Hydraulic Engineering Tools
Colebrook-White Equation Calculator
Calculate the Darcy friction factor for turbulent pipe flow using the Colebrook-White equation. Instant results with step-by-step iterative solution.
Colebrook-White Equation Calculator
Professional Pipe Friction & Friction Factor Calculator — SI Units
Primary Results
3 valuesFlow Analysis
3 valuesEnergy Loss
2 valuesSolution Details
3 valuesUser Manual
Learn how to use the Colebrook-White calculator effectively
Purpose
Compute unknown pipe flow parameters using the Colebrook-White equation. This calculator supports SI (metric) and US Customary units. It can determine head loss, flow rate, pipe diameter, Darcy friction factor (f), velocity, Reynolds number, and pressure drop.
How to Use
- Choose Unit System: Select SI (Metric) for metres, m³/s or US Customary for feet, gpm from the unit toggle bar below the calculator header.
- Select Calculation Mode: Choose which variable to solve for — Friction Factor, Head Loss, Reynolds Number, or Roughness.
- Enter Known Values: Fill in the required input fields. The unknown field is automatically disabled.
- Use Smart Options: Click the Smart Options panel to access presets, fluid properties, optimization suggestions, and method comparisons.
- Select Pipe Material (optional): Check Auto-estimate f to compute f directly from pipe roughness (fully rough turbulent flow), then either type the roughness value or choose a pipe material to auto-fill it.
- Press Calculate (or use Ctrl + Enter).
- Review Results: Inspect computed values, status badge, pipe section properties, and smart alerts.
Tips
- Use consistent units within the selected unit system.
- Use the Quick Presets tab in Smart Options for common engineering scenarios.
- Check velocity against recommended ranges for the pipe material and application.
- Review the Smart Alerts tab for real-time warnings and suggestions.
- Compare methods in the Method Compare tab to understand approximation accuracy.
Darcy Friction Factor (f) — Typical Values
The Darcy friction factor depends on pipe roughness (ε) and Reynolds number. For fully turbulent flow, it can be approximated using the Colebrook equation. The following table lists typical absolute roughness values for common materials.
Pipe Material Roughness (ε)
| PIPE MATERIAL | ROUGHNESS ε (MM) | ROUGHNESS ε (FT) |
|---|---|---|
| Drawn tubing (glass, plastic, PVC, HDPE) | 0.0015 | 0.000005 |
| Copper / Brass | 0.0015 | 0.000005 |
| Commercial steel (new, welded) | 0.045 | 0.00015 |
| Galvanized iron | 0.15 | 0.0005 |
| Cast iron (new) | 0.26 | 0.00085 |
| Cast iron (aged, 10+ years) | 0.8 | 0.0026 |
| Ductile iron (cement-lined) | 0.12 | 0.0004 |
| Asbestos Cement | 0.03 | 0.0001 |
| Concrete (smooth) | 0.3 | 0.001 |
| Concrete (rough) | 1.5 | 0.005 |
| Riveted steel | 3.0 | 0.01 |
| Steel (corroded) | 2.0 | 0.0065 |
| Vitrified Clay | 0.3 | 0.001 |
| Wood stave | 0.5 | 0.0018 |
| Corrugated Metal | 45 | 0.15 |
Note
The Darcy friction factor f (also called Moody friction factor) is typically in the range 0.008–0.10 for water systems. For new smooth pipes, f ≈ 0.01–0.02. Use the Colebrook equation for precise calculations.
What Is the Colebrook-White Equation?
Understanding the fundamental equation for turbulent pipe flow friction
The Colebrook-White equation (1939) is an implicit equation used to calculate the Darcy friction factor for turbulent flow in pipes. It combines experimental data from both smooth pipe and rough pipe flow regimes, relating the friction factor to the Reynolds number and relative roughness of the pipe.
Parameters
| SYMBOL | PARAMETER | SI UNITS | US UNITS | DESCRIPTION |
|---|---|---|---|---|
| f | Darcy Friction Factor | — | — | Dimensionless resistance coefficient |
| ε | Absolute Roughness | m (mm) | ft (in) | Height of surface irregularities |
| D | Pipe Diameter | m | ft (in) | Internal pipe diameter |
| Re | Reynolds Number | — | — | Flow regime indicator (inertial/viscous) |
| L | Pipe Length | m | ft | Total pipe length |
| V | Velocity | m/s | ft/s | Average flow velocity = Q / A |
| hf | Head Loss | m | ft | Friction energy loss over pipe length |
| g | Gravitational Acceleration | 9.81 m/s² | 32.174 ft/s² | Standard gravity (constant) |
| ρ | Fluid Density | kg/m³ | lb/ft³ | Used only for pressure drop |
Special Cases
1/√f = 2.0 × log₁₀(Re × √f) − 0.8
1/√f = −2.0 × log₁₀( ε / (3.7 × D) )
Why is it called "implicit"?
The friction factor f appears on both sides of the equation, meaning it cannot be solved directly. Iterative numerical methods must be used to find the solution.
Applications of the Colebrook-White Equation
The Colebrook-White equation is the most universally accepted method for pipe friction loss. Typical applications include:
Water Supply Systems
Design of municipal water distribution networks with precise head loss estimates.
Process Piping
Sizing pipes for chemical plants, refineries, and power stations.
Irrigation Networks
Calculating pressure requirements for drip and sprinkler systems.
Fire Protection
Hydraulic calculations for sprinkler systems per NFPA 13.
Cooling & Chilled Water
Design of HVAC hydronic systems.
Oil & Gas Pipelines
Analysis of crude oil and natural gas transmission lines.
Pipe Velocity Guidelines
Recommended flow velocities for water in pipes
| APPLICATION | RECOMMENDED VELOCITY (M/S) | RECOMMENDED VELOCITY (FT/S) |
|---|---|---|
| Water mains (normal) | 0.6 – 2.5 | 2 – 8 |
| Water mains (peak) | Up to 3.5 | Up to 12 |
| Fire sprinkler systems | 1.5 – 3.0 | 5 – 10 |
| Pump suction lines | 0.6 – 1.2 | 2 – 4 |
| Pump discharge lines | 1.5 – 3.0 | 5 – 10 |
| Gravity sewers | 0.6 – 2.5 | 2 – 8 |
| Maximum to avoid surge | < 5.0 | < 16 |
Important
Excessive velocity causes water hammer, erosion, and noise. Too low velocity may lead to sedimentation and water quality issues.
Frequently Asked Questions (FAQ)
Click on any question to reveal the answer.
About the Colebrook-White Equation
The Darcy friction factor (also called Moody friction factor) is 4 times the Fanning friction factor: f_Darcy = 4 × f_Fanning. The Darcy friction factor is commonly used in civil and mechanical engineering (pipe flow), while the Fanning friction factor is more common in chemical engineering. This calculator uses the Darcy friction factor.
The friction factor can be determined using the Colebrook-White equation (iterative), the Moody chart (graphical), or explicit approximations like Swamee-Jain or Haaland equations. This calculator uses fixed-point iteration with Swamee-Jain as initial guess for fast convergence.
The Colebrook-White equation is valid for turbulent flow (Re > 4,000) and relative roughness (ε/D) between 0 and 0.05. For laminar flow (Re < 2,300), use f = 64/Re directly. The transitional zone (2,300 < Re < 4,000) is unstable.
Using This Calculator
For new commercial steel pipe, use ε = 0.045 mm (0.000045 m). Select "Commercial Steel (new, welded)" from the pipe material dropdown to auto-fill this value. The resulting friction factor will depend on the Reynolds number.
Yes. Set the calculation mode to solve for diameter, enter the flow rate, available pressure drop, and pipe length. The calculator will iterate to find the required diameter. Note that this requires iterative solution since diameter appears in both Re and the Colebrook equation.
Yes, the Colebrook-White equation applies to any Newtonian fluid in turbulent pipe flow, including gases. Enter the appropriate fluid density and viscosity (or Reynolds number) for your gas. For compressible flow at high velocities, additional corrections may be needed.
Features
Smart Options is a panel that provides quick presets for common engineering scenarios, fluid property databases with temperature adjustment, optimization suggestions (velocity rating, suggested diameter), method comparison (Colebrook vs Swamee-Jain vs Haaland), and real-time smart alerts for your inputs.
Yes! All calculations are performed in your browser using JavaScript. No data is sent to servers. Once the page is loaded, you can use it offline.
Yes. Use the Copy button to copy results to clipboard, the Print button to print or save as PDF, or the CSV button to export results as a CSV file for use in spreadsheets.
Yes, this calculator is 100% free to use with no registration required. It is part of INAR Learn's collection of free engineering tools.