Pipe Flow Calculator
Determine pressure drop in circular pipes using the Darcy-Weisbach equation. Use this when designing water supply lines, HVAC ducts, or industrial piping systems to ensure adequate flow.
Last updated: September 2026
Formula below · 2 sources (asme.org, Wikipedia) · Updated Sep 2026
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About this calculator
This calculator uses the Darcy-Weisbach equation to find the friction head loss in a full circular pipe: h_f = f × (L/D) × (v²/2g), where f is the Darcy friction factor, L is pipe length, D is pipe diameter, v is flow velocity, and g is 9.81 m/s². The result is in metres of fluid column; multiply by ρg (9,810 for water) for the pressure drop in pascals. The Reynolds number Re = v × D / ν, where ν is kinematic viscosity, sets the regime. For laminar flow (Re < 2,300) f = 64/Re. For turbulent flow the calculator uses the Haaland equation, an explicit approximation of Colebrook-White accurate to about 2%: 1/√f = −1.8 × log₁₀[(ε/D / 3.7)^1.11 + 6.9/Re], where ε is the absolute roughness of the selected material in metres (commercial steel 0.045 mm, drawn tubing 0.0015 mm, cast iron 0.26 mm, PVC 0.007 mm). Engineers use these results to size pumps, select pipe diameters, and validate system designs.
How to use
Suppose water (ν = 1×10⁻⁶ m²/s) flows at v = 2 m/s through a commercial steel pipe of diameter D = 0.1 m and length L = 50 m. First calculate Re = 2 × 0.1 / 1×10⁻⁶ = 200,000. With roughness ε = 0.045 mm (ε/D = 0.00045), the Haaland equation gives f = [−1.8 × log₁₀((0.00045/3.7)^1.11 + 6.9/200,000)]⁻² ≈ 0.0184. Head loss h_f = 0.0184 × (50/0.1) × (2²/(2 × 9.81)) = 0.0184 × 500 × 0.2039 ≈ 1.87 m, or about 18.4 kPa for water. The defaults (100 m, 2.5 m/s) give about 5.7 m.
Frequently asked questions
What is the Darcy-Weisbach equation and when should I use it?
The Darcy-Weisbach equation calculates head loss due to friction in a pipe: h_f = f × (L/D) × (v²/2g). It is the most accurate and universally applicable method for pressure drop calculations in both laminar and turbulent flow regimes. Unlike the Hazen-Williams formula, it works for any fluid, not just water, making it the preferred choice in engineering design. Use it whenever you need precise pressure drop estimates for pipe sizing, pump selection, or system analysis.
How does pipe diameter affect pressure drop in a piping system?
Pipe diameter has a dramatic effect on pressure drop: reducing the diameter increases velocity (for the same flow rate) and also increases the L/D ratio, so pressure drop rises steeply. In general, halving the pipe diameter can increase head loss by a factor of roughly 32 for turbulent flow when flow rate is held constant. This is why engineers always balance pipe cost against pump energy cost when selecting pipe sizes. Larger pipes cost more upfront but save significantly on long-term pumping energy.
What is the Blasius friction factor correlation and what are its limits?
The Blasius correlation, f = 0.316 × Re^(−0.25), estimates the Darcy friction factor in smooth pipes for Reynolds numbers roughly between 4,000 and 100,000. It ignores roughness, so this calculator uses the Haaland equation instead, which covers rough pipes and Reynolds numbers up to about 10⁸ within about 2% of Colebrook-White. For laminar flow (Re < 2,300), the friction factor is simply f = 64/Re, an exact analytical result.