Equivalent Round Duct Diameter

Friction charts and duct calculators are drawn for round duct, but the world is full of rectangular duct squeezed between joists. Huebscher's 1948 equation gives the round duct that would carry the same air with the same pressure drop, so you can look the rectangle up on a round chart. It is dimensionally homogeneous — the exponents 0.625 and 0.25 differ by exactly one — so the same 1.30 coefficient works whether you feed it inches, feet or millimetres, which is unusual among trade formulas and worth appreciating.

Worked example: a 12 × 8 inch duct gives Dₑ = 1.30 × 96^0.625 ÷ 20^0.25 = 1.30 × 17.33 ÷ 2.115 = 10.66 inches, matching the 10.7 in printed in the ASHRAE Fundamentals table. A 24 × 12 comes out at 18.3 inches. The trap is thinking equivalent diameter means equivalent area: the 12 × 8 duct has 96 in² of cross-section but the equivalent round has 89 in², because a flat rectangle drags more perimeter through the same air. Push the aspect ratio past about 4:1 and the equation loses accuracy along with the duct losing efficiency — which is why designers fight so hard to avoid 30 × 6 pancakes. This page solves for Dₑ; the sides a and b appear inside a product and a sum raised to different powers, so there is no closed form for them.