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When calculating the diameter equivalent ($\text{de}$) of a round duct in a HVAC system, and we know the rectangular duct size, we can use the following formula:

$$\text{de} = 1.30 \times \frac{(a \times b)^{0.625}}{(a + b)^{0.25}}$$

BUT IF we know $\text{de}$, and we know $a$, what formula could be used to solve for $b$? For testing purposes, I am assuming $\text{de}$ is 18" and $a$ is 16".

Using WolframAlpha...I was able to achieve an answer but they graphed to achieve the solution by using the intersecting lines...but I would like to solve this without graphing.

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    I am not familiar with LaTeX syntax. . . That should be (a*b)^.625/(a+b)^.25.2012-02-25
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    Ah, that makes more sense.2012-02-25
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    Thanks guys...I'll study LaTeX syntax before posting a question next time...2012-02-25

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