How to use it
- Enter the flow rate in L/s, m³/h or US gallons per minute.
- Enter the inside diameter in mm and the length in metres.
- Enter the absolute roughness of the pipe wall in mm (0.045 mm for commercial steel, 0.0015 mm for smooth tube).
- Enter the fluid’s density and dynamic viscosity (water at 20 °C: 998.2 kg/m³ and 1.002 mPa·s).
- Read the pressure drop, head loss and the intermediate values.
Formulas
- Velocity: v = Q / (π D² / 4).
- Reynolds number: Re = ρ v D / μ.
- Friction factor: f = 64 / Re for laminar flow; otherwise Colebrook–White, 1/√f = −2 log10(ε/(3.7D) + 2.51/(Re√f)).
- Pressure drop: Δp = f × (L / D) × ρ v² / 2.
- Head loss: h_f = Δp / (ρ g), g = 9.80665 m/s².
Worked example
2 L/s of water through 100 m of 50 mm commercial steel pipe (ε = 0.045 mm):
- v = 0.002 ÷ (π × 0.05² ÷ 4) = 1.019 m/s;
- Re = 998.2 × 1.0186 × 0.05 ÷ 0.001002 = 50,736, turbulent;
- Colebrook gives f = 0.02369;
- Δp = 0.02369 × (100 ÷ 0.05) × 998.2 × 1.0186² ÷ 2 = 24.539 kPa (0.2454 bar, 3.559 psi), a head loss of 2.507 m.
Laminar case: oil of 900 kg/m³ and 50 mPa·s, 0.5 L/s in 10 m of 25 mm pipe: Re = 458, f = 64 ÷ 458.37 = 0.13963, Δp = 26.076 kPa.
Tips
- Diameter dominates: at the same flow, Δp scales roughly with 1/D⁵ in turbulent flow, so one size up cuts the loss several times.
- Transitional flow (2,300 to 4,000) is unpredictable; the result there is only a rough guide.
- Elevation is separate: add ρ g Δz for pipes that climb to get the pump’s total head.