Pipe Pressure Drop Calculator (Darcy–Weisbach)
Work out the pressure lost to friction in a pipe. The Darcy–Weisbach equation with a Colebrook–White friction factor gives the pressure drop, head loss and pumping power, or solves for the flow, the pipe size or the longest run, and plots the result on a Moody chart.
How to Use
- Pick what to solve for: the pressure drop, the flow rate a pressure can push, the pipe diameter for a flow, or the longest pipe a pressure allows.
- Choose the fluid (water or air at 20 °C, glycerol, or your own density and viscosity) and the pipe material, which sets the wall roughness.
- Enter the flow, the inside diameter and the length, each with its own unit. Add the fittings as a total loss coefficient ΣK from the table below.
- Read the answer in the highlighted field, the head loss, the Reynolds number and the friction factor, and see the operating point on the Moody chart.
- Press a preset to load an example, and check Show Work for each Colebrook pass and every unit conversion.
Worked Example
Water through 100 m of 50 mm steel pipe. 5 L/s of water at 20 °C (998.2 kg/m³, 1.0016 mPa·s). The bore area is π × 0.05² ÷ 4 = 0.0019635 m², so v = 0.005 ÷ 0.0019635 = 2.546 m/s and Re = 998.2 × 2.546 × 0.05 ÷ 0.0010016 = 126,892: turbulent. With ε/D = 0.045 ÷ 50 = 0.0009, Colebrook–White gives f = 0.02135. The dynamic pressure is ρv²/2 = 3,236 Pa, so Δp = 0.02135 × (100 ÷ 0.05) × 3,236 = 138.2 kPa (1.382 bar, 20.05 psi), a head loss of 14.12 m. Pushing it takes 0.005 × 138,206 = 691 W of hydraulic power.
A copper line with fittings. 20 L/min in 15 m of 20 mm bore copper: v = 1.061 m/s, Re = 21,149, f = 0.02570, ρv²/2 = 561.9 Pa. The pipe loses 0.0257 × 750 × 561.9 = 10.83 kPa, and fittings with ΣK = 5 add 5 × 561.9 = 2.809 kPa, for 13.64 kPa in all.
The common mistake: using a Fanning friction factor in the Darcy equation. Some chemical-engineering texts use the Fanning factor, which is a quarter of the Darcy factor: 0.02135 ÷ 4 = 0.005338 for the steel pipe above. Put into Δp = f(L/D)ρv²/2 it gives 34.55 kPa, a quarter of the real 138.2 kPa. If a chart’s laminar line reads 16/Re it is Fanning; this calculator and the Moody chart use Darcy, where laminar flow is 64/Re.
Show Work
Formulas
Typical loss coefficients K (order-of-magnitude textbook values; real fittings vary with size and make, so use the maker’s data when it matters):
| Fitting | K (typical) |
|---|---|
| Pipe entrance, sharp-edged | 0.5 |
| Pipe entrance, well rounded | 0.03 |
| Pipe exit into a tank | 1.0 |
| 90° elbow, threaded | 1.5 |
| 90° elbow, flanged smooth bend | 0.3 |
| 45° elbow, threaded | 0.4 |
| Tee, flow through the branch (threaded) | 2.0 |
| Tee, flow straight through (threaded) | 0.9 |
| Gate valve, fully open | 0.2 |
| Ball valve, fully open | 0.05 |
| Globe valve, fully open | 10 |
| Swing check valve | 2 |
Add up the K of every fitting in the run and enter the total as ΣK. Roughness values in the material list are the typical ones from Moody’s 1944 chart and later textbook tables; old or corroded pipe can be many times rougher.
From Weisbach and Darcy to the Moody Chart
The equation carries two names. The Saxon engineer Julius Weisbach wrote the friction loss in the modern form, proportional to L/D and to v²/2g, in his 1845 textbook of engineering mechanics. The French engineer Henry Darcy, who had built the water supply of Dijon, measured flow in pipes of many sizes and materials and published the results in 1857, showing that the friction coefficient depends on the pipe wall and size. Osborne Reynolds’ dye experiments in 1883 showed the switch between smooth laminar and churning turbulent flow that the Reynolds number now predicts.
The turbulent friction factor took longer. Johann Nikuradse glued graded sand to the inside of pipes in Ludwig Prandtl’s laboratory and published the measurements in 1933. Cyril Colebrook, working with Cedric White, combined the smooth-pipe and fully rough laws into one formula in 1939, which fitted commercial pipe better than sand grains did. In 1944 Lewis Moody plotted that formula on log–log axes, and the Moody chart became the standard tool of pipe design. The explicit Swamee–Jain approximation (1976) arrived when engineers wanted an answer in one line on a pocket calculator.
About This Tool
This calculator applies the Darcy–Weisbach equation to a straight, full, round pipe carrying a fluid of constant density. It works out the velocity and Reynolds number, finds the friction factor from 64/Re in laminar flow or by iterating Colebrook–White to full precision in turbulent flow (with Swamee–Jain shown alongside), adds fitting losses from ΣK, and gives the pressure drop, head loss and pumping power. It can also run backwards: the flow a pressure will push, the smallest pipe that keeps the loss in limit, or the longest run a pressure allows. Every value has its own unit, and the Moody chart shows where the pipe sits. It does not include changes in height; add ρgΔz for a pipe that climbs or falls, and for gases treat it as valid only while the pressure drop is a small part of the line pressure.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Fluid Flow Rate & Reynolds Number Calculator, Bernoulli & Fluid Pressure Calculator, and Pump & Fan Affinity Laws Calculator.
Frequently Asked Questions
What is the Darcy–Weisbach equation?
It gives the pressure lost to wall friction: Δp = f × (L/D) × ρv²/2. For 5 L/s of water in a 50 mm steel pipe, v = 2.546 m/s, so ρv²/2 = 3,236 Pa; with f = 0.02135 over 100 m (L/D = 2,000) the drop is 0.02135 × 2,000 × 3,236 = 138.2 kPa, a head loss of 14.12 m.
How is the friction factor found?
Below a Reynolds number of about 2,300 the flow is laminar and f = 64/Re exactly. In turbulent flow it comes from the Colebrook–White equation, which has f on both sides and must be iterated. For the 50 mm steel pipe at Re = 126,892 it settles at f = 0.021352; the Swamee–Jain shortcut gives 0.021509, 0.74% higher, which is usually close enough.
How much does pipe size matter?
A great deal: at a fixed flow the drop scales roughly with 1/D⁵. Moving the same 5 L/s of water from 100 m of 50 mm steel pipe to 100 mm pipe cuts the drop from 138.2 kPa to 4.355 kPa, 31.7 times less.
What are minor losses and K values?
Each fitting, valve, entrance and exit adds a loss of K × ρv²/2. In a 20 mm copper line carrying 20 L/min (1.061 m/s) with fittings totalling ΣK = 5, the fittings lose 2.809 kPa of the 13.64 kPa total, about 21%. In long straight runs they matter less; in short runs full of bends they can dominate.
Does the pipe roughness always matter?
Not in laminar flow, where f = 64/Re whatever the wall is like. In turbulent flow it matters more the higher the Reynolds number: the same 5 L/s through 100 m of 50 mm pipe loses 138.2 kPa in commercial steel (ε = 0.045 mm) but 203.6 kPa in cast iron (ε = 0.26 mm), 47% more.
How do I use the Pipe Pressure Drop Calculator (Darcy–Weisbach)?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Sizing a water main
To carry 2 L/s through 100 m with no more than 50 kPa lost, a steel pipe needs an inside diameter of at least 43.34 mm, so the next standard size up is chosen.
Choosing a pump
5 L/s against 138.2 kPa of pipe friction needs 691 W of hydraulic power, or 987 W at the shaft of a 70% efficient pump.
Plumbing with fittings
A 15 m copper run of 20 mm bore at 20 L/min, with elbows and valves adding ΣK = 5, loses 13.64 kPa, 1.393 m of head.
Ventilation ducts
0.5 m³/s of air through 20 m of 200 mm galvanised duct runs at 15.92 m/s and loses 303.8 Pa.
Viscous liquids
Glycerol at 0.5 L/s in a 50 mm pipe flows at Re = 11.37, fully laminar, with f = 64/Re = 5.628 and 46.02 kPa lost per 10 m.
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