🚰 Darcy-Weisbach Pipe Pressure Drop Calculator

Last updated: June 3, 2026

🚰 Darcy-Weisbach Pressure Drop Calculator

Friction head loss & pressure drop via Colebrook-White iteration

m³/s
meters
meters
meters (0 = smooth)
kg/m³ (water=1000)
m²/s (water≈1×10⁻⁶)
Results
Flow Velocity (V) —
Reynolds Number (Re) —
Flow Regime —
Relative Roughness (ε/D) —
Friction Factor (f) —
Head Loss (hf) —
Pressure Drop (ΔP) —

How to Calculate Pipe Pressure Drop Using the Darcy-Weisbach Equation

Every time water flows through a pipe — whether in a municipal water system, a chemical plant heat exchanger, or a home plumbing installation — energy is lost to friction between the moving fluid and the pipe wall. Quantifying that loss is the job of the Darcy-Weisbach equation, one of the most reliable and widely used relationships in fluid mechanics. Unlike empirical shortcuts that only work for specific fluids or limited flow regimes, Darcy-Weisbach is dimensionally consistent and applies equally well to water, oil, gas, and anything in between.

The Core Equation

The Darcy-Weisbach equation for head loss due to pipe friction is:

hf = f × (L/D) × (V² / 2g)

Where:

  • hf = friction head loss (meters of fluid)
  • f = Darcy friction factor (dimensionless)
  • L = pipe length (m)
  • D = internal pipe diameter (m)
  • V = mean flow velocity (m/s)
  • g = gravitational acceleration = 9.81 m/s²

To convert head loss into a pressure drop that pumps and engineers care about, multiply by fluid density and gravity:

ΔP = ρ × g × hf

So in Pascals: ΔP = ρ × g × f × (L/D) × V²/2.

Step 1 — Find the Flow Velocity

You usually know the flow rate Q (in m³/s or L/min) rather than velocity directly. Convert it using the pipe cross-sectional area:

V = Q / A, where A = π D² / 4

For example, a flow rate of 5 L/min (0.0000833 m³/s) through a 25 mm diameter pipe gives A = 4.91 × 10⁻⁴ m² and V ≈ 0.170 m/s. This velocity feeds directly into both the Reynolds number and the head loss formula.

Step 2 — Calculate the Reynolds Number

The Reynolds number determines whether the flow is laminar, turbulent, or somewhere in the unstable transition zone between the two:

Re = V × D / ν

Where ν is the kinematic viscosity of the fluid in m²/s (water at 20°C has ν ≈ 1.004 × 10⁻⁶ m²/s). The three regimes are:

  • Re < 2300: Laminar — fluid layers slide smoothly past each other; friction is purely viscous.
  • 2300 < Re < 4000: Transitional — unstable, unpredictable behaviour; avoid designing in this range when possible.
  • Re > 4000: Turbulent — chaotic mixing dominates; friction depends heavily on surface roughness.

Step 3 — Determine the Friction Factor

This is where the real engineering challenge sits. The friction factor f is not a constant — it changes with flow regime and pipe wall roughness.

Laminar flow (Re < 2300): The friction factor has an exact analytical solution:

f = 64 / Re

No roughness involved — in laminar flow, wall texture is irrelevant because the fluid adjacent to the wall is stationary regardless.

Turbulent flow (Re > 4000): Here you need the Colebrook-White equation, an implicit relation that must be solved iteratively:

1/√f = −2 × log₁₀ [ (ε/D)/3.7 + 2.51 / (Re × √f) ]

Where ε is the absolute pipe roughness in meters. Common values: commercial steel ≈ 0.000046 m, cast iron ≈ 0.00026 m, PVC/drawn tubing ≈ 0.0000015 m.

The iteration works by starting with a reasonable initial guess — the Swamee-Jain explicit approximation is excellent — then plugging that into the right-hand side of the Colebrook equation to get a new f, repeating until consecutive values differ by less than 10⁻¹², which typically takes 10–30 iterations. Our calculator does exactly this automatically.

Step 4 — Read the Moody Chart (Conceptually)

The Moody chart is a log-log plot of f versus Re, parameterised by relative roughness ε/D. Understanding its regions helps build intuition:

  • The laminar line (f = 64/Re) falls steeply on the left — friction factor drops sharply as velocity rises.
  • In turbulent flow, higher roughness pushes the curves upward — a rougher pipe always wastes more energy.
  • At very high Reynolds numbers, curves become flat ("fully rough" or "wholly turbulent" regime) — f depends only on ε/D, not on Re anymore. This is the zone where the Moody chart lines are horizontal.

Knowing where your operating point sits on the Moody chart tells you whether reducing roughness (lining, cleaning, material choice) or increasing pipe diameter will yield better efficiency gains.

Worked Example

Suppose you need to pump water (ρ = 1000 kg/m³, ν = 1×10⁻⁶ m²/s) through 100 m of commercial steel pipe (ε = 0.000046 m) with an internal diameter of 50 mm at 0.005 m³/s.

  1. Velocity: A = π(0.05)²/4 = 0.001963 m² → V = 0.005 / 0.001963 = 2.548 m/s
  2. Reynolds number: Re = 2.548 × 0.05 / 1×10⁻⁶ = 127,400 → fully turbulent
  3. Relative roughness: ε/D = 0.000046 / 0.05 = 0.00092
  4. Friction factor (Colebrook): f ≈ 0.02139 (after iteration converges)
  5. Head loss: hf = 0.02139 × (100/0.05) × (2.548²)/(2×9.81) = 0.02139 × 2000 × 0.3309 ≈ 14.15 m
  6. Pressure drop: ΔP = 1000 × 9.81 × 14.15 ≈ 138,800 Pa ≈ 138.8 kPa

That pump must supply at least 139 kPa just to overcome pipe friction — before accounting for fittings, elevation changes, or exit losses.

Practical Tips for Pipe System Design

Diameter matters most. Because velocity appears squared in the Darcy-Weisbach equation and also appears in the Reynolds number affecting f, doubling the diameter (at constant flow rate) cuts the head loss by roughly a factor of 32. Pipe material cost versus pumping energy cost is therefore a classic economic optimisation problem.

Account for minor losses. The Darcy-Weisbach equation covers only major (friction) losses in straight pipe. Real systems also have valves, bends, tees, expansions, and contractions — each adds a loss expressed as K × V²/2g. For long pipelines these are often negligible; in short, complex piping they can dominate.

Temperature changes viscosity dramatically. Water at 80°C has ν ≈ 0.365 × 10⁻⁶ m²/s — about one-third the value at 20°C. This raises Re significantly, pushing the flow deeper into turbulent territory and often slightly increasing f. Always use the actual operating temperature's viscosity.

Verify units at every step. Mixing imperial and SI units is the single most common source of errors in pipe flow calculations. This calculator works entirely in SI (metres, kg, seconds, Pascals) — convert all inputs before entering them.

With the Darcy-Weisbach equation and the iterative Colebrook solver working together, you have a complete, physically rigorous method for any Newtonian fluid in any pipe at any Reynolds number — the foundation of competent pipe system design.

FAQ

What is the difference between Darcy friction factor and Fanning friction factor?
The Darcy-Weisbach (or Moody) friction factor f is four times larger than the Fanning friction factor f_F. The Darcy version is used with the formula hf = f(L/D)(V²/2g), while the Fanning version uses hf = 4f_F(L/D)(V²/2g). This calculator uses the Darcy friction factor, which is the standard in most engineering references and the Moody chart.
Why does the Colebrook equation need to be solved iteratively?
The Colebrook-White equation is implicit — the unknown friction factor f appears on both sides of the equation inside a square root and a logarithm. There is no algebraic rearrangement that isolates f exactly. The iterative approach starts with a good initial guess (usually the Swamee-Jain explicit approximation) and repeatedly substitutes values until two successive answers agree to within a very tight tolerance, typically converging in under 30 steps.
What pipe roughness value should I use for my material?
Typical absolute roughness values: drawn copper or PVC tubing ≈ 0.0000015 m (1.5 µm); commercial steel or wrought iron ≈ 0.000046 m (46 µm); galvanised steel ≈ 0.00015 m; cast iron ≈ 0.00026 m; concrete ≈ 0.0003–0.003 m depending on quality. For a new, smooth plastic pipe you can enter 0.0000015 or simply 0. These values increase over time due to corrosion and scale buildup.
Can I use this calculator for gases or compressible fluids?
The Darcy-Weisbach equation applies to incompressible fluids (liquids) directly. For gases at low to moderate pressures where density change along the pipe is less than about 10%, you can use an average density and the result is acceptably accurate. For high-pressure gas lines, steam, or situations where significant density change occurs, compressible flow equations are required and this calculator should not be used alone.
How do I convert head loss in metres to pressure drop in bar or psi?
The calculator shows pressure drop in Pascals or kPa. To convert: 1 bar = 100,000 Pa, so divide the Pa result by 100,000 to get bar. For psi: 1 psi = 6,894.76 Pa, so divide by 6894.76. Example: 138,800 Pa = 1.388 bar = 20.1 psi. The head loss in metres is fluid-specific — 14 m of water head is very different energy from 14 m of mercury head.
What happens in the transitional flow regime (Re between 2300 and 4000)?
The transitional regime is physically unstable — flow can flicker between laminar and turbulent states unpredictably, and the friction factor is neither reliably given by 64/Re nor by the Colebrook equation. In practice, engineers usually avoid designing systems to operate in this range. When it is unavoidable, a conservative approach is to use the turbulent (Colebrook) friction factor, which gives a higher, safer estimate of pressure drop.