What is the difference between Fanning and Darcy friction factors?

The Darcy-Weisbach friction factor (fd) is exactly four times larger than the Fanning friction factor (f/2 or f_f). Darcy friction factor is most commonly used in civil and mechanical engineering for pipe flow calculations, while Fanning is often preferred by chemical engineers.

Why is the Churchill correlation preferred over Colebrook-White?

The Colebrook-White equation is implicit and requires iterative numerical methods to solve. The Churchill correlation is explicit, meaning it can be solved directly without iteration, and it spans all flow regimes seamlessly: laminar, critical transition, and fully turbulent flow.

Friction Factor Calculator (Online & Excel)

1. Definition of friction factor

The friction factor represents the loss of pressure of a fluid in a pipe due to the shear stress interactions between the fluid and the pipe wall.

\[ \frac{f}{2} = \frac{D}{4 \cdot \rho \cdot u_m^2} \frac{\Delta P_f}{L} \] Calculation Friction Factor

\(f/2\) = friction factor - Fanning (dimensionless)
\(D\) = Pipe internal diameter (m)
\(u_m\) = mean fluid velocity (m/s)
\(\Delta P_f\) = pressure drop due to friction (Pa)
\(L\) = length of pipe (m)
\(\rho\) = density of fluid (kg/m³)

⚠️ 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.

Interactive Pipe Friction & Pressure Drop Sizing Tool

SI Metric US Customary

Pipe Internal Diameter (D)

mm

Pipe Absolute Roughness (e)

mm

Fluid Density (ρ)

kg/m³

Dynamic Viscosity (μ)

cP

Mean Flow Velocity (u_m)

m/s

Pipe Length (L)

m

Calculation Results

Reynolds Number (Re): 153,450

Flow Regime: Turbulent

Fanning Friction Factor (f/2): 0.00427

Darcy Friction Factor (f_D): 0.01709

Pressure Gradient: 1.88 kPa/m

Total Friction Pressure Drop (ΔP_f): 0.188 bar

2. Calculation of friction factor

How to find the friction factor of a pipe? The different mathematical equations below allow you to calculate the friction factor of a pipe depending on the fluid flow regime.

Flow Regimes:

Laminar regime (\(\text{Re} \le 2000\)): The friction factor is independent of pipe roughness and depends only on velocity and viscosity. \[ \frac{f}{2} = \frac{8}{\text{Re}} \]
Turbulent regime (\(\text{Re} \ge 4000\)): The flow is highly disturbed and friction depends heavily on the relative roughness of the wall.

Turbulent Flow Empirical Correlations:

Blasius Correlation (applicable to smooth pipes only and for \(\text{Re} < 10^5\)):

\[ \frac{f}{2} = 0.023 \cdot \text{Re}^{-0.20} \]

Churchill Correlation (applicable for any Reynolds number \(\text{Re}\) and relative roughness ratio \(e/D\). This explicit equation handles laminar, transitional, and turbulent regimes seamlessly):

\[ \frac{f}{2} = \left[ \left( \frac{8}{\text{Re}} \right)^{12} + \frac{1}{(A + B)^{3/2}} \right]^{1/12} \] \[ A = \left\{ 2.457 \ln \left[ \left( \left( \frac{7}{\text{Re}} \right)^{0.9} + 0.27 \frac{e}{D} \right)^{-1} \right] \right\}^{16} \] \[ B = \left( \frac{37530}{\text{Re}} \right)^{16} \] Calculation of Churchill Correlation

With \(e\) representing the absolute internal pipe roughness in meters (m).

Another common sizing method is using the graphical Moody Diagram, which is a log-log friction factor chart plotting friction factor as a function of the Reynolds number with absolute roughness as a parameter.

💡 Industrial Piping Best Practices & Safety Limits

Liquid Velocity Limits: Design velocities for standard pump discharge lines should ideally stay between 1.0 and 2.5 m/s (3 to 8 ft/s) to balance capital costs of larger piping and pumping energy consumption. Avoid values over 3.0 m/s to prevent erosion-corrosion.
Gas Velocity Limits: Dry gas velocities can safely range from 15 to 30 m/s (50 to 100 ft/s), while wet/corrosive gas velocity must be capped below its calculated erosional velocity limit.
Transition Zone Warning: In the transition zone (\(2000 < \text{Re} < 4000\)), flow fluctuates dynamically. Engineering designs should avoid running processes continuously inside this band due to flow instability.
Fanning vs Darcy: Always confirm which friction factor is being used. Fanning (\(f_F\)) is four times smaller than Darcy-Weisbach (\(f_D\)). Moody Charts generally plot Darcy, whereas chemical thermodynamics literature often uses Fanning.

3. Hagen-Poiseuille relation

In laminar flow regimes (\(\text{Re} \le 2000\)), the volumetric flow rate of an incompressible viscous fluid through a cylindrical pipe of constant cross-section can be calculated directly using the classic Hagen-Poiseuille equation:

\[ Q = \frac{\pi \cdot D^4}{128 \cdot \mu} \frac{\Delta P_f}{L} \] Hagen Poiseuille Law

\(Q\) = volumetric flow rate (m³/s)
\(\mu\) = dynamic viscosity of fluid (Pa·s)

Source

Mecanique et Rheologie des fluides en genie chimique, Midoux, Lavoisier 1993, page 162, page 274-275

Friction factor