# Darcy Friction Factor Calculator

Created by Luis Hoyos
Based on research by
Viktor Mileikovskyi, Tetiana Tkachenko Precise Explicit Approximations of the Colebrook-White Equation for Engineering Systems Proceedings of EcoComfort 2020 (2021)
Last updated: Aug 12, 2022

Welcome to our Darcy friction factor calculator, where you'll be able to find the Darcy-Weisbach friction factor used in pressure loss calculations.

This tool uses the Mileikovskyi-Tkachenko approximation of the classical Colebrook-White equation. With this approximation, we can calculate the Darcy friction factor for turbulent flow within 2320 ≤ Re ≤ 109 and 0 ≤ k/D ≤ 0.65 ranges with a 0.00072% deviation.

If you don't know the Reynolds number, click on the advanced mode, and our calculator will ask for the inputs to calculate it for you. You can also calculate it using our Reynolds number calculator.

Read on to learn about the importance of the friction factor and more details about the Mileikovskyi-Tkachenko Darcy friction factor formula.

🙋 Once you calculate the friction factor, you can calculate the head loss using our Darcy-Weisbach equation calculator

## Why do we need to calculate the darcy friction factor?

The loss in energy of fluids while traveling through a pipe or ducts causes a reduction in pressure and velocity, known as head loss. The principal causes of head losses include surface roughness and friction.

Additionally, changes in pipe cross-section, like enlargements, contractions, bends, and branching, contribute to minor losses.

The Darcy-Weisbach equation estimates the head loss caused by friction:

$\small h_l = f \frac{L}{D} \frac{V^2}{2g}$

where:

• $h_l$ — head loss;
• $f$ — Darcy–Weisbach friction factor;
• $L$ — Pipe length;
• $D$ — Hydraulic diameter;
• $V$ — Fluid velocity;

For laminar flow, the Darcy friction factor equation is simple:

$f_\text{laminar} = \frac{64}{Re}$

Where $Re$ is the Reynolds number:

Reynolds number is a function of pipe geometry, fluid velocity, viscosity, and density. You can calculate the latter with .

For turbulent flow, the calculation is more tricky.

## Darcy friction factor equation for turbulent flow

The more exact way to calculate the Darcy friction factor for turbulent flow is using the phenomenological Colebrook-White equation:

$\frac{1}{\sqrt{f}} = -2 \log{\left(\frac{k/D}{3.7} + \frac{2.52}{Re\sqrt{f}}\right)}$

where:

• $k$ — Surface roughness;
• $D$ — Hydraulic diameter; and
• $Re$ — Reynold's number.
• $f$ — Darcy friction factor (for turbulent flow, in this case).

As you could note, the Darcy–friction factor is implicit in the previous equation, making it imperative to perform iterations until finding its value.

Since 1947 different explicit approximations of the Colebrook-White equation have arisen, although their accuracy has been improvable. Recently, Mileikovskyi and Tkachenko developed an approximation with excellent accuracy (up to 0.00072% deviation in a wide range of parameters). The Darcy friction factor formula proposed by the authors is:

$\small f = \left(\frac{8.128943 + A_1}{8.128943 A_0 - 0.86859209 A_1 ln{\left(\frac{A_1}{3.7099535 Re}\right)}}\right)^2$
$\small A_1 = Re \frac{k}{D} + 9.3120665 A_0$
$\small A_0 = -0.79638 ln{\left(\frac{k/D}{8.208}\ + \frac{7.3357}{Re} \right)}$

This calculator relies on that approximation to find the friction factor value.

Be sure to check our other tool that uses the Hagen-Poiseuille equation to analyze a pipe's flow.

Luis Hoyos
Reynold's number (Re)
Surface roughness (k)
m
Hydraulic diameter (D)
m
Relative roughness (k/D)
Friction factor (ƒ)
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