Colebrook-White Formula

Colebrook-White Equation:

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

Friction Factor (f):

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1. What is the Colebrook-White Formula?

The Colebrook-White formula is an implicit equation that calculates the friction factor for fluid flow in pipes. It applies to both turbulent and transitional flow regimes and is widely used in hydraulic engineering for pressure drop calculations.

2. How Does the Calculator Work?

The calculator uses the Colebrook-White equation:

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

Where:

\( f \) — Friction factor (dimensionless)
\( \varepsilon \) — Absolute 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 methods to converge to the solution.

3. Importance of Friction Factor Calculation

Details: Accurate friction factor calculation is essential for determining pressure losses in piping systems, sizing pumps, designing water distribution networks, and optimizing energy consumption in fluid transport systems.

4. Using the Calculator

Tips: Enter pipe roughness in meters, diameter in meters, and Reynolds number (dimensionless). 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 implicit?
A: The equation contains the friction factor on both sides, making it impossible to solve explicitly. Iterative numerical methods are required for solution.

Q2: What is the range of validity for this equation?
A: The Colebrook-White equation is valid for turbulent flow (Re > 4000) and covers both hydraulically smooth and rough pipe regimes.

Q3: Are there explicit approximations available?
A: Yes, the Swamee-Jain and Haaland equations provide explicit approximations with good accuracy for most engineering applications.

Q4: What are typical roughness values for common pipes?
A: Steel: 0.045 mm, Cast iron: 0.26 mm, PVC: 0.0015 mm, Concrete: 0.3-3.0 mm depending on finish.

Q5: How does Reynolds number affect the friction factor?
A: At low Reynolds numbers in turbulent flow, friction factor decreases with increasing Re. At high Reynolds numbers, it becomes constant (fully rough regime).