Colebrook White Equation Calculator

Colebrook-White Equation:

\[ \frac{1}{\sqrt{f}} = -2 \log\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}}\right) \]

Friction Factor (f):

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1. What is the Colebrook-White Equation?

The Colebrook-White equation is an implicit formula that calculates the Darcy-Weisbach friction factor for turbulent flow in pipes. It relates the friction factor to the Reynolds number and relative roughness of the pipe.

2. How Does the Calculator Work?

The calculator uses the Colebrook-White equation:

\[ \frac{1}{\sqrt{f}} = -2 \log\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}}\right) \]

Where:

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

Explanation: The equation is solved iteratively since it's implicit in the friction factor. The calculator uses numerical iteration to converge on the solution.

3. Importance of Friction Factor Calculation

Details: Accurate friction factor calculation is essential for determining pressure drops in pipe systems, designing pumping systems, and optimizing fluid transport in various engineering applications.

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

Q2: What is the range of validity for this equation?
A: The Colebrook-White equation is valid for turbulent flow (Re > 4000) in commercial pipes with relative roughness between 0 and 0.05.

Q3: Are there explicit approximations available?
A: Yes, the Swamee-Jain and Haaland equations provide explicit approximations that are accurate within 1-2% of the Colebrook-White solution.

Q4: What are typical roughness values for pipes?
A: Roughness varies by material: steel (0.045 mm), cast iron (0.26 mm), concrete (0.3-3.0 mm), plastic (0.0015 mm).

Q5: How does Reynolds number affect the friction factor?
A: For smooth pipes, friction factor decreases with increasing Reynolds number. For rough pipes, friction factor becomes constant at high Reynolds numbers.