Taking the mystery out of equivalent duct size calculations
Intro
Has this ever happened to you during coordination? You are measuring up the duct required for the building and the duct size specified by the engineer will not fit in the ceiling space. You think that you can just change the size and make it fit. As long as you use the same cross sectional area, you’re safe, right? Not really. Let’s dig into the Duct Size, Flow Rate, Friction Loss dependency to understand how it works.
You will also learn how to:
- calculate duct sizes based on the project requirements
- change round on rectangular duct and vice versa
- find rectangular duct size equivalents
The airflow through a duct is limited by velocity and pressure loss. With a specific flow rate and a round (or rectangular) duct size, both the velocity and friction loss can be directly read off of the ductulator. Take a look at the diagram below. It’s based on standard air density in pounds per cubic foot (0.075 lb/ft³) in clean round galvanized metal ducts.
For example, the friction loss in a 20 inches duct with air flow 4000 cfm can be estimated to approximately 0.23 inches water per 100 feet duct as shown in the diagram below. The air velocity can be estimated to approximately 1850 feet per minute.
Duct friction loss is a function of the roughness of the inside surface of the duct and the perimeter of the duct. The higher the velocity of the air traveling through the duct, the higher the friction loss. The rougher the surface, the higher the friction loss. Pretty obvious so far. What is not so obvious is the effect that perimeter has on the friction loss.
All the calculations are based on the round duct because the most efficient duct size is round. But due to space limitations, round cannot always be used. Rectangular duct is often used in place of round to reduce the amount of space required above the ceiling. I’ll give you an example where you can see the potential problems that could come up in the process of switching from round to rectangular duct.
The Issue
The project calls for 7,500 CFM in a 30 inch round duct to be installed above the ceiling in a long corridor. As always, there are a lot of additional services to be installed in the same space, so we have to change this round duct to rectangular.
Looking into the engineer’s approval we can see the maximum allowable velocity is 1,500 FPM and the pressure loss of the new duct size cannot exceed 0.1 inches of water per 100 ft of duct. The contractor agrees to follow this design criteria and to size the duct accordingly.
We can easily find that cross sectional area of the 30 inch round duct is:
Looks like we can use a 35x20" (700 in²) duct, a 39x18" (702 in²), a 44x16" (704 in²) or even a 50x14" (700 in²). The cross-sectional areas of all of these sizes are within 1% of the area of the original 30 inch round duct, so everything is ok. Absolutely not. This method does not account for the increase in the surface area of the duct that is in contact with the air stream. The greater the surface area of the duct, the greater the friction loss. To calculate the equivalent round duct size, you need to use the following formula:
where de — equivalent duct diameter, a — duct length, b — duct width.
So the equivalent diameter of a 35x20" duct is:
When you use this formula and enter the sizes, you find that the 35x20" rectangular duct is equivalent to 28.6 inch round duct. It is smaller than the original 30 inch round duct. Equivalent in the sense that the 35x20" duct behaves exactly as a 28.6 inch round duct. The 39x18" is now 28.4 inch round, the 44x16" is 28.1 inch round and the 50x14" is 27.6 inch round. By checking these sizes on a ductulator, you can see that for 7,500 CFM, the velocity in 35x20" duct has increased to about 1,700 FPM and the friction loss is now up to about 0.13 inches of water per 100 ft of duct. The 39x18 and 44x16 ducts are far away from the design parameters. The 50x14" duct is the worst, which has about 1,850 FPM and 0.15 inches of water friction loss of.
Calculations
Lesson learned. To choose the right duct we need to take into consideration all the given parameters per contract documents. What would be the best rectangular ducts to have in this case? Well, we need to learn how to calculate the air velocity and the friction loss. Duct friction loss is a function of the roughness of the inside surface of the duct and the perimeter of the duct.
The friction loss in a circular duct in galvanized steel can expressed:
where dh — friction loss, in of water per 100 ft of duct, q — air flow (CFM), (ft³/min), de — equivalent duct diameter (in).
To calculate the air velocity in the duct we have to use this formula:
where V — air velocity (ft/min), q — air flow (ft³/min), A — area of duct (ft²), d — duct diameter (in), a — duct width (in), b — duct width (in).
Now, let’s use the formulas above to find the ideal duct size. It turns out that the 34x22" duct perfectly fits all the parameters. 34x22" inch rectangular duct is equivalent to 30 inch round duct even if the cross section in this case is 748 in².
But what if this duct still doesn’t fit in the ceiling area? No problem, we can also use 20x38" and 19x42" duct sizes.
Coming to the conclusion
Be careful when changing duct sizes that are shown on your contract documents. It is always better to go to a bigger size than a smaller one. And, if you are in doubt, get written approval of the sizes that you plan on using prior to fabrication.
