A: Use DE (equivalent diameter) whenever you have a duct — that formula is specifically designed for converting rectangular duct dimensions to a round equivalent for pressure drop calculations. Hydraulic diameter DH = 4A/P is a more general tool for unusual geometries like partially filled pipes or open channels, but it's less precise for duct work. On the rounding: keeping the unrounded diameter gives you more precision, and if you find it changes your answer meaningfully, that's worth noting — but in this case the answer choices are spaced far enough apart that it doesn't matter.

A: Simple rule: if it's a duct, use the circular equivalent diameter (DE = 1.3(ab)^0.625 / (a+b)^0.25). That formula was specifically developed for rectangular ducts — it gives you the diameter of a round duct with the same pressure drop. Hydraulic diameter (DH = 4A/P) is your fallback for anything else: non-circular pipes, open channels, unusual cross-sections.

A: Both the Darcy equation and the friction loss tables should reconcile — the 20% relative error sounds alarming, but the absolute difference is only 0.03 in. w.g., which is negligible for duct sizing. I designed the answer choices to be spaced far enough apart that either approach lands you on the same selection. Know both methods; the tables tend to be faster once you're comfortable with them.

A: Equivalent diameter is exclusively for rectangular ducts — that's its one job. Hydraulic diameter is more general and can handle any shape: pipes, open channels, hexagons, whatever. So the rule is: rectangular duct → DE; everything else → DH. Also, check the archived office hours spreadsheet if you want more discussion on this one — it's come up many times before.

A: Because the problem is specifically about ductwork, the rectangular duct equivalent diameter equation is the better targeted tool. Hydraulic diameter is more general and can apply to many geometries, but the duct formula is built for this case.