Colebrook White Formula Calculator

Colebrook-White Equation:

\[ \frac{1}{\sqrt{f}} = -2 \log_{10}\left[\frac{\varepsilon}{3.7D} + \frac{2.51}{Re \sqrt{f}}\right] \]

Darcy Friction Factor (f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Colebrook-White Formula?

The Colebrook-White equation is an implicit formula that relates the Darcy friction factor to the Reynolds number and relative roughness of a pipe. It describes friction losses in turbulent flow through rough pipes and is widely used in fluid mechanics and hydraulic engineering.

2. How Does the Calculator Work?

The calculator solves the Colebrook-White equation:

\[ \frac{1}{\sqrt{f}} = -2 \log_{10}\left[\frac{\varepsilon}{3.7D} + \frac{2.51}{Re \sqrt{f}}\right] \]

Where:

\( f \) — Darcy friction factor (dimensionless)
\( \varepsilon \) — Absolute roughness (m)
\( D \) — Pipe diameter (m)
\( Re \) — Reynolds number (dimensionless)

Explanation: The equation is solved iteratively using the Newton-Raphson method to find the friction factor that satisfies the implicit relationship.

3. Importance of Friction Factor Calculation

Details: Accurate friction factor calculation is essential for determining pressure drops, pipe sizing, pump selection, and energy consumption in fluid transport systems.

4. Using the Calculator

Tips: Enter pipe roughness in meters, diameter in meters, and Reynolds number. All values must be positive, with diameter and Reynolds number greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for Colebrook-White equation?
A: The equation is valid for turbulent flow (Re > 4000) and covers both hydraulically smooth and rough pipe regimes.

Q2: Why is the equation solved iteratively?
A: The Colebrook-White equation is implicit in the friction factor, meaning the friction factor appears on both sides of the equation, requiring numerical methods for solution.

Q3: What are typical roughness values for common pipes?
A: Steel: 0.045 mm, Cast iron: 0.26 mm, Concrete: 0.3-3.0 mm, PVC: 0.0015 mm. Values vary with pipe age and condition.

Q4: Are there explicit approximations available?
A: Yes, approximations like Swamee-Jain and Haaland provide explicit solutions with good accuracy for most engineering applications.

Q5: When is the friction factor calculation most critical?
A: Critical in long pipelines, high-flow systems, and when optimizing energy efficiency in pumping systems.