# Friction Factor Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Nov 07, 2022

This friction factor calculator estimates the value of friction factor for pipe flows, which is used in several design calculations to determine the energy loss due to friction in pipe flows. The friction factor is commonly used in the Darcy-Weisbach equation and is also referred to as the Darcy friction factor. This value depends on parameters like hydraulic radius, fluid viscosity, surface roughness, and Reynold's number. Read on to understand how to calculate friction factor using the Colebrook equation.

## What are pipe losses and how to calculate friction factor?

The loss in energy of fluids while traveling through a pipe or ducts causes reduction in pressure and velocity which is known as head loss. The major causes of these losses include surface roughness and friction. In addition to this, changes in pipe cross-section like enlargement or contraction, bends, and branching contributes to minor losses. The friction head loss is used in the Darcy-Weisbach equation to estimate the pressure drop $\Delta p$ for a fluid flowing at a velocity $V$, in a pipe having length $L$ and the hydraulic diameter $D$, and friction factor $f$, such that:

$\footnotesize \Delta p = \cfrac{f L V^2}{2gD}$

where $g$ is the acceleration due to gravity.

You can read more about the pressure drop calculation with our dedicated Darcy-Weisbech calculator.

The term $f$, or friction factor, can be estimated for a pipe having surface roughness $k$ using the Colebrook equation:

$\footnotesize \cfrac{1}{\sqrt f} = -2 \log \left(\cfrac{k}{3.7 D}\right) + \cfrac{2.51}{\text{Re} \sqrt f}$

where $\text{Re}$ is the Reynold's number for the fluid flow. The Colebrook-White equation can only be solved using numerical approximations. One of the commonly used approximation is given by Lewis Moody, otherwise known as Moody chart or Moody diagram. This calculator utilizes Moody's approximation to determine the Darcy friction factor. Moody's approximation or otherwise known as Moody equation is given as:

$\footnotesize f = 0.0055 \left( 1+ \left(2\cdot 10 ^4 \frac{k}{D} + \frac{10^6}{\text{Re}}\right)^{1/3}\right)$

This approximation is valid for flow regimes where Reynold's number is between $4,000$ and $5\cdot10^8$, and pipes with a $k/D$ ratio less than $0.01$. This approximation is also used for this Moody diagram calculator.

🙋 Are you unsure how to calculate a pipe's hydraulic diameter or how to find the velocity of a flowing fluid? Then you might like to take a look at the hydraulic radius calculator or the pipe flow calculator to find out.

## How to calculate friction factor?

Follow the steps below to use the Moody equation to estimate the Darcy friction factor.

• Step 1: Enter the hydraulic diameter of the pipe or conduit.

• Step 2: Input the surface roughness of the pipe. Note that the equation is only valid for k/D ratio less than 0.01.

• Step 3: Insert the Reynold's number for the flow regime. **Note that the equation is only valid for pipe flows having Reynold's number in the range $4000 < \text{Re} < 5\cdot10^8$.

• Step 3A: You can use the advanced mode of calculator to estimate the Reynold's number. Use the fluid properties – density, viscosity, and flow velocity to find the Reynold's number. You can also use advanced mode to enter a value for the relative roughness $k/D$ directly.

• Step 4: The Moody diagram calculator will return the value of Darcy friction factor.

## Example: Using the Moody chart calculator

Find the friction factor for a pipe having a hydraulic diameter of $2 \text m$, a surface roughness of $0.01 \text m$. Take Reynold's number as $4500$.

• Step 1: Enter the hydraulic diameter of the pipe or conduit, $D = 2 \text m$.

• Step 2: Input the surface roughness of the pipe, $k = 0.01 \text m$. Here, $k/D$ ratio is $0.005$ and therefore, acceptable.

• Step 3: Insert the Reynold's number for the flow regime, $Re = 4500$.

$\footnotesize \begin{split} f &= 0.0055 \left( 1+ \left(2\cdot 10 ^4 \frac{k}{D} + \frac{10^6}{\text{Re}}\right)^{1/3}\right) \\ &= 0.0055 \left( 1+ \left(2\cdot 10 ^4 \frac{0.01}{2} + \frac{10^6}{\text{4500}}\right)^{1/3}\right) \\ &= 0.04321 \end{split}$
• Step 4: The Moody chart calculator will return the value of Darcy friction factor, $f = 0.04321$.

## FAQ

### What are the factors affecting friction?

There are three main factors affecting friction – pipe diameter, Reynold’s number, and surface roughness. Reynold’s number for the flow depends on the flow velocity, fluid density and viscosity, and pipe length.

### How to calculate friction factor for turbulent flow?

1. Calculate the Reynold’s number for the flow (using ρ × V × D / μ).
2. Check the relative roughness (k/D) to be under 0.01.
3. Use the Reynold’s number, roughness in the Moody formula - f = 0.0055 × ( 1 + (2×104 × k/D + 106/Re)1/3)

### How to use a moody friction factor chart?

To use a Moody friction factor chart, you need values for the Reynold’s number a relative roughness (k/D). Trace the relative roughness curve and draw a line from Reynold’s number on the x-axis. The point where the Reynold’s number line intersects the roughness curve gives the Moody friction factor.

### How to calculate relative roughness of a surface?

You can calculate relative roughness of a surface using the formula: k/D, where k is the surface roughness and D is hydraulic diameter.

Rahul Dhari
Hydraulic diameter (D)
m
Surface roughness (k)
m
Reynold's number (Re)
Friction factor (f)
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