more.

I've tried to do the calculation for a single hole, with 1/253 of the flow rate and I obtain the same result as per a single big hole with all the flow rate.

Thinking about this process I image that while for a single hole there are no neighbour turbulence that choke the pressure recovery, for a multiple hole plate the expansions of one jet will impact with the expansions of the others limiting the pressure recovery. That's why, for high pressure drop, multiple hole orifices are chosen.
These are only my thought because I do not have any study or formula that correlate these parameter.
I will take some data when the plant will start.

Thanks to all
dvd (Mechanical)
17 Dec 07 13:31
lots of good information on pressure drop through perforated material at:
Latexman (Chemical)
17 Dec 07 14:04
In the 7th Edition on page 6-21 and 6-22 use equation (6-111) for flow across a perforated plate with open area Ao and total area A.

Good luck,

katmar (Chemical)
17 Dec 07 14:35
A few words of caution on the methods being discussed here. I do believe that a sufficiently accurate answer can be obtained with a few intelligent assumptions, but be aware of the limitations.

The Crane method is for a single concentric orifice, and you are going to have to guess an orifice bore to pipe diameter ratio that makes sense.  It is also strictly for thin, sharp edged orifices.  The thickness of the plate is important here.

In Van Winkles method the top curve is for a Reynolds number in the hole of 20,000.  In this instance we have about 500,000.  Extrapolate with great care.  Also, the Van Winkle method is virtually the same as Crane's, but with a correction factor for the fractional free area.  With a 35 mm orifice your free area is about 16% and this makes a correction (1 - (Af /Ap)2) which is equal to about 2.5%.  This is less than what I would bother about in this instance.

If I use a Crane type formula for a sharp edged 35 mm orifice in a 100 mm pipe I get a pressure drop of 2.4 bar, but using the Hooper method for "thick" orifices that I referred to earlier the pressure drop is 1.5 bar.  I am happy to regard each orifice as independent because of the low free area ratio.


Katmar Software
Engineering & Risk Analysis Software

herman74 (Chemical) (OP)
17 Dec 07 18:14
Hi Katmar

Thanks a lot for your advice. I've searched around, but I wasn't able to find any information about the William B Hooper method, can you give me some advice where to find a paper that can explain this proceeding.

I have no access to Chemical Engineering, November 7 1988, pgs 89-92

Thanks in advance
insult2injury (Mechanical)
19 Dec 07 21:08
There is an old EPRI guideline for designing single and multistage multiorifice sparger pipes for large dumps to the condenser.  It clearly outlines a method to ensure uniform and pressure drop through the orifices.


Zapster (Electrical)
20 Dec 07 2:20
herman74 your problem is discussed in detail with formulas and coefficients in the “Handbook of Hydraulic Resistance” third edition, by I.E. Idelchik.
herman74 (Chemical) (OP)
20 Dec 07 3:46
Many thanks to all, after a very wide search on internet I found that Zapster is right: “Handbook of Hydraulic Resistance” third edition, by I.E. Idelchik could help me on this issue.
Now my problem is to have this book, but in some ways I will be able to read it, I've contacted my university library.

When I will finish my search I will post a reply with the results.

Helpful Member!  casflo (Mechanical)
2 Jan 08 12:02
herman74, the Idelchik´s handbook treats the multi hole orifice plates in its section IV for high Mach numbers. This is not the case for the normal flow of water.
I have designed, tested and installed many multi hole orifice plates in different water systems of spanish nuclear power plants and they are performing right without cavitation. The results of my initial tests about multihole orifice plates can be found in POWER magazine, September 1991.
herman74 (Chemical) (OP)
2 Jan 08 12:20
Many thanks casflo

I've been away from work for the christmas holidays till yesterday.
Now I will try to find if there are some useful informations in the Idelchick's handbook, and I will search for the article in the POWER magazine, but I don't now where to find this mag, if you have a pdf of this article could you gently mail it to me?

Thanks in advance
simo78 (Mechanical)
22 Feb 08 5:24
dissipation in multi-hole orifices is the topic of my research. i have looked for the article of casflo in power magazine, but I have not found it. Can you tell me the title please?

casflo (Mechanical)
22 Feb 08 9:31
simo 78 the title is "Look at orifice plates to cut piping noise, cavitation" and it was published in POWER, September 1991.
I revised this article in October 2003, but it was published in a spanish magazine.
insult2injury (Mechanical)
22 Feb 08 19:39

I'd be interested in seeing a list of your other references.  Thanks.


simo78 (Mechanical)
25 Feb 08 6:31
Many thanks casflo for your answer! are you still studing orifices plates? have you other references on this topic, please?
unfortunately I have not many references:
Ball J.W. (1973), Tullis J.P. (1975)
Fratino U. (1999, 2000)
casflo (Mechanical)
25 Feb 08 13:20
simo 78, try in and look for the paper ESDU 81039 titled "Flow of liquids. Pressure losses across orifice plates, perforated plates and thick orifice plates in ducts".

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