# Need help from a math whiz.

• 01-15-2005, 05:45 PM
midhvac
I'm havin one of them brain spasms. Tripped up by 8th grade math once again.

If we have a 10" round duct, then the area inside the duct is 78.54 sq in. We open it up and lay it flat on the table, it's 31.416" long.

So we take that piece of 31.416" long metal and shape it into a square duct. It will have 4 sides, each 7.854" long. That would give our square duct an inside area of 7.854 x 7.854 = 61.685 sq in, compared to a round duct made from the same piece of metal having an inside area of 78.54 sq in.

Is this possible or am I overlooking something?
• 01-15-2005, 05:56 PM
tin_fab
edit
• 01-15-2005, 06:09 PM
condenseddave
Sure it's possible. You saw it yourself.

Remember that a round duct and a square duct have different cross sections.

Your "8 x 8" square duct, (For the sake of argument, I'm calling it 8 x 8----get over it.:D ) is the square equivalent of 9" round duct.

In other words, to get the same airflow from the same size duct, the round will be larger than the square size, even though it appears visually that the square duct will be the same.

Another example is flat oval. Say, for the sake of argument, that a 7" oval will carry 150 cfm at .1".

A 7" round is actually good for 170 cfm at .1".

That's because there is more free area in a round duc than in the flat oval, or square.

Once you move into rectangular duct, though, the free area that you need is easier to attain, because of the geometry of the rectangle.

Or, I could be over-medicated and missing the point.:D
• 01-15-2005, 06:29 PM
billva
i think it's because you are not carrying all the decimals to the same place. are you rounding pi and then rounding the results of the equations. this will throw off the equivalence.

good brain teaser, my calculator is on fire.
• 01-15-2005, 06:50 PM
Guy
That just illustrates why a round shape is the most effecient border (in terms of perimiter length) to enclose an area. This also shows up in high school math problems like: If a farmer has 500 feet of wire to make a fence around a patch, what is the greatest area he can make?
• 01-15-2005, 09:34 PM
midhvac
Quote:

Originally posted by Guy
That just illustrates why a round shape is the most effecient border (in terms of perimiter length) to enclose an area. This also shows up in high school math problems like: If a farmer has 500 feet of wire to make a fence around a patch, what is the greatest area he can make?
I skipped math that day, cause I was mad at him for giving me "trick questions."
• 01-16-2005, 10:21 AM
sirtab
You can also take that piece of metal and make a
14.7" x 1" piece of duct and have only 14.7 sq" of free area.