What is the difference between Darcy and Fanning friction factors?

The Darcy friction factor (f_D) is 4× the Fanning friction factor (f_F). Both are correct but used in different regional and disciplinary traditions. Always verify which convention a reference or textbook uses. The Darcy-Weisbach equation uses the Darcy factor.

Why is the Colebrook equation implicit?

The Colebrook-White equation has f on both sides: 1/√f = −2 log(ε/(3.7D) + 2.51/(Re√f)). This requires iterative solution (Newton-Raphson or fixed-point iteration). Explicit approximations like Swamee-Jain avoid this iteration with minimal accuracy loss.

What happens in the transitional regime?

Between Re ≈ 2100 and 4000, flow can be either laminar or turbulent depending on disturbances. The friction factor is unpredictable in this range. Pipe design should avoid operating in the transition zone if possible.

Why does roughness matter more for large Re?

At very high Reynolds numbers, the viscous sublayer becomes thinner than the roughness elements, so turbulent eddies interact directly with surface features. This is why the Moody chart lines become horizontal (fully rough regime) at high Re.

Is this the same friction factor as for solid surfaces?

No. The pipe friction factor (Darcy/Fanning) relates to fluid shear stress in internal flow. The coefficient of friction (μ) for solid surfaces relates to contact friction. Different physics, different definitions, same word "friction."

How does temperature affect the result?

Temperature mainly affects viscosity (and thus Reynolds number). Water at 20°C has ν = 1.004×10⁻⁶ m²/s; at 80°C, ν = 0.365×10⁻⁶ m²/s — nearly 3× lower, which triples Re. Higher Re generally means higher friction factor for turbulent flow.

Friction Factor Calculator (Darcy-Weisbach)

Calculate Darcy and Fanning friction factors for pipe flow. Moody chart calculation with Colebrook-White equation, Reynolds number, pipe material roughness, and head loss per meter.

Pipe Inner Diameter

Flow Velocity

m/s

Surface Roughness (ε)

Kinematic Viscosity (ν)

m²/s

Fluid Density

kg/m³

Darcy Friction Factor (f)

0.018605

Turbulent flow regime

Fanning Friction Factor

0.004651

f_Fanning = f_Darcy / 4

Reynolds Number

202,390

Turbulent: Re > 4000

Relative Roughness (ε/D)

4.4291e-4

ε/D — key parameter for Moody chart

Head Loss per Meter

0.0373 m/m

h_f/L = f/D × v²/(2g) — Darcy-Weisbach

Pressure Drop per Meter

365.51 Pa/m

ΔP/L = f/D × ρv²/2

Pipe Material Roughness Reference

Material	ε (mm)	Relative Roughness (ε/D)
	0.0015	1.4764e-5
	0.0015	1.4764e-5
	0.0015	1.4764e-5
	0.045	4.4291e-4
	0.15	1.4764e-3
	0.26	2.5591e-3
	0.3	2.9528e-3
	3	2.9528e-2
	45	4.4291e-1

Velocity vs Friction Factor

Velocity (m/s)	Re	Regime	f (Darcy)	Head Loss (m/m)
0.01	1,012	Laminar	0.06324	0.00000
0.05	5,060	Turb.	0.03828	0.00005
0.1	10,120	Turb.	0.03164	0.00016
0.5	50,598	Turb.	0.02238	0.00281
1	101,195	Turb.	0.02013	0.01010
2	202,390	Turb.	0.01861	0.03733
3	303,586	Turb.	0.01798	0.08116
5	505,976	Turb.	0.01740	0.21819
8	809,562	Turb.	0.01703	0.54670
10	1,011,952	Turb.	0.01689	0.84754

Flow Regime Indicator

Laminar

Trans.

Turbulent

▲ Re = 202,390

Planning notes, formulas, and examples

About the Friction Factor Calculator (Darcy-Weisbach)

The Darcy friction factor (f) is a dimensionless parameter used in the Darcy-Weisbach equation to calculate pressure drop and head loss in pipe flow. For laminar flow (Re < 2100), f = 64/Re. For turbulent flow, f depends on both the Reynolds number and the relative roughness ε/D, described by the implicit Colebrook-White equation.

The Moody chart is a graphical way to read friction factor against Reynolds number for different roughness values. This calculator replaces that lookup with a direct numerical estimate and also reports Darcy and Fanning factors, Reynolds number, and head loss per length.

When This Page Helps

Pipe flow calculations usually need more than a single friction number. Seeing the Reynolds number, roughness, and resulting head loss together makes it easier to size piping or compare operating conditions without switching between a chart and a worksheet.

How to Use the Inputs

Enter the pipe inner diameter in meters.
Enter the flow velocity in m/s.
Set the surface roughness (click a pipe material or enter manually in mm).
Enter the kinematic viscosity (default: water at 20°C = 1.004×10⁻⁶ m²/s).
Read the Darcy friction factor, Reynolds number, and flow regime.
Use the head loss and pressure drop values for pipe system design.
Review the velocity table to understand how friction factor changes with flow rate.

Formula used

Reynolds Number: Re = vD/ν

Laminar (Re < 2100): f = 64/Re

Turbulent (Colebrook-White):
  1/√f = −2 log₁₀(ε/(3.7D) + 2.51/(Re√f))

Swamee-Jain (explicit approximation):
  f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]²

Darcy-Weisbach: h_f = f × (L/D) × v²/(2g)
Pressure drop: ΔP = f × (L/D) × ρv²/2
Fanning factor: f_F = f_D / 4

Example Calculation

Result: f = 0.0218, Re = 202,390 (Turbulent)

4" commercial steel pipe (ε = 0.045 mm) with water at 2 m/s: Re = 2 × 0.1016 / 1.004e-6 = 202,390 (turbulent). Swamee-Jain: f = 0.0218. Head loss: 0.0047 m per meter of pipe.

Tips & Best Practices

For smooth pipes at high Re, f ≈ 0.316/Re^0.25 (Blasius formula) is a quick estimate.
Laminar flow: f is inversely proportional to Re and independent of roughness.
Fully rough turbulent flow: f depends only on ε/D, not on Re.
The Moody chart has four regions: laminar, transition, smooth turbulent, and fully rough turbulent.
PVC and copper pipes are effectively "hydraulically smooth" for most practical flow rates.
Aging and corrosion can increase roughness by 10-100× — use aged values for existing pipe systems.

Understanding the Moody Chart

The Moody chart, published by Lewis Moody in 1944, plots the Darcy friction factor versus Reynolds number for various relative roughnesses. It consolidates decades of experimental and theoretical work into a single, universally used tool. The chart reveals four distinct flow regimes: laminar (f = 64/Re), critical/transitional (unstable), smooth turbulent (f depends on Re only), and fully rough (f depends on ε/D only).

The Colebrook-White Equation

Derived in 1939, the Colebrook-White equation bridges the smooth and rough turbulent regimes with a single implicit formula. Its implicit nature was acceptable in 1939 (solved by trial-and-error or nomographs), but modern computers and explicit approximations (Swamee-Jain 1976, Haaland 1983) make iterative solution unnecessary. The Swamee-Jain approximation used here is accurate to within 1% for 5×10³ < Re < 10⁸ and 10⁻⁶ < ε/D < 5×10⁻².

Practical Engineering Significance

Friction factor is the key input for pipe system sizing — the single most common calculation in fluid engineering. A 10% error in f translates to 10% error in pressure drop, which affects pump sizing, energy costs, and system capacity. For a typical water distribution system operating millions of hours, even small accuracy improvements in friction factor calculation yield significant cost savings.

Sources & Methodology

Last updated: March 7, 2026

Frequently Asked Questions

The Darcy friction factor (f_D) is 4× the Fanning friction factor (f_F). Both are correct but used in different regional and disciplinary traditions. Always verify which convention a reference or textbook uses. The Darcy-Weisbach equation uses the Darcy factor.