Pipe Pressure Drop Calculation: Darcy–Weisbach Worked Example

Pressure drop versus head loss

Friction pressure drop is mechanical energy loss expressed as pressure, such as Pa or kPa. Head loss expresses that same loss as meters of the flowing fluid: h = Δp / (ρg). Static elevation change is a different term and is not included in this tool’s friction result.

Darcy–Weisbach formula

For steady incompressible full-pipe flow: Δp = [f × L / D + ΣK] × ρ × v² / 2. Calculate velocity v = 4Q / (πD²). Use flow Q in m³/s, internal diameter D and length L in meters, density ρ in kg/m³, Darcy factor f and total fitting-loss coefficient ΣK.

Convert m³/h to m³/s by dividing by 3600 and millimeters to meters by dividing by 1000. ΣK represents the fittings included in your model; do not count the same losses again as equivalent length.

Worked water example

Use 3.6 m³/h, 50 mm internal diameter, 20 m length, density 998 kg/m³, Darcy f = 0.02 and ΣK = 2. Flow is 0.001 m³/s and velocity is approximately 0.50930 m/s.

The multiplier is 0.02 × 20 / 0.05 + 2 = 10. Δp ≈ 1294.32 Pa, or 1.29432 kPa. With g = 9.80665 m/s², head loss is approximately 0.13225 m. The entered f and K values are illustrative assumptions, not universal values.

Choose the correct friction factor

This calculator takes a user-entered Darcy friction factor. Determine it from the flow regime and pipe conditions using an appropriate method or validated data. Do not substitute a Fanning factor directly: the Darcy factor is four times the corresponding Fanning factor.

Use the Pipe Pressure Drop Calculator

Enter flow, internal diameter, length, fluid density, Darcy factor and total K. Read velocity, pressure loss in Pa and kPa, and head loss in meters. Compare alternative diameters while revisiting f and fitting data rather than keeping inappropriate assumptions fixed.

Connect loss to pump calculations

Suction-line losses reduce available NPSH and belong in a suction-side calculation. Total pump head can also include elevation, pressure difference and other system losses. This tool excludes pumps, static elevation, compressible gases and partially filled pipes; it is not a full network solver.