Calculating Pressure Drop - Rectangular Orifice 1

[Engineer6512]

I have a rectangular duct measuring 80" x 40", containing a 1/4" thick orifice plate with a rectangular opening size of 70" x 28". I have air flowing at 100,000 CFM through the duct at 40" W.C. static pressure.

I am trying to calculate the pressure drop across this orifice. The only equations I can find are for circular orifices in a circular pipe. As I don't need a 100% accurate calculation, I was thinking of converting the rectangular areas to their equivalent circular areas and using the standard equations.

Is this an acceptable approach? Does anyone have an equation for rectangular orifices they can provide?

Thanks.

 

[proinwv2]

I seriously doubt that you can use the area alone because the wetted perimeter to area ratios are different for circles and squares and the losses, which is what you are measuring, are different.

You need to find research data on this subject or do your own testing to calibrate your orifice. I realize that this is probably not practical at your size, but you could do lab testing on models with a known meter in the line to enable calculations.

Certainly more to it than I mention but that is my thoughts. I lookd forward to reading others posts here on this. If you do some research, let us know what you find.

Paul Ostand

http://www.ostand.com

 

[25362]

You may find help in the Fan engineering handbook by the Buffalo Forge Company (Buffalo, New York).

 

[rcooper]

From the "Handbook of hydraulics", 1996, Ernest F Brater et al, Seventh edition, McGraw Hill, ISBN 0-07-007247-7

Where Q=C.a.SQRT(2.g.h)

Q is discharge
C is loss coefficient
a is area
g is 9.81 m/s2
h is head loss

For a circular orifice, C varies from 0.591 to 0.657
For a square orifice C varies from 0.598 to 0.661
For a rectangular orifice C varies from 0.600 to 0.708

If you are used to "K factors", K = 1/(C^2)

All these factors and equations are for uncompressible fluids. They will need to be modified for compressible fluids.

As you can see, the coefficient varies for different shapes of orifices with different conditions. When ever possible I have taken direct measurements of the losses to assess how my particular orifice is behaving.

 

[Engineer6512]

Thanks rcooper, that's a great help to me. We are replacing the orifice flow measurement station with an averaged-pitot tube device for higher accuracy and I simply need to confirm that we will have equal to or less pressure drop with the new system.

Now I'll just have to figure out how to convert the formulas you provided to those applicable for a compressible fluid (air) and I should be all set.

Thanks again.

 

[zdas04]

Be careful not to over-smart yourself here. Flow equations in compressible Newtonian fluids treat those fluids as incompressible until they reach a significant fraction of the speed of sound (that was one of the first assumptions by both Euler and Bernoulli). I'd do the calcs and if the velocity within the reduced area is less than 0.3M I would use the incompressible arithmetic with confidence. If it is less than 0.6M I'd probably still use them but with less confidence. Above 0.6M none of the standard equations for relating dP across a restriction to average velocity (and therefore related to volume flow rate) have any validity at all.


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[Engineer6512]

Thanks for the tip zdas. Yes I'm significantly less than 0.3M so I'll go ahead and use the equations for incompressible fluids. I got a start on developing an equation for compressible, and it was starting to look ugly really fast. Thanks for saving me some time.

Regards.

 

[MortenA]

Is the duct flowing full? If not then a weir may be a more appropriate approximation?

Best regards

Morten

 

[proinwv2]

Look at Crane "Flow of Fluids" TP410. It is available on line.

All of the comp flow equations are there and you will see that they can be more involved than non-comp fluid flow.



Paul Ostand

http://www.ostand.com

 

[trashcanman]

As per ASHRAE Handbook of Fundamentals - Duct Design, for an orifice in a duct with hole/duct area ratio of 0.6125 (70x28)/(80x40), Cp is about 1.85.

For 100,000 CFM in 80x40 duct, Vel = 4900 fpm. Vp = (4900/4005)^2 = 1.496" W.C.

Loss across orifce is then = 1.85 x 1.496 = 2.77" W.C.

Hope this helps.

 

[Engineer6512]

Thanks trashcanman,

I have ASHRAE Fundamentals 2001... maybe I'm blind but I just finished looking through it and can't find the example you are referring to. Is it maybe included in a newer version?

 

[trashcanman]

Nope. 1977 ASHRAE Handbook., chap. 31, item 7.8 - Obstructions, perforated plate. Don't tell the air that the equations are that old, it might doubt you.....