What is the difference between the Darcy and Fanning friction factors?

Whichever reference, correlation, or Moody chart you're handed, check its convention before using its number in this calculator, plugging a Fanning value into a Darcy-based formula (or vice versa) is a silent factor-of-4 error that produces a plausible-looking wrong answer rather than an obvious one.

Why is the Colebrook equation solved iteratively?

Practically, that means this calculator (and any spreadsheet or hand-solve doing the same thing) starts from a reasonable guess, usually the Swamee-Jain explicit result, and refines it a handful of times until the value stops moving, rather than solving for f in one algebraic step the way the laminar case allows.

What is the Swamee-Jain equation, and how accurate is it?

The Swamee-Jain equation is an explicit (non-iterative) approximation to the Colebrook equation, typically accurate to within about 1% over the normal turbulent flow range (Re between 5000 and 10^8). It's commonly used as a quick estimate or as the starting guess for an iterative Colebrook solve.

What is relative roughness ε/D?

Relative roughness is the pipe's internal surface roughness height ε divided by its internal diameter D. It's dimensionless and depends on the pipe material and condition, smooth drawn tubing has ε/D near zero, while corroded cast iron can have ε/D of 0.01 or more.

Does friction factor depend on flow rate?

Yes, indirectly, friction factor depends on Reynolds number, which depends on velocity (and hence flow rate) for a fixed pipe and fluid. In the laminar regime f = 64/Re decreases directly with increasing Re (and hence flow rate); in the turbulent regime the dependence is weaker and also involves relative roughness.

What happens to the friction factor at the laminar-turbulent transition (Re ≈ 2100–4000)?

The transitional regime is inherently unpredictable, friction factor correlations for both laminar and turbulent flow become unreliable here, since the flow can intermittently switch between laminar and turbulent behavior. Engineering practice is typically to avoid designing for steady operation in this range.

Does this calculator work for non-Newtonian fluids?

No, the 64/Re laminar result and the Colebrook/Swamee-Jain turbulent correlations here assume a Newtonian fluid with a single, shear-independent viscosity. Non-Newtonian fluids (slurries, polymer solutions, many food and pharma products) need a generalized Reynolds number and friction-factor correlation specific to their rheology (e.g., power-law or Bingham-plastic models) instead of this Newtonian form.

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Darcy · Colebrook · Swamee-Jain

Friction Factor
Calculator

Compute the Darcy friction factor for laminar and turbulent pipe flow, with full step-by-step solutions.

Formula

$f = \dfrac{64}{Re}$

Quick Answer

The Darcy friction factor quantifies frictional pressure loss in pipe flow. For laminar flow (Re < 2100), f = 64/Re exactly. For turbulent flow, f is found from the implicit Colebrook equation (solved iteratively) or approximated directly with the explicit Swamee-Jain equation, both using Reynolds number and relative pipe roughness ε/D as inputs. This calculator computes both and shows every step.

Friction Factor Calculator

$f = 64/Re$ (laminar) · $\dfrac{1}{\sqrt f} = -2\log_{10}\left(\dfrac{\varepsilon/D}{3.7}+\dfrac{2.51}{Re\sqrt f}\right)$ (Colebrook)

Reynolds Number Re

Relative Roughness ε/D

How to Use the Friction Factor Calculator

1
Enter the Reynolds number
Enter the flow's Reynolds number Re (from the Reynolds Number Calculator if you don't already have it).
2
Enter the relative roughness
Enter the pipe's relative roughness ε/D (roughness height divided by pipe diameter), or pick a common material preset.
3
Click Calculate
Click Calculate to determine the flow regime and compute the Darcy friction factor.
4
Read the friction factor result
For laminar flow, read the exact f = 64/Re result. For turbulent flow, compare the iterative Colebrook solution against the explicit Swamee-Jain approximation.

Need the Reynolds number first? Use the Reynolds Number Calculator, or see the full Fluid Mechanics topic guide.

What Is the Darcy Friction Factor?

The Darcy friction factor f quantifies how much a pipe's internal surface resists flow, feeding directly into the Darcy-Weisbach equation $\Delta P = f\left(\dfrac{L}{D}\right)\left(\dfrac{\rho v^2}{2}\right)$ for frictional pressure drop. For laminar flow it has an exact analytical value; for turbulent flow it depends on both the Reynolds number and the pipe's relative roughness, and must be found from the implicit Colebrook equation or an explicit approximation like Swamee-Jain.

This calculator computes both, the exact laminar result when Re < 2100, and both the Colebrook (iterative) and Swamee-Jain (explicit) turbulent results when Re > 4000, so you can see how closely the fast approximation tracks the more rigorous iterative solution.

The corroded, pitted interior surface of an old metal pipe — This is what relative roughness ε/D is actually measuring — real surface texture, not an abstract number picked from a table. NIOSH, Public domain, via Wikimedia Commons.

Derivation: From Force Balance to Colebrook

In laminar flow, the friction factor comes directly from the exact Hagen-Poiseuille solution to the Navier-Stokes equations for fully developed pipe flow. Equating the Hagen-Poiseuille pressure drop to the Darcy-Weisbach definition of f gives a closed-form result with no empirical fitting at all:

\Delta P = \dfrac{32\mu L v}{D^2} \;\overset{!}{=}\; f\left(\dfrac{L}{D}\right)\left(\dfrac{\rho v^2}{2}\right) \;\Rightarrow\; f = \dfrac{64\mu}{\rho v D} = \dfrac{64}{Re}

Turbulent flow has no equivalent closed-form solution, the velocity profile is chaotic and not analytically tractable, so the Colebrook equation is instead a semi-empirical fit combining the smooth-pipe turbulent correlation with a roughness term, validated against a huge body of experimental friction-factor data (the same data underlying the Moody chart):

\dfrac{1}{\sqrt f} = -2\log_{10}\left(\dfrac{\varepsilon/D}{3.7}+\dfrac{2.51}{Re\sqrt f}\right)

Because f appears on both sides, once outside the logarithm, once inside it, this equation has no algebraic solution for f. It's solved by fixed-point iteration: guess an initial f (commonly from Swamee-Jain), substitute it into the right-hand side to get an improved f, and repeat until the value stops changing meaningfully, usually only 3–5 iterations for engineering accuracy. The Swamee-Jain equation itself was derived by algebraically rearranging Colebrook into an explicit approximate form, trading a small amount of accuracy for the convenience of a direct formula.

The Moody Chart

The laminar line and the Colebrook turbulent curves below are computed live from the same equations derived above, not traced from a scanned image, so the two amber-marked points line up exactly with the worked examples further down this page.

Curves computed live from f = 64/Re (laminar) and the Colebrook-White equation (turbulent) — the same equations derived above, not a scanned chart. Amber dots mark the two worked examples.

When You'll Need It in GATE Chemical Engineering

Friction factor rarely stands alone, it's the missing piece a pipe-flow pressure-drop or pumping-power problem needs:

Pressure drop / pumping power problems, any question asking for frictional pressure loss or the power needed to overcome it requires f from the Darcy-Weisbach equation, after first checking the flow regime via Reynolds number.
Moody chart reading questions, GATE sometimes gives a Moody chart directly and asks you to read off f for a stated Re and ε/D, which is exactly what the Colebrook equation reproduces numerically.
Pipe network / sizing problems, selecting a pipe diameter for a target pressure drop is an iterative problem that repeatedly calls the friction-factor calculation at each trial diameter.
Fanning-vs-Darcy conversion checks, some reference correlations use the Fanning friction factor; recognizing and converting between the two conventions is a common trap (see Common Mistakes below).

Two Fully Worked Examples

Example 1: Laminar Flow in a Small-Bore Pipe

Problem: Oil flows through a pipe at Re = 1200. Find the Darcy friction factor.

Re = 1200 < 2100 \Rightarrow \text{laminar flow}

f = \dfrac{64}{Re} = \dfrac{64}{1200}

Answer: f = 0.0533 (exact, no roughness dependence)

Example 2: Turbulent Flow in Commercial Steel Pipe

Problem: Water flows through a commercial steel pipe (ε/D = 0.00015) at Re = 100,000. Estimate f using Swamee-Jain, then refine with one Colebrook iteration.

f_{SJ} = \dfrac{0.25}{\left[\log_{10}\left(\frac{0.00015}{3.7}+\frac{5.74}{100{,}000^{0.9}}\right)\right]^2} \approx 0.01798

\dfrac{1}{\sqrt{f}} = -2\log_{10}\left(\dfrac{0.00015}{3.7}+\dfrac{2.51}{100{,}000\sqrt{0.01798}}\right)

f_{Colebrook} \approx 0.01791\ \text{(after iterating)}

Answer: f ≈ 0.0179, Swamee-Jain and Colebrook agree to within about 0.4% here.

Common Mistakes GATE Students Make

Using f = 64/Re for turbulent flow.That formula is exact only for laminar flow (Re < 2100), using it for turbulent flow ignores roughness entirely and gives a badly wrong answer.
Confusing Darcy and Fanning friction factors. fDarcy = 4 × fFanning, always check which convention a given correlation, textbook, or Moody chart uses before plugging into Darcy-Weisbach.
Forgetting relative roughness entirely. In the turbulent regime, f depends on both Re and ε/D, using a smooth-pipe (ε/D = 0) assumption for a rough pipe underestimates pressure drop.
Starting Colebrook iteration from a poor initial guess. The iteration converges quickly from almost any reasonable starting point, but a wildly wrong guess (like f = 1) wastes iterations, starting from the Swamee-Jain estimate is standard practice.

Key Takeaways

Laminar flow (Re < 2100): f = 64/Re exactly, no roughness dependence.
Turbulent flow (Re > 4000): f depends on both Re and relative roughness ε/D.
Colebrook is implicit (solved iteratively); Swamee-Jain is explicit (direct formula, ~1% accurate).
Darcy friction factor is 4× the Fanning friction factor, check which convention applies.
Avoid designing for steady operation in the transitional regime (2100 < Re < 4000).

Frequently Asked Questions

Almost always as an input to something else, not the final answer, it feeds the pressure-drop and pump-power calculations that actually answer the question a problem is asking. See the derivation below for where the Darcy-Weisbach relationship it plugs into comes from.

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Derivation: From Force Balance to Colebrook

The Moody Chart

When You'll Need It in GATE Chemical Engineering

Two Fully Worked Examples

Example 1: Laminar Flow in a Small-Bore Pipe

Example 2: Turbulent Flow in Commercial Steel Pipe

Common Mistakes GATE Students Make

Key Takeaways

Frequently Asked Questions

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Derivation: From Force Balance to Colebrook

The Moody Chart

When You'll Need It in GATE Chemical Engineering

Two Fully Worked Examples

Example 1: Laminar Flow in a Small-Bore Pipe

Example 2: Turbulent Flow in Commercial Steel Pipe

Common Mistakes GATE Students Make

Key Takeaways

Frequently Asked Questions

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Fluid Mechanics

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GATE CH Formula Sheet

GATE Practice Tests by Year

Friction Factor
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