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.
About this calculator
This calculator uses the Darcy-Weisbach equation to find the head loss (pressure drop) in a 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. For turbulent flow in smooth pipes, the Blasius correlation estimates the friction factor: f = 0.316 × Re^(−0.25), which is valid for Reynolds numbers up to about 100,000. The Reynolds number Re = v × D / ν, where ν is kinematic viscosity, determines whether flow is laminar (Re < 2,300) or turbulent. Combining these expressions gives the full pressure drop formula used here. 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 pipe of diameter D = 0.1 m and length L = 50 m. First calculate Re = 2 × 0.1 / 1×10⁻⁶ = 200,000. Then f = 0.316 × (200,000)^(−0.25) = 0.316 / 21.15 ≈ 0.01494. Finally, head loss h_f = 0.01494 × (50/0.1) × (2²/(2×9.81)) = 0.01494 × 500 × 0.2039 ≈ 1.52 m. Enter your pipe diameter, length, velocity, and kinematic viscosity to get instant results.
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), is an empirical formula for estimating the Darcy friction factor in smooth pipes under turbulent flow conditions. It is accurate for Reynolds numbers roughly between 4,000 and 100,000. Beyond Re = 100,000, the Colebrook-White or Swamee-Jain equations, which also account for pipe roughness, give better results. For laminar flow (Re < 2,300), the friction factor is simply f = 64/Re, which is an exact analytical result.