The friction loss calculator above works out how much head water loses to wall friction along a straight full pipe, using the Hazen–Williams equation. It is a water-only, pressurised-pipe method, and it is the one used across water distribution, irrigation and building services because it needs a single roughness number rather than a fluid property set.
Arb Digital builds free physics calculators that each own one job and say where their boundary is. The pipe flow calculator solves the same physical problem with Darcy–Weisbach and a Colebrook friction factor, which works for any fluid at any temperature and needs density, viscosity and an absolute roughness. This page is the empirical water shortcut: fewer inputs, one coefficient, and a narrower range of validity.
What This Friction Loss Calculator Does — and What It Does Not
The tool takes a flow rate, an internal diameter, a length of straight pipe and a Hazen–Williams C factor, and returns the head lost to friction in metres of water. It converts that into a pressure drop, reports the mean velocity, gives the loss per 100 metres so runs of different length can be compared, and back-calculates the Darcy friction factor the result implies so you can see how it compares with the Darcy–Weisbach world.
It does not compute fire-hose friction loss. The fire service uses a different published relation of the form FL = CQ²L, with a coefficient tabulated per hose diameter and flow expressed in hundreds of gallons per minute, because lay-flat hose behaves differently from rigid pipe and fireground arithmetic is done in the head. Those coefficients are set by fire service training material and vary between authorities. Using a pipe method for hose, or hose coefficients for pipe, gives answers that are wrong by a wide margin, so this page stays firmly on the pipe side.
It also does not cover fittings. Every bend, valve, tee and reducer adds a local loss that must be accounted for separately, either as an equivalent length of straight pipe or through a loss coefficient. On a long buried main those are negligible; in a compact plant room they can exceed the straight-pipe loss entirely.
How to Use It
- Enter the flow rate in whatever unit you have. Litres per second, cubic metres per hour and US gallons per minute are all accepted and converted internally.
- Enter the internal diameter, not the nominal size. This is the input that matters most, because the loss scales with diameter to the power 4.87.
- Give the straight-run length. Add an equivalent length for fittings if you have one; the tool treats whatever you enter as straight pipe.
- Pick a material or type a C factor. For an existing metal main, use a value that reflects its age rather than the as-new figure.
- Check the velocity before trusting the head loss. Hazen–Williams was fitted to ordinary water-supply conditions, and the tool warns when the velocity moves outside them.
The Formula: How Hazen–Williams Friction Loss Is Calculated
In SI units the head loss is hf = 10.67 L Q1.852 ÷ (C1.852 D4.8704), with L and D in metres, Q in cubic metres per second and hf in metres of water. The exponents are not derived from theory; they were fitted to measurements of water flowing in ordinary pipes, which is precisely why the method is fast to use and limited in scope.
Hazen–Williams is one of the three friction options implemented in EPANET, the US Environmental Protection Agency's application for modelling drinking water distribution systems, alongside Darcy–Weisbach and Chezy–Manning. That it survives as a default in serious network modelling says something about how well it performs inside its range, and that it sits next to two alternatives says something about where it stops.
The pressure drop follows from the head as Δp = ρghf. The mean velocity is the flow rate divided by the cross-sectional area. The implied Darcy friction factor comes from rearranging the Darcy–Weisbach equation, f = 2gDhf ÷ (Lv²), which lets you compare the answer against a Moody-chart value. OpenStax University Physics Volume 1, section 14.7 on viscosity and turbulence, sets out the Reynolds number thresholds that decide which flow regime applies, and Hazen–Williams is a turbulent-flow correlation only.
Work the defaults by hand. Ten litres per second is 0.01 m³/s; a 100 mm bore is 0.1 m; the run is 100 m; C is 130. Then Q1.852 = 1.97697 × 10−4, C1.852 = 8,222.9 and D4.8704 = 1.34772 × 10−5. So hf = 10.67 × 100 × 1.97697 × 10−4 ÷ (8,222.9 × 1.34772 × 10−5) = 0.210943 ÷ 0.110821 = 1.903 m. With water at 998 kg/m³ that is 18.63 kPa, or 2.702 psi. The velocity is 0.01 ÷ (π × 0.05²) = 1.273 m/s, and the implied Darcy factor is 0.0230.
When Hazen–Williams Is the Right Method and When It Is Not
The equation was fitted for water at ordinary ambient temperatures, in pipes of about 50 mm bore and larger, at velocities up to roughly 3 metres per second, in fully turbulent flow. Inside that envelope it is accurate enough for design and enormously quicker than solving Colebrook.
Outside it, the method degrades in ways that are not obvious from the output. It carries no viscosity term at all, so it cannot know about temperature: chilled water at 5 °C is roughly 50 per cent more viscous than water at 20 °C, and Hazen–Williams returns the same answer for both. It has no Reynolds number, so it cannot detect laminar flow, and in a small-bore pipe at low flow it will quietly return a turbulent-style answer for a laminar situation.
It is also wrong for any fluid that is not water. Oil, glycol mixtures, slurries and compressed air all need a method that takes fluid properties as inputs. For any of those, use the pipe flow calculator with Darcy–Weisbach instead, or get the coefficient directly from the friction factor calculator.
Why the C Factor Dominates the Answer
Of all the inputs, C is the one carrying the most uncertainty, and it is the one people copy from a table without thinking. New plastic pipe is genuinely around 150. New lined ductile iron is around 130 to 140. But an unlined iron main forty years into service can be down at 80 or lower, and in extreme tuberculation cases lower still.
Because loss scales as C to the power −1.852, dropping from 130 to 80 multiplies the head loss by (130/80)1.852, which is about 2.4. Two and a half times the friction, from an input that is invisible on a drawing. This is why water utilities measure C on real mains by pressure-testing a section rather than assuming it, and why an old system often needs far more pump head than its original design suggested.
Diameter matters even more, but it is usually known. The 4.87 exponent means a nominal 100 mm pipe whose true bore has been reduced to 90 mm by deposits sees loss rise by (100/90)4.87, a factor of 1.7 — on top of whatever the C factor has done. The two effects compound, which is why ageing mains deteriorate faster than either factor alone would suggest.
Head, Pressure and What the Pump Actually Sees
Friction loss is naturally a head, a height of the fluid itself, and that is how pump curves are drawn. Converting to pressure is only a multiplication by ρg, but keeping the two straight matters: a pump develops head, and the pressure that produces depends on what is flowing through it.
The total head a pump must supply is the static lift plus the friction loss plus any velocity head and fitting losses. Only the friction component grows with flow, and it grows steeply — nearly as the square. Doubling the flow through a fixed pipe multiplies friction loss by about 3.6, which is why a system that works comfortably at design flow can fail badly when someone opens more outlets.
For the static component and the conversion between head and pressure, use the hydrostatic pressure calculator, and for the unit arithmetic the pressure converter and the flow rate converter. Once you have a total head and a flow, the pump horsepower calculator turns them into a shaft power.
Where This Sits Next to the Other Flow Tools
This page is the empirical water method for pressurised pipe. The pipe flow calculator is the general Darcy–Weisbach treatment with Colebrook solved numerically, and it is the right choice whenever the fluid is not water or the temperature matters. The friction factor calculator gives the coefficient alone when that is what you need for a spreadsheet.
For flow that is not in a full pipe at all, the open channel flow calculator applies Manning's equation to ditches, culverts and part-full pipes, which is a genuinely different problem because the free surface changes the geometry. The Reynolds number calculator tells you whether a turbulent-flow correlation is even applicable.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using nominal diameter instead of internal bore — with an exponent of 4.87, the difference between a nominal size and a real bore is a large error, not a rounding one.
- Applying it to anything but water — there is no viscosity term, so oil, glycol and air results are meaningless. Use a Darcy–Weisbach method for those.
- Confusing pipe and hose methods — fire-hose friction loss uses its own coefficients and its own equation form, and the two are not interchangeable in either direction.
- Taking an as-new C factor for an old main — ageing can more than double the friction loss, and it is invisible unless the pipe is tested.
- Ignoring fittings on a short run — bends and valves in a plant room can contribute more loss than the straight pipe they connect.
Related Free Tools From Arb Digital
For the general case with any fluid, use the pipe flow calculator, and for the coefficient by itself the friction factor calculator. Regime questions are settled by the Reynolds number calculator and free-surface flow by the open channel flow calculator. Head and pressure conversions live in the hydrostatic pressure calculator and the pressure converter, flow units in the flow rate converter, and pump sizing in the pump horsepower calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Pipe. It uses the Hazen-Williams equation for water in a pressurised pipe. Fire-hose friction loss uses a different published relation with coefficients tabulated per hose size, and the two methods are not interchangeable.
It is an empirical roughness coefficient for the pipe. Higher values mean smoother pipe and less loss: about 150 for plastic, 130 to 140 for new lined iron, and as low as 80 for old tuberculated metal mains.
Whenever the fluid is not water, the temperature matters, the flow might be laminar, or the pipe is very small. Darcy-Weisbach takes density and viscosity as inputs and covers all of those cases properly.
Because head loss scales with diameter to the power 4.87. A ten per cent reduction in bore raises the friction loss by about 70 per cent, which is why deposits in an old main have such a large effect.
No. It covers straight pipe only. Fittings are handled separately as equivalent lengths or loss coefficients, and on short runs they can dominate the total.
It was fitted for water at ordinary temperatures at velocities up to roughly three metres per second in pipes of about 50 mm bore and above. Outside that range the accuracy falls away without any warning in the arithmetic.
Multiply the head in metres by the fluid density and by the acceleration due to gravity. For water that works out at roughly 9.8 kilopascals, or 1.42 psi, per metre of head.
Because it lets you compare a Hazen-Williams answer against a Moody chart value for the same pipe. A large disagreement usually means the flow conditions have drifted outside the range the empirical method was fitted for.
This tool is provided for educational and study use. It applies an empirical correlation for water in straight full pipe, excludes fittings, temperature effects, laminar flow and fire-service hose methods, and is not a substitute for a hydraulic design carried out by a qualified engineer.
