Colebrook Formula Calculator

Calculate Friction Factor (f)



Formula

The formula to calculate the friction factor (f) using the Colebrook equation is:

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

Where:

Example

Let's say the relative roughness (\( \epsilon/D \)) is 0.005 and the Reynolds number (\( Re \)) is 100,000. Using the Colebrook formula and an iterative method:

\[ \frac{1}{\sqrt{f}} = -2 \log_{10}\left(\frac{0.005}{3.7} + \frac{2.51}{100000 \sqrt{f}}\right) \]

After solving iteratively, we find the friction factor (\( f \)) to be approximately 0.031.

What is the Colebrook Formula?

The Colebrook formula is widely used in fluid mechanics to estimate the friction factor for turbulent flow in smooth and rough pipes. It is an empirical formula derived from experimental data and is considered to be accurate for a wide range of Reynolds numbers and relative roughness values.

Extended information about "Colebrook-Formula-Calculator"

What is the Colebrook Equation

Definition: The Colebrook equation is used to calculate the Darcy-Weisbach friction factor for turbulent flow in pipes.

Formula: \( \frac{1}{\sqrt{f}} = -2 \log \left( \frac{\epsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \)

Example: \( \frac{1}{\sqrt{0.02}} = -2 \log \left( \frac{0.0001/0.05}{3.7} + \frac{2.51}{5000 \sqrt{0.02}} \right) \)

How to Solve Colebrook Equation

Definition: Solving the Colebrook equation involves iterative methods due to its implicit nature.

Formula: \( \frac{1}{\sqrt{f}} = -2 \log \left( \frac{\epsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \)

Example: \( \frac{1}{\sqrt{0.03}} = -2 \log \left( \frac{0.0002/0.1}{3.7} + \frac{2.51}{10000 \sqrt{0.03}} \right) \)

Colebrook Equation Solved for Roughness

Definition: Solving the Colebrook equation for roughness involves isolating the roughness term.

Formula: \( \epsilon = 3.7 D \left( 10^{\frac{1}{-2 \log \left( \frac{1}{\sqrt{f}} - \frac{2.51}{Re \sqrt{f}} \right)}} - \frac{2.51}{Re \sqrt{f}} \right) \)

Example: \( \epsilon = 3.7 \times 0.05 \left( 10^{\frac{1}{-2 \log \left( \frac{1}{\sqrt{0.02}} - \frac{2.51}{5000 \sqrt{0.02}} \right)}} - \frac{2.51}{5000 \sqrt{0.02}} \right) \)