HVAC Ductwork Sizing, ASHRAE Equal-Friction Design & Building Mechanical Engineering
ASHRAE Huebscher Rectangular Equivalent Duct Diameter Formula
Calculate Huebscher Equal-Friction Circular Equivalent Diameter De (mm), Wetted-Perimeter Hydraulic Diameter Dh (mm), Rectangular Duct Air Velocity (m/s), and Velocity Pressure Pv (Pa).
Never size rectangular HVAC ducts on a round ductulator using hydraulic diameter Dh—equal Dh does NOT carry equal airflow!
HVAC duct friction charts plot pressure loss per meter `Delta_P / L` against Volumetric Airflow `Q` for round spiral ducts of diameter `D_round`. When low ceiling plenums force a rectangular duct of width `a` (mm) and height `b` (mm), substituting Hydraulic Diameter `D_h = 4*A / P = 2*a*b / (a + b)` directly into the round friction chart under-predicts capacity because `D_h` preserves mean velocity rather than volumetric flow at equal friction! Richard Huebscher (ASHRAE Fundamentals) solved Darcy-Weisbach equal pressure drop per unit length AT EQUAL VOLUMETRIC AIRFLOW `Q`, yielding the universal Equal-Friction Circular Equivalent Diameter `D_e = 1.30 * ((a * b)^0.625) / ((a + b)^0.25)`!
Test a 600 mm x 250 mm Supply Trunk Carrying 4,500 m³/h—Duct_Width `a` = 600.0 mm (B2), Duct_Height `b` = 250.0 mm (B3), Volumetric_Airflow `Q` = 4,500.0 m³/h (B4), and Air_Density `rho` = 1.20 kg/m³ (B5): Huebscher Equivalent Round Diameter `D_e` equals `413.66` mm (E2, vs `352.94` mm Hydraulic Diameter `D_h` in E3!), Mean Trunk Velocity hits `8.33` m/s (E4), and Velocity Pressure `P_v = 0.5 * rho * v^2` equals `41.67` Pa (E5)!
| ASHRAE Duct Sizing KPI (600x250 mm Trunk, Q=4,500 m³/h, rho=1.20 kg/m³) | Formula | Verified Output |
|---|---|---|
| Huebscher Equivalent Diameter De (mm) | 1.30 * ((a * b)^0.625) / ((a + b)^0.25) | 413.66 mm (383.55 mm @ flat 1000x150!) |
| Hydraulic Diameter Dh (mm) | (2 * a * b) / (a + b) | 352.94 mm (260.87 mm @ flat 1000x150) |
| Mean Duct Air Velocity (m/s) | (Q_m3_hr / 3600) / ((a/1000)*(b/1000)) | 8.33 m/s (unchanged at equal 0.15 m²!) |
| Duct Velocity Pressure Pv (Pa) | 0.5 * Air_Density * (Velocity_m_s ^ 2) | 41.67 Pa |
ASHRAE Huebscher Equal-Friction Diameter & Dynamic Velocity Pressure Formula
Validate Duct_Width `a > 0`, Duct_Height `b > 0` (ASHRAE recommends aspect ratio `MAX(a,b)/MIN(a,b) <= 8` to avoid excessive corner friction and sheet-metal drumming!), Airflow `Q > 0`, and Air_Density in `[0.5, 2.0]` kg/m³. When a mechanical consultant shares a duct riser schedule in Arte Sheets, a commissioning `suggester` can test tight soffit flattening scenarios in Suggest Mode without overwriting locked design static-pressure baselines!
=LET(da_m, B2, db_m, B3, qf_h, B4, rh_a, B5, IF(OR(da_m <= 0, db_m <= 0, (MAX(da_m, db_m) / MIN(da_m, db_m)) > 10, qf_h <= 0, rh_a < 0.5, rh_a > 2), "Invalid Duct Input", LET(va_s, (qf_h / 3600) / ((da_m / 1000) * (db_m / 1000)), ROUND(0.5 * rh_a * (va_s ^ 2), 2))))High-Aspect-Ratio 1,000 x 150 mm Pancake Soffit Penalty Check (Same 0.15 m² Cross-Section!)
Flatten the exact same `0.15` m² cross-sectional area into a `6.67:1` pancake duct (`a` B2 = 1,000.0 mm, `b` B3 = 150.0 mm): Air Velocity E4 stays `8.33` m/s, yet wetted-perimeter friction shrinks Huebscher Equivalent Round Diameter E2 from `413.66` mm down to `383.55` mm (`D_h` E3 drops to `260.87` mm)—proving high-aspect pancake ducts choke fan static pressure!
=IF(ISTEXT(E5), E5, ROUND((1.3 * ((B2 * B3) ^ 0.625)) / ((B2 + B3) ^ 0.25), 2))Try the example
Use the original values or change them to test your understanding.