Velocity is one division, and people still get it wrong
Airflow divided by free area. The only way to break it is to leave a duct dimension in inches — an 8 in round duct has an area of 0.349 square feet, not 50.3, and dividing 400 CFM by the wrong one puts the answer out by a factor of 144 in the direction that makes a screaming duct look like a whisper. That is the whole trap. Once the area is in square feet, 400 CFM through 8 in round is 1,146 fpm and there is nothing else to it.
The rectangular case has a second trap sitting behind the first. A 14 by 8 duct has a free area of 0.778 square feet, so at 400 CFM it runs 514 fpm. Its equivalent round diameter is 11.46 in, and a round duct that size runs 558 fpm at the same flow — nine percent faster. Both numbers are correct and they answer different questions. The 514 is the velocity in the duct. The 11.46 is the diameter that would drop the same pressure. Reading the velocity off the equivalent round is a common and quiet error.
Equivalent round is Huebscher, not a perimeter match
The relation is 1.30 times the area to the power 0.625, over the sum of the sides to the power 0.25 — and it is a friction equivalence, arrived at by matching pressure drop, not by matching perimeter or area. Take the 14 by 8. Match it by area and you get 11.94 in; match it by perimeter and you get 14.01 in. The friction equivalent is 11.46, smaller than both, and that ordering is the physics rather than an accident: a flat duct wets more perimeter for the air it carries than a round one does, so it drops more pressure than its area alone would suggest and its friction equivalent has to come out below the area match.
Which means a duct fabricator working from a perimeter match is buying sheet metal correctly and sizing the airflow badly wrong — 14 in against 11.46 in is a factor of nearly three in friction rate at the same flow.
Flat oval is handled the same way with its own constant. The area of a flat oval is the semicircular ends plus the flat middle, and both go into a hydraulic-diameter form that produces a round equivalent in the same sense.
The fifth power is the part worth internalising
Friction rate carries diameter to about the 5.02 power. Take the 11.46 in equivalent round above at 400 CFM: the page gives 0.046 in wg per 100 ft. Move to a 10 in round at the same flow and it becomes 0.092 — exactly double, for an inch and a half of diameter. Go the other way to 14 in and it falls to 0.017, a third of what it was. The ratio between two sizes never depends on the flow, only on the sizes, which is why a table of size ratios is worth more than a table of friction rates.
It also means the cheapest pressure in a system is almost always bought with metal rather than with fan power, and that a duct crushed to two thirds of its diameter by a joist is not two thirds as good. It is about an eighth as good. Flex duct pulled tight round a corner and left compressed is the everyday version of that arithmetic.
What this cannot know
It does not know whether the 400 CFM is real. Airflow at a branch is the thing least often measured and most often assumed, and if the number going in is a design figure rather than a measurement, everything downstream of it inherits that. It does not know the fitting equivalent lengths for your fittings — the field is there because published tables disagree with each other badly, and a takeoff with a scoop is a different animal from one without. It does not know whether the duct is round any more; oval-crushed flex has the free area of the crush, not of the label.
And it issues no verdict. There is no velocity on this page that is called too fast and no friction rate called too high, because those depend on what the system was designed to, what noise the room will take and what the equipment can carry — none of which are in the form.
Questions people ask
How do I work out air velocity in a duct?
Divide the airflow in CFM by the free area of the duct in square feet. The one thing to be careful about is the units: a duct measured in inches has to be converted, so an 8 in round duct is 0.349 square feet and 400 CFM through it is 1,146 fpm. Leaving the area in square inches is the mistake that puts the answer out by 144 times, and it looks plausible enough that it can survive a long way.
What is the equivalent round of a rectangular duct?
It is the round diameter that would drop the same pressure at the same airflow, from the Huebscher relation: 1.30 times the area to the 0.625 power, divided by the sum of the sides to the 0.25 power. For a 14 by 8 duct that is 11.46 in. It is not a perimeter match, which would give 14.01 in, and it is not an area match, which would give 11.94 in — the friction equivalent comes out below both, because a flat duct wets more perimeter for the air it carries. Use it for friction and pressure work, and use the real area for velocity.
Does the velocity in a rectangular duct match its equivalent round?
No, and assuming it does is a routine error. A 14 by 8 duct at 400 CFM runs 514 fpm on its own area. Its 11.46 in equivalent round holds less air and runs 558 fpm at the same flow. The two are matched on pressure drop, not on velocity, and the gap grows as the rectangle gets flatter.
How much does one duct size up actually save?
More than most people expect, because the friction rate carries diameter to about the fifth power. At the same airflow the ratio between two sizes is the diameter ratio to the 5.02, and it does not change with the flow. Ten inches to twelve is a twenty percent change in diameter and cuts the friction rate to about forty percent of what it was. That is why a pinched or crushed section costs so much more than its length suggests.
Why is the fitting equivalent length a field rather than a built-in figure?
Because published tables disagree with each other by a factor of several for the same nominal fitting, and the fitting on your job is a particular one with a particular radius, a particular takeoff and a particular amount of flex hanging off it. Whatever total effective length matters to a decision should come from the table the design was worked to, not from a page that does not know what is in your ceiling.