Formula
Friction head loss uses the Darcy–Weisbach equation. The friction factor f comes from the explicit Swamee–Jain equation in turbulent flow and from 64/Re in laminar flow.
V = Q / (πD²/4) Re = V·D / ν f = 0.25 / [ log₁₀( ε/(3.7D) + 5.74/Re⁰·⁹ ) ]² (Re ≥ 2,300) f = 64 / Re (Re < 2,300) hf = f · (L/D) · V²/(2g) hm = ΣK · V²/(2g) ΔP = ρ·g·(hf + hm)
The Swamee–Jain equation approximates the Colebrook–White equation without iteration. It agrees with Colebrook to about 1 % for Reynolds numbers of 5,000 to 10⁸ and relative roughness of 10⁻⁶ to 10⁻². This site's automated tests also check that it stays within 1.5 % of the Colebrook solution across several conditions.
Choosing inputs
Absolute roughness by pipe material
| Material | ε (mm) |
|---|
These are typical values for new pipe. Old steel and cast iron pipe can be several times rougher because of rust and scale, so allow a margin.
Kinematic viscosity of water
The calculator interpolates linearly between table values for the water temperature. It is 1.004×10⁻⁶ m²/s at 20 °C and 0.474×10⁻⁶ m²/s at 60 °C, so hot water has slightly lower losses.
Worked example
Water at 20 °C flowing at 12 m³/h through 100 m of carbon steel pipe (ε 0.045 mm) with an inside diameter of 52.9 mm:
- Velocity V = 0.003333 / (π × 0.0529² / 4) ≈ 1.52 m/s
- Reynolds number Re ≈ 79,900 (turbulent)
- Friction factor f ≈ 0.0223
- Friction head loss hf ≈ 4.95 m, pressure drop ≈ 48.5 kPa
The calculator opens with these values.
Limitations
- Reynolds numbers between 2,300 and 4,000 are in the transition zone, where real losses vary widely. Treat the turbulent result there as a conservative estimate only.
- Building water supply pipework is often sized for velocities of about 2 m/s or less to limit noise and water hammer. If the velocity comes out high, try the next pipe size up.
- This method does not apply to fluids other than water, to part-full flow (open channels) or to gases.
- Before finalizing a design, confirm with the applicable building services standard and manufacturer data.
References
- Swamee, P. K. & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, ASCE, 102(5).
- Colebrook, C. F. (1939). Turbulent flow in pipes. Journal of the ICE, 11(4).
- Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the ASME, 66. (Typical roughness values by material)
- Water density and kinematic viscosity: standard property tables at atmospheric pressure (for example, White, Fluid Mechanics, appendix tables)