Static Pressure Drop Calculator for Duct Systems

Formulas Used

Darcy-Weisbach Equation:

ΔP = f × (L / D_h) × (ρ × V²) / 2

Where:

• ΔP = Static pressure drop (Pa or in. w.g.)
• f = Darcy friction factor (dimensionless)
• L = Duct length (m)
• D_h = Hydraulic diameter (m)
• ρ = Air density (kg/m³)
• V = Mean air velocity (m/s)

Hydraulic Diameter (rectangular duct):

D_h = (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 × D_h) + 2.51/(Re × √f))

Swamee-Jain Explicit Approximation (initial estimate):

f = 0.25 / [log₁₀(ε/(3.7 × D_h) + 5.74/Re⁰·⁹)]²

Reynolds Number:

Re = ρ × V × D_h / μ

Air Density (altitude & temperature corrected):

ρ = 1.2929 × (273.15 / T_K) × (P_alt / 101325)

P_alt = 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)