Air Duct Friction Pressure Loss (Darcy-Weisbach)
Air Duct Friction Pressure Loss (Darcy-Weisbach)
HVAC designers size fan systems by first predicting how much pressure the air loses to friction as it travels through duct runs, because the fan must be selected to overcome the worst-case (longest or highest-resistance) path in the system. The Darcy-Weisbach equation, normally associated with liquid pipe flow, applies equally well to air ducts once air density and duct diameter are substituted in. Undersizing a duct run — using too small a diameter for the required airflow — causes the friction term to grow rapidly because it depends on velocity squared and inversely on diameter, which is why even modest duct downsizing can force a disproportionately larger fan and higher energy cost.
Duct friction pressure loss is dP = f*(L/D)*(rho*v^2/2), the Darcy-Weisbach equation. where f_duct is the Darcy friction factor, L_duct is the duct run length, D_duct is the duct diameter, rho_air2 is air density, and v_duct is the mean air velocity.
Inputs
f_duct := 0.02=0.02
L_duct := 30 m=30 m
D_duct := 0.4 m=400 mm
rho_air2 := 1.2 kg/m^3=1.2 kg/m^3
v_duct := 6 m/s=6 m/s
The L/D ratio counts how many duct-diameters of travel the air experiences, and the rho*v^2/2 term is the dynamic (velocity) pressure that friction dissipates over that length.
dP_duct := f_duct·(L_duct/D_duct)·(rho_air2·v_duct^2/2)=32.4 Pa
Results
A friction loss on the order of tens of pascals over a 30 m run at this velocity is a typical, unremarkable value for supply ductwork, and the fan must be selected to overcome this loss plus any fitting and equipment losses in the system. Because loss scales with v^2, doubling the airflow through the same duct roughly quadruples this pressure drop, which is why oversized ducts are often preferred for quiet, low-energy systems.
Assumptions & limitations
- Fully developed, turbulent flow with a representative constant friction factor f.
- Circular duct of uniform diameter assumed.
- Straight-run friction only — elbow, damper, and diffuser losses are excluded.
- Air treated as incompressible at typical HVAC velocities.