Colebrook Equation Calculator

Colebrook 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 Equation?

The Colebrook equation is an implicit equation that relates the Darcy-Weisbach friction factor (f) to the Reynolds number (Re) and relative roughness (ε/D) 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 uses the Colebrook 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 absolute roughness (m)
\( D \) — Pipe diameter (m)
\( Re \) — Reynolds number (dimensionless)

Explanation: The equation is solved iteratively using numerical methods since it cannot be solved explicitly for the friction factor.

3. Importance of Friction Factor Calculation

Details: Accurate friction factor calculation is essential for determining pressure drops, flow rates, and energy losses in pipe systems. It helps in designing efficient fluid transport systems and selecting appropriate pumping equipment.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the Colebrook equation implicit?
A: The friction factor appears on both sides of the equation, making it impossible to solve explicitly. Numerical methods are required for solution.

Q3: What are typical roughness values for common pipes?
A: Steel: 0.000045-0.00009 m, Cast iron: 0.00026 m, Concrete: 0.0003-0.003 m, PVC: 0.0000015 m.

Q4: Are there explicit approximations to the Colebrook equation?
A: Yes, the Swamee-Jain and Haaland equations provide explicit approximations with good accuracy for most engineering applications.

Q5: When should I use the Moody chart instead?
A: The Moody chart provides a graphical solution and is useful for understanding the relationship between parameters, but numerical solutions are more precise for calculations.