Free Engineering Tool
Pipe Pressure Drop Calculator
Darcy-Weisbach equation with iterative Colebrook-White friction factor. Supports laminar/turbulent flow, pipe roughness presets, and minor losses from fittings.
Results
Darcy-Weisbach Equation
The fundamental equation for pressure drop due to friction in a pipe:
- f — Darcy friction factor (dimensionless)
- L — pipe length (m)
- D — pipe inner diameter (m)
- ρ — fluid density (kg/m³)
- v — mean flow velocity (m/s)
Colebrook-White Equation (Turbulent Flow)
For turbulent flow (Re > 4000), the friction factor is found iteratively:
This calculator uses the iterative Newton-Raphson method (50 iterations) for accurate results matching the Moody diagram.
Laminar Flow
For Re < 2300 (laminar flow), the friction factor is simply:
Minor Losses
Fittings, valves, elbows, and other components add additional pressure drop expressed via K-factors:
| Fitting | K-factor | Fitting | K-factor |
|---|---|---|---|
| 90° elbow (standard) | 0.9 | 45° elbow | 0.4 |
| Tee (through) | 0.4 | Tee (branch) | 1.8 |
| Gate valve (full open) | 0.15 | Ball valve (full open) | 0.05 |
| Check valve (swing) | 2.5 | Globe valve (full open) | 10 |
| Pipe entrance (sharp) | 0.5 | Pipe exit | 1.0 |
| Sudden expansion | ~1.0 | Sudden contraction | ~0.5 |
Pipe Roughness Values
| Material | Roughness ε (mm) | Notes |
|---|---|---|
| Carbon steel | 0.045 | New commercial pipe |
| Stainless steel | 0.015 | Smooth welded |
| Copper | 0.0015 | Drawn tubing |
| Plastic (PE, PVC) | 0.0015 | Very smooth |
| Cast iron | 0.25 | New; aged can be 1–3 mm |
| Hydraulic hose | 0.005 | Rubber inner liner |
| Concrete | 0.3 – 3.0 | Depends on finish |
Practical Example
Given: Q = 60 L/min, D = 25 mm, L = 10 m, steel pipe (ε = 0.045 mm), oil ν = 32 cSt, ρ = 870 kg/m³
v = 4 × 0.001 / (π × 0.025²) = 2.037 m/s
Re = 2.037 × 0.025 / (32 × 10⁻⁶) = 1,592 → Laminar
f = 64 / 1592 = 0.04020
ΔP = 0.04020 × (10/0.025) × 870 × 2.037² / 2 = 29,045 Pa = 0.290 bar
⚠️ Note: In the transition region (Re 2300–4000) the friction factor is interpolated. Real flow may oscillate between laminar and turbulent. Avoid designing systems to operate in this region.
The Darcy-Weisbach equation calculates friction pressure drop in pipes: ΔP = f × (L/D) × ρv²/2. It applies to both laminar and turbulent flow — only the friction factor f changes.
It is more accurate and versatile than Hazen-Williams (which only works for water in turbulent flow).
The Colebrook-White equation is implicit — f appears on both sides — so it must be solved iteratively:
1/√f = -2 log₁₀(ε/3.7D + 2.51/(Re√f))
This calculator uses 50 iterations starting from the Swamee-Jain approximation, achieving accuracy better than 0.01%.
Common roughness values (ε):
- Steel: 0.045 mm (new commercial)
- Stainless: 0.015 mm (smooth welded)
- Copper/plastic: 0.0015 mm (very smooth)
- Cast iron: 0.25 mm (new); aged pipes can be 1–3 mm
- Hydraulic hose: 0.005 mm
For aged or corroded pipes, increase roughness by 2–10×.
Each fitting has a K-factor. Sum all K-factors for your system and enter the total in the ΣK field. The minor loss is: ΔP = ΣK × ρv²/2.
Example: A system with two 90° elbows (K=0.9 each), one tee branch (K=1.8), and one check valve (K=2.5): ΣK = 0.9 + 0.9 + 1.8 + 2.5 = 6.1.
Rules of thumb:
- Hydraulic pressure lines: 3–5 bar per 10 m is common
- Hydraulic return lines: 0.5–1 bar per 10 m
- Water supply: 0.1–0.3 bar per 100 m of pipe
- Total system ΔP must not exceed available pump pressure
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
