The equation and the awkward part
Everything in Darcy–Weisbach is straightforward except f. In laminar flow it is exactly 64/Re. In turbulent flow it comes from Colebrook–White:
Notice that f appears on both sides — the equation is implicit and has no closed-form solution. That is precisely why generations of engineers read the Moody chart instead. This calculator iterates it to convergence, which is both more accurate than reading a log-log chart and, conveniently, something a search snippet cannot do for you.
Worked example
Water, 50 m³/h through 100 mm commercial steel, 100 m run:
- Velocity = 1.77 m/s, Reynolds number ≈ 176,800 → turbulent
- Relative roughness ε/D = 0.00045
- Colebrook converges to f ≈ 0.0189
- ΔP = 0.0189 × (100/0.1) × (1000 × 1.77²/2) ≈ 29.6 kPa = 3.0 m head
Add four elbows and two gate valves and the equivalent length grows by 13.6 m — about 14% more loss from fittings alone, on a run that looked like plain pipe on the drawing.
Equivalent lengths for common fittings
| Fitting | L/D | On 100 mm pipe |
|---|---|---|
| 90° elbow, standard | 30 | 3.0 m |
| 90° elbow, long radius | 20 | 2.0 m |
| 45° elbow | 16 | 1.6 m |
| Tee, run through | 20 | 2.0 m |
| Tee, branch flow | 60 | 6.0 m |
| Gate valve, open | 8 | 0.8 m |
| Globe valve, open | 340 | 34 m |
| Swing check valve | 100 | 10 m |
The globe valve figure is not a misprint. One open globe valve can add more loss than the entire straight run — which is why they appear in throttling service and rarely as isolation.
Field notes
- Use the true internal bore. Nominal 100 mm pipe in SCH 40 actually measures 102.26 mm, and since loss scales with roughly the fifth power of diameter, that 2% error becomes over 10% in pressure drop. Get the real figure from the pipe schedule lookup.
- Roughness is a design assumption that ages. A line calculated at 0.045 mm and running at 1 mm after fifteen years of scaling drops roughly 60% more pressure. When a pump stops meeting duty, this is often why.
- Check the regime, not just the number. Viscous fluids can run laminar, where the friction factor law changes entirely and roughness stops mattering — see the Reynolds calculator.
- Suction-side drop is the one that bites. Friction in the suction line subtracts directly from cavitation margin; feed this result into the NPSH available calculator.
- This covers incompressible flow. For gases with significant pressure change along the line, density varies and a segmented or compressible treatment is needed.
Frequently asked questions
What is the Darcy-Weisbach equation?
ΔP = f × (L/D) × (ρv²/2). It gives frictional pressure loss from the friction factor f, pipe length and diameter, fluid density and velocity. It is valid for laminar and turbulent flow of any fluid, unlike empirical formulas such as Hazen-Williams that are limited to water.
How is the friction factor calculated?
Below Reynolds 2300 the flow is laminar and f = 64/Re exactly. Above it, the Colebrook-White equation relates f to Reynolds number and relative roughness — but it is implicit, so f appears on both sides and must be solved iteratively.
What pipe roughness should I use?
Commercial steel is about 0.045 mm, stainless around 0.015 mm, PVC and drawn tubing near 0.0015 mm, and cast iron about 0.26 mm. Corroded or scaled pipe can exceed 1 mm, which is why old lines drop far more pressure than their design calculation predicted.
How do I include fittings and valves?
The equivalent length method converts each fitting to a length of straight pipe that would cause the same loss, expressed as a multiple of diameter. A standard elbow is roughly 30 diameters, a gate valve 8, a globe valve 340. Add them to the straight run before calculating.
Provided for reference and education. Detailed hydraulic design should use validated software and confirmed fluid properties. See our disclaimer.