Enter the Reynolds Number and the Relative Roughness into the calculator to determine the friction factor using the Colebrook formula. This calculator provides an approximation of the friction factor for turbulent flow in pipes.

## Colebrook Formula

The Colebrook formula is an implicit equation used to calculate the friction factor for turbulent flow in pipes, which is a measure of the resistance caused by the roughness of the pipe's interior surface. The formula is given by:

1 / √f = -2 * log10((ε/D) / 3.7 + (2.51 / (Re * √f)))

Variables:

- f is the Darcy-Weisbach friction factor
- ε/D is the relative roughness of the pipe's interior surface
- Re is the Reynolds Number, a dimensionless quantity representing the ratio of inertial forces to viscous forces

To calculate the friction factor, an iterative method such as the Newton-Raphson method is used due to the implicit nature of the Colebrook formula.

## 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.

## How to Calculate Friction Factor using the Colebrook Formula?

The following steps outline how to calculate the friction factor using the Colebrook formula.

- First, determine the Reynolds Number (Re).
- Next, determine the Relative Roughness (ε/D).
- Use an iterative method to solve the implicit Colebrook equation for the friction factor (f).
- Finally, obtain the friction factor (f) which is dimensionless.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Reynolds Number (Re) = 100000

Relative Roughness (ε/D) = 0.0005