In short: friction head loss in a pipe grows with the square of velocity and directly with length, but shrinks sharply as diameter increases. For 10 GPM through 50 ft of 1-inch PVC pipe at 20 °C, that works out to about 3.6 ft of head (1.6 psi). Double the flow rate and the loss roughly quadruples — use the calculator above for your exact pipe and job.
These figures are planning aids based on the Darcy-Weisbach equation. For code-governed or safety-critical piping design, confirm with a licensed engineer.
How to calculate friction loss with Darcy-Weisbach
The Darcy-Weisbach equation relates head loss to velocity, pipe geometry and a friction factor that captures how rough the pipe wall is and how turbulent the flow is:
The friction factor f itself depends on the flow regime. Below a Reynolds number of 2,300 the flow is laminar and f = 64/Re. Above roughly 4,000 the flow is turbulent, and this calculator solves the Swamee-Jain equation — an explicit, non-iterative approximation of the classic Colebrook-White formula:
Worked example. Take 10 US GPM through 50 ft of 1-inch (nominal) PVC pipe at 20 °C — the calculator's default. Converting units: Q = 0.000631 m³/s, D = 0.0254 m, L = 15.24 m. Cross-sectional area A = πD²/4 = 0.000507 m², so velocity V = Q/A = 1.245 m/s (4.08 ft/s). At 20 °C water has a kinematic viscosity of about 1.004×10⁻⁶ m²/s, giving Reynolds number Re = VD/ν ≈ 31,500 — turbulent. With PVC's roughness of 0.0015 mm, Swamee-Jain gives f ≈ 0.0233. Plugging into the head-loss formula: h_f = 0.0233 × (15.24/0.0254) × (1.245²/19.613) ≈ 1.10 m, which is 3.62 ft — matching the tool's default result. Multiplying by density and gravity converts that to a pressure drop of about 1.57 psi.
Laminar, transitional, turbulent. Most building and irrigation plumbing runs turbulent (Re above 4,000). Laminar flow (Re below 2,300) shows up mainly in very slow flows through small tubing, like lab or dosing lines. Between 2,300 and 4,000 the flow is transitional and no formula is fully reliable — the calculator still reports a number there, flagged as approximate.
Why diameter, roughness and temperature change the answer
Diameter dominates. Because velocity appears squared in the head-loss formula and area grows with the square of diameter, halving a pipe's diameter for the same flow rate multiplies velocity by four and roughly multiplies head loss by thirty or more once the friction-factor shift is included. This is the single biggest lever in any friction-loss calculation — undersizing a pipe is expensive in lost pressure.
Roughness sets the friction factor. A rougher pipe wall disrupts the boundary layer more, raising f for the same Reynolds number. New PVC and copper are hydraulically smooth; old, scaled or corroded metal pipe can behave as though its roughness were five to ten times its "new" catalog value — which is why an aging system often needs re-checking against measured, not textbook, roughness.
Temperature works through viscosity. Warmer water is less viscous, which raises the Reynolds number and nudges the friction factor down for turbulent flow. Running the same 10 GPM through 50 ft of ¾-inch copper pipe at 5 °C gives a head loss of about 15.7 ft; at 80 °C it drops to about 11.7 ft — roughly a 26% swing from temperature alone, smaller than the effect of diameter but not negligible for hot-water or process-piping design.
Absolute roughness of common pipe materials
These are the values the calculator uses. The table below holds flow, diameter and length fixed (1-inch pipe, 100 ft, 10 GPM, 20 °C water) and varies only the material, so you can see roughness alone drive the result — reproduce any row by entering those exact settings above.
| Material | Roughness ε (mm) | Friction factor (f) | Head loss (ft) | Pressure drop (psi) |
|---|---|---|---|---|
| PVC / plastic / copper (smoothest) | 0.0015 | 0.0233 | 7.25 | 3.14 |
| Commercial steel (new) | 0.045 | 0.0277 | 8.62 | 3.73 |
| Asphalted cast iron | 0.12 | 0.0331 | 10.31 | 4.46 |
| Galvanized steel | 0.15 | 0.0349 | 10.87 | 4.70 |
| Cast iron (new) | 0.26 | 0.0405 | 12.61 | 5.46 |
| Concrete (average) (roughest) | 1.0 | 0.0656 | 20.41 | 8.83 |
Worked examples
Garden hose at full flow
35.4 ft head
10 GPM through 50 ft of ⅝-inch garden hose at 15 °C loses about 35 ft of head (15.3 psi) to friction alone — why a sprinkler at the far end of a long hose loses so much pressure.
Copper line to a fixture
14.4 ft head
The same 10 GPM through 50 ft of ¾-inch copper pipe at 20 °C loses about 14.4 ft (6.2 psi) — far less than the hose, because the pipe is over 40% larger in diameter.
HVAC circulation loop
39.2 ft head
100 GPM through 200 ft of 2-inch commercial steel pipe at 60 °C loses about 39 ft of head (16.7 psi) — a figure a circulator pump must be sized to overcome.
What else affects the result
Fittings and valves. Elbows, tees, valves and other fittings add "minor losses" on top of the straight-pipe friction this calculator computes. Add them with the Minor Loss Calculator, or convert each fitting to an equivalent length of straight pipe with the Equivalent Length Calculator and add it to your pipe length here.
Pipe aging. Roughness values in the table above describe new pipe. Mineral scale, corrosion and biofilm raise effective roughness over time, sometimes dramatically in old iron or steel mains — a system designed to new-pipe figures can under-predict real-world loss after years of service.
Non-circular ducts. For rectangular or annular cross-sections, replace diameter with the hydraulic diameter, D_h = 4A/P (four times cross-sectional area divided by wetted perimeter), and the same equation still applies reasonably well.
Entrance and developing flow. Right after a valve, elbow or pipe inlet, the velocity profile hasn't fully developed and local losses run higher than the fully-developed friction factor predicts. This calculator assumes fully-developed flow along the pipe length entered.
Frequently asked questions
What is the Darcy-Weisbach equation used for?
The Darcy-Weisbach equation calculates the head loss (or pressure drop) caused by friction as fluid flows through a pipe. Unlike simpler methods, it works for any fluid, in both laminar and turbulent flow, which is why it is the standard method taught in fluid mechanics and used in serious engineering design.
How is the friction factor calculated?
Below a Reynolds number of 2,300 (laminar flow), the friction factor is simply 64 divided by the Reynolds number. Above about 4,000 (turbulent flow), this calculator uses the Swamee-Jain equation, an explicit approximation of the Colebrook-White equation that depends on the pipe's relative roughness and Reynolds number. Between 2,300 and 4,000 flow is transitional and the result is only approximate.
What pipe roughness value should I use?
Use the absolute roughness of the pipe material: about 0.0015 mm for PVC, copper or other drawn tubing, 0.045 mm for new commercial steel, and up to 1 mm or more for older concrete or corroded cast iron. The reference table on this page lists common values. Aged or scaled pipes can have several times the roughness of new pipe, so measured or inspected data is always better than a textbook default.
Is the Darcy-Weisbach equation more accurate than Hazen-Williams?
Generally yes. Darcy-Weisbach is dimensionally consistent and valid for any fluid and flow regime, while the Hazen-Williams equation is an empirical fit calibrated to water in turbulent flow within a limited velocity range. Hazen-Williams is faster to use by hand, which is why it remains common in municipal water-main design, but Darcy-Weisbach is the more rigorous and broadly applicable method.
Does water temperature affect friction loss?
Yes. Warmer water is less viscous, which raises the Reynolds number and slightly lowers the friction factor for the same flow rate and pipe. The effect is modest compared to pipe diameter or roughness, but it is measurable — for example, head loss through the same pipe can drop by roughly a quarter between near-freezing and near-boiling water.
What is the difference between head loss and pressure drop?
Head loss expresses friction loss as a height of fluid column, in feet or meters, and does not depend on fluid density. Pressure drop expresses the same loss in force per area, such as psi or pascals, and does depend on density. The two are directly related: pressure drop equals fluid density times gravitational acceleration times head loss.
Sources & references
- Darcy, H. (1857). Recherches expérimentales relatives au mouvement de l'eau dans les tuyaux. Mallet-Bachelier.
- Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, ASCE, 102(5), 657–664.
- Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the ASME, 66(8), 671–684.
- Crane Co. (2013). Flow of Fluids Through Valves, Fittings, and Pipe (Technical Paper No. 410).
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)