# Online calculator

## Friction factor correlations for turbulent flow regime

Welcome to the online calculator for friction factor correlations in turbulent flow regimes.

In fluid dynamics, the friction factor is a measure of the drag or resistance to flow in a pipe or duct. It is an important parameter in the calculation of the pressure drop that occurs in a piping or duct system due to the resistance to flow. The friction factor is commonly used in the calculation of the Darcy-Weisbach equation, which is used to determine the head loss or pressure drop in a pipe due to friction.

This page provides a selection of correlations that can be used to calculate the friction factor for turbulent flow regimes. The correlations provided include the Colebrook-White, Nikuradse, Von Karman, Filonenko, and Fang et al. correlations. Each of these correlations is described in more detail below, along with the required input parameters and the range of validity for each correlation. The nomenclature section provides a list of the variables used in the correlations.

### Correlations

### Nomenclature

*f*: Darcy friction factor*e*: pipe roughness height*ε*: relative roughness*D*: hydraulic diameter

Re: Reynolds number

### 1a) Colebrook-White correlation

Valid for 4000 < Re < 10^{8} [1].

The fields below are required.

Enter Reynolds number (Re):

Enter pipe roughness height (*e*):

Enter hydraulic diameter (D):

The result is: *f* = …

### 1b) Colebrook-White correlation

Valid for 4000 < Re < 10^{8} [1].

The fields below are required.

Enter Reynolds number (Re):

Enter relative roughness (*ɛ* = *e*/D):

The result is: *f* = …

### 2) Nikuradse correlation

Valid for Re > 0 [2].

The fields below are required.

Enter Reynolds number (Re):

The result is: *f* = …

### 3a) Von Karman correlation

Valid for 4000 < Re < 1/(0.01*ɛ*√*f*_{F}), where *f*_{F} is the Fanning friction factor [3].

The fields below are required.

Enter pipe roughness height (*e*):

Enter hydraulic diameter (D):

The result is: *f* = …

### 3b) Von Karman correlation

Valid for 4000 < Re < 1/(0.01*ɛ*√*f*_{F}), where *f*_{F} is the Fanning friction factor [3].

The fields below are required.

Enter relative roughness (*ɛ* = *e*/D):

The result is: *f* = …

### 4) Filonenko correlation

Valid for 10^{4} < Re < 10^{8} [4].

The fields below are required.

Enter Reynolds number (Re):

The result is: *f* = …

### 5a) Fang et al. correlation

Valid for 3000 < Re < 10^{8} [5].

The fields below are required.

Enter Reynolds number (Re):

Enter pipe roughness height (*e*):

Enter hydraulic diameter (D):

The result is: *f* = …

### 5b) Fang et al. correlation

Valid for 3000 < Re < 10^{8}.

The fields below are required.

Enter Reynolds number (Re):

Enter relative roughness (*ɛ* = *e*/D):

The result is: *f* = …

### References

[1] Colebrook, C.F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws.

[2] Nikuradse, J. (1933). Stromungsgesetze in Rauhem Rohren.

[3] Von Kármán, T. (1930). Mechanische Ähnlichkeit und Turbulenz.

[4] Filonenko, G.K. (1954). Hydraulic resistance in pipes.

[5] Fang X. (2011). New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations.

[6] Pallippattu Krishnan Vijayan (2019). Single-Phase, Two-Phase and Supercritical Natural Circulation Systems.