What is the primary benefit of using the Churchill equation?

The Churchill equation is explicit, meaning it does not require iterative calculation methods like the Colebrook-White equation, while maintaining high accuracy across laminar, transition, and turbulent flow regimes.

Does Churchill correlation compute Fanning or Darcy friction factor?

It computes the Darcy friction factor (also called Darcy-Weisbach or Moody friction factor), which is exactly 4 times larger than the Fanning friction factor.

What is the equation for the Churchill correlation?

The Churchill correlation computes the Darcy friction factor using parameters A and B which depend on the Reynolds Number (Re) and relative pipe roughness (ε/D).

Churchill Friction Factor Calculator (Online + Excel)

The Churchill equation allows to calculate the friction factor for all flow regimes from laminar to turbulent.

1. Introduction

The friction factor is used to calculate the pressure drop due to the flow of a fluid in a pipe. It represents the interaction in between the fluid and the pipe. There are different ways to calculate it, one can be graphical, using a Moody graph, but for automating calculation it is not practical, thus correlations are required. The Colebrook correlation is usually admitted as being accurate enough for most industrial applications but presents a difficulty as it does not explicitly express the friction factor, that is why it may be interesting to consider Churchill equation that allows to directly calculate the friction factor.

Note that the friction factor used here is Darcy (also called Darcy-Weisbach or Moody) friction factor.

2. Churchill equation

The explicit Churchill correlation (1977) is given by the following set of equations:

\[f = 8 \left[ \left(\frac{8}{Re}\right)^{12} + \frac{1}{(A + B)^{1.5}} \right]^{1/12}\]

Where the coefficients \(A\) and \(B\) are defined as:

\[A = \left[ 2.457 \ln \left( \frac{1}{\left(\frac{7}{Re}\right)^{0.9} + 0.27 \frac{\epsilon}{D}} \right) \right]^{16}\] \[B = \left( \frac{37530}{Re} \right)^{16}\]

Original Equation reference image:

With :
f = Darcy friction factor
D = Pipe diameter (m)
Re = Reynolds number
ε = pipe roughness (m)

💡 Churchill Friction Factor Calculator

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Pipe Inside Diameter (D) mm

Pipe Absolute Roughness (ε) mm

Reynolds Number (Re) Dimensionless

⚠️ Design Alerts detected:

Calculated Hydraulics Output

0.00045

Relative Roughness (ε/D)

0.0235

Darcy Friction Factor (f)

Turbulent

Flow Regime

📌 Plant Engineering Rules of Thumb: Pipe Roughness & Hydraulics

Roughness Values (ε): Steel pipes typically scale with corrosion. Use 0.045 mm (0.0018 in) for brand-new commercial steel and 0.15 mm (0.006 in) or more for design margins representing aged/scaled piping.
Transition Flow Limit: The region between \(2100 < Re < 4000\) is unstable. Churchill yields continuous solutions across this gap, but standard design guidelines advise avoiding operating control valves or pumps in this volatile hydrodynamics zone.
Hydraulic Sizing Guidelines: Maintain liquid velocities between 1.0 - 1.5 m/s to balance erosional limits against pumping pressure drop penalties.

3. Excel calculation tool

Please access this page to download the free xls calculation tool for Churchill correlation.

Churchill correlation (friction factor)