Engineering
Darcy-Weisbach pipe friction head loss (hf) and pressure drop (kPa) formula
Calculate major pipe friction head loss in meters (hf = f*(L/D)*(v^2/2g)) and pressure drop in kilopascals (kPa) across water, HVAC, and process piping.
Straight-pipe friction loss with a supplied Darcy factor
This form of Darcy–Weisbach describes steady, fully developed flow with approximately constant density through a straight, constant-diameter pipe. Supply the Darcy friction factor, not the Fanning factor (Darcy is four times Fanning). Compressible gas flow with significant density changes needs an appropriate extended model.
The pressure-drop expression follows from density*g*head loss. Doubling speed quadruples loss only if the friction factor and other inputs stay fixed. In a real system the factor depends on Reynolds number and roughness and may change with speed. This example omits fittings, entrance/exit losses, elevation and pump efficiency, so it does not size a pump by itself.
| Piping Metric (f=0.020, L=150 m, D=0.10 m, rho=1000 kg/m^3) | Formula | Result |
|---|---|---|
| Head Loss hf at v = 2 m/s | 0.020 * (150 / 0.10) * (2^2 / (2 * 9.81)) | 6.12 m of head |
| Pressure Drop DeltaP at v = 2 m/s | 0.020 * 1500 * (1000 * 4 / 2) / 1000 | 60.0 kPa (0.60 bar) |
| Pressure Drop DeltaP at v = 4 m/s (2x speed) | Quadratic v^2 scaling (4x) | 240.0 kPa (2.40 bar) |
Darcy-Weisbach friction head loss (meters of fluid)
A2=FrictionFactor f (0.020), B2=Length_m (150), C2=Diameter_m (0.10), D2=Velocity_m_s (2), E2=Gravity (9.81).
=IF(OR(COUNT(A2:F2)<>6,A2<0,B2<0,C2<=0,D2<0,E2<=0,F2<=0),"Invalid inputs",ROUND(A2 * (B2 / C2) * ((D2 ^ 2) / (2 * E2)), 2))Pipe friction pressure drop in kilopascals (kPa)
F2 holds fluid density rho in kg/m^3 (1,000 for water).
=IF(OR(COUNT(A2:F2)<>6,A2<0,B2<0,C2<=0,D2<0,E2<=0,F2<=0),"Invalid inputs",ROUND(A2 * (B2 / C2) * (F2 * (D2 ^ 2) / 2) / 1000, 2))Try the example
Use the original values or change them to test your understanding.