Static Pressure Drop Calculator for Duct Systems
Calculate the static pressure drop in HVAC duct systems for both circular and rectangular ducts using the Darcy-Weisbach equation with the Colebrook-White friction factor.
Formulas Used
Darcy-Weisbach Equation:
ΔP = f × (L / Dh) × (ρ × V²) / 2
Where:
- ΔP = Static pressure drop (Pa or in. w.g.)
- f = Darcy friction factor (dimensionless)
- L = Duct length (m)
- Dh = Hydraulic diameter (m)
- ρ = Air density (kg/m³)
- V = Mean air velocity (m/s)
Hydraulic Diameter (rectangular duct):
Dh = (4 × W × H) / (2 × (W + H)) = (2 × W × H) / (W + H)
Colebrook-White Equation (implicit, solved iteratively):
1/√f = −2.0 × log₁₀(ε/(3.7 × Dh) + 2.51/(Re × √f))
Swamee-Jain Explicit Approximation (initial estimate):
f = 0.25 / [log₁₀(ε/(3.7 × Dh) + 5.74/Re⁰·⁹)]²
Reynolds Number:
Re = ρ × V × Dh / μ
Air Density (altitude & temperature corrected):
ρ = 1.2929 × (273.15 / TK) × (Palt / 101325)
Palt = 101325 × (1 − 2.25577×10⁻⁵ × altitude_m)^5.25588
Dynamic Viscosity of Air (Sutherland's Law):
μ = μ₀ × (T/T₀)^(3/2) × (T₀ + S)/(T + S)
where μ₀ = 1.716×10⁻⁵ Pa·s, T₀ = 273.15 K, S = 110.4 K
Pressure drop per 100 ft (common HVAC metric):
ΔP/100ft = ΔP_total × (100 / L_ft)
Assumptions & References
- Fully developed, steady, incompressible turbulent flow assumed throughout the duct.
- Friction factor solved using Colebrook-White equation (10 iterations of Newton-Raphson for convergence to <0.0001%).
- For laminar flow (Re < 2300): f = 64/Re (Hagen-Poiseuille).
- For transitional flow (2300 ≤ Re < 4000): linear interpolation between laminar and turbulent friction factors.
- Air density corrected for altitude using the International Standard Atmosphere (ISA) model.
- Dynamic viscosity corrected for temperature using Sutherland's Law.
- Rectangular duct uses hydraulic diameter equivalent for friction calculations.
- Results include straight-duct friction losses only; fittings, elbows, and transitions require additional loss coefficients (not included).
- ASHRAE recommends design pressure drop of 0.08–0.10 in. w.g. per 100 ft for typical HVAC systems.
- References: ASHRAE Fundamentals Handbook (2021), Chapter 21 — Duct Design; Darcy-Weisbach equation; Colebrook (1939); Swamee & Jain (1976).