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(OP)
I have attached an image of a square throat elbow whose aspect ratio is around 1:8. (Width 32in, height 4in). Contractor has used 2 of these elbows to cross a beam. and there is some length of straight duct section of these dimensions too (around 6-7ft). i want to know HOW MUCH bad it is? As per my rough calculations the duct friction loss came out to be 1.53, equivalent dia 13in and equivalent length 39ft. However, i need someone more expert in design to vet these parameters as standard charts and tables are not telling much beyond aspect ratio of 1:4. After that, I am a bit confused on how to interpret these parameters to convert these into simple pressure drop loss, cfm loss, AHU energy consumption increase or any other parameter which I dont know. Can somebody help me through this in order to quantify the damage this elbow will bring?

The duct tapped into the other duct at the top of the picture probably a very large pressure drop as well. Very poor change of direction!

(OP)
yes thats also quite frightening! but how to quantify the losses that is the question!

You need to look at the complete system to evaluate the damage. I ask what is the end game? Are you trying to check the fan or go after others that are responsible for this design? As others pointed out, an offset of 2 elbows is not the only issue. Entry fittings into and exiting the elbows will also have very high losses as compared to an “ideal” fitting. If you are checking the design, did you take ½ the flow and run math based upon a 4:1? You will need to advise more info to evaluate the system. Is this a transfer duct between to spaces at 600fpm or an exhaust duct running at 1800 fpm? If this is lined with 1”, your ratio will now be 15. Don’t be quick to blame the installer/fabricator/designer, his hands are tied based upon space allowed and design. Did someone omit a beam pocket detail? In most cases, the system fan has been selected with enough sp to move the volume but the owner will pay operating delta \$ for the life of the building but gets the space plan he required WITHOUT a low ceiling or an added cost of an additional 12” of building height. Square T and square H with 1 vane may minor have help here but flow and insulation details are needed.

(OP)
its basically the architects fault. my end game was to make sure this solution will not result in such a huge pressure drop that it blocks the airflow. The solution has been implemented without any objective calculations. however, as DrTRU says, the solution is gonna work with the side effect being increased energy consumption by AHU as it will have to exert more power (VFDs are there).

"If you are checking the design, did you take ½ the flow and run math based upon a 4:1? You will need to advise more info to evaluate the system. Is this a transfer duct between to spaces at 600fpm or an exhaust duct running at 1800 fpm? If this is lined with 1”, your ratio will now be 15."

Yes that is what I want to have a grip on. I am not much into design. Could you please elaborate more on this? or could you please point me to some good resource where I can learn this design process from start to end? I know how to calculate cooling load tonnage and CFM required zone-wise. Once I get those things, what are the next steps involved? How to size ducts? How to select equipment? What is the ordering?

Long story short, if the velocity in this duct is low (e.g., less than ~1200 fpm), weird transitions like this are ok. If the air velocity in this transition is ~1600 fpm or more, these types of fittings pose a problem...

You will need to utilize an engineer with experience in design of duct systems. SMACNA and ASHRAE have duct design guides and apps that present flow vs. dp. I would simulate the system with a load estimating software based upon fan eff. and power cost. You will end up with a delta operating cost per year. In most cases, you could do a rough estimate of increased dp and look at increased hp and sum increased KWh (year or life time total) at the power rate to give a rough number.

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