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  1. #1
    Join Date
    Feb 2004
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    Midwest
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    9,937
    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?

  2. #2
    Join Date
    Nov 2004
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    125
    edit

  3. #3
    Join Date
    Sep 2001
    Location
    East Stroudsburg, PA
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    13,215
    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. ) 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.

  4. #4
    Join Date
    Feb 2004
    Posts
    2,597
    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.

  5. #5
    Join Date
    Jan 2001
    Posts
    1,371
    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?
    If you don't know what you're doing, do it neatly

  6. #6
    Join Date
    Feb 2004
    Location
    Midwest
    Posts
    9,937
    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."

  7. #7
    Join Date
    Oct 2002
    Posts
    398
    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.
    It's all about girth.
    Add enough pressure and it will be 10" round again.

    [Edited by sirtab on 01-16-2005 at 09:25 AM]

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