The formulas to calculate the return air duct size are:
For a rectangular duct:
\[ D_{rect} = \sqrt{AS \times 144} \]
For a circular duct:
\[ D_{circle} = 2 \times \sqrt{\frac{AS \times 144}{\pi}} \]
Where:
A return air duct is a square or circular column used to return air into an air conditioner. The size of the air duct is how large that duct should be based on the size of the air conditioner.
Let's assume the following value:
Step 1: Calculate the rectangular duct size:
\[ D_{rect} = \sqrt{2 \times 144} = \sqrt{288} \approx 16.97 \text{ inches} \]
Step 2: Calculate the circular duct diameter:
\[ D_{circle} = 2 \times \sqrt{\frac{2 \times 144}{\pi}} = 2 \times \sqrt{\frac{288}{\pi}} \approx 19.15 \text{ inches} \]
The Rectangle Duct Size is approximately 16.97 inches, and the Circular Duct Diameter is approximately 19.15 inches.