Taking the mystery out of equivalent size of duct
Maybe, maybe not.
Ductulators and duct sizing programs are all based on an equivalent round duct size. The airflow through a duct is limited by both velocity and pressure loss. With a specific flow rate, in cubic feet per minute (CFM), and a round (or rectangular) duct size, both the velocity, in feet per minute (FPM), and friction loss, in inches of water per 100 ft of duct, can be directly read off of the ductulator. Friction loss in a duct 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. What is not so obvious is the effect that perimeter has on the friction loss.
The most efficient duct size is round, but due to space limitations, round cannot always be used due to the limited space available above the corridor ceilings. Rectangular duct is often used in place of round to reduce the amount of space required above the ceiling. The following example will examine the potential problems that could arise in the changing from round to rectangular duct.
The project calls for 7,500 CFM in a 30 inch round duct to be installed above the ceiling in a long corridor. Additional services are to be installed that pass through the corridor, perpendicular to the ductwork. In a quick call to the engineer, the sheet metal contractor obtained approval to change the duct from round to rectangular.
Reaching an agreementBased on the engineer's approval, the maximum allowable velocity is 1,500 FPM and the pressure loss of the new duct size is NOT to exceed 0.1 inches of water per 100 ft of duct. The contractor agrees to abide by this design criteria and to size the duct accordingly.
The cross-sectional area of a circle is where D is the duct diameter. So the contractor uses his calculator and determines that cross sectional area of the 30 inch round duct is:
30x30x3.1416/4=706.9 SQ IN
No problem. He can use a 35x20 duct, a 39x18, a 44x16 or even a 50x14. The cross-sectional areas of all of theses sizes are within 1% of the area of the original 30 inch round duct, so everything is okay.
Well, maybe it's 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, ASHRAE uses
DIA = 1.3*(L*W)^0.625/(Ltw)^0.25
to calculate the equivalent diameter of a rectangular duct where DIA is the equivalent duct diameter, L is the duct length and W is the duct width. So the equivalent diameter of a 35x20 duct is:
1.3*(35*20)^.625/(35+20)^0.25=28.6 inch round
When you use this formula and enter the sizes, you find that the equivalent round duct is somewhat smaller then the original 30 inch round duct. The 35x20 is equivalent to 28.6 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 both drift farther away from the design parameters with the 50x14 being the worst at about 1,850 FPM and friction loss of 0.15 inches of water. The maximum velocity and pressure drop for the system have both been exceeded.
In the event that there is a problem with the system as installed, this could come back to haunt the contractor because he did not follow the design criteria established by the engineer. As a worst-case scenario, the contractor could be forced to replace the ductwork already installed because it is not the same size as the duct shown on the contract documents.
Take care 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.