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.