Pipe Flow Pressure Drop Calculator
Calculate the pressure drop along a pipe section using the Darcy-Weisbach equation. Use this when designing water distribution systems, HVAC ductwork, or any piping network where flow resistance must be quantified.
About this calculator
The Darcy-Weisbach equation gives pressure drop as: ΔP = f × (L/D) × (ρv²/2), where f is the Darcy friction factor, L is pipe length (m), D is pipe diameter (m), ρ is fluid density (kg/m³), and v is mean flow velocity (m/s). Velocity is derived from flow rate Q and pipe cross-section: v = Q / (π × (D/2)²). This calculator uses a fixed friction factor f = 0.02 (typical for turbulent flow in smooth pipes), so the formula becomes: ΔP = 0.02 × (L/D) × (ρ × v²) / 2. Pressure drop increases with the square of velocity, meaning doubling flow rate quadruples ΔP. In real systems the friction factor depends on Reynolds number and pipe roughness (Moody chart), so the 0.02 approximation is best used for preliminary design.
How to use
Water (ρ = 1000 kg/m³) flows at Q = 0.01 m³/s through a 50 m pipe of diameter D = 0.1 m. Velocity: v = 0.01 / (π × 0.05²) = 0.01 / 0.007854 = 1.273 m/s. Now: ΔP = 0.02 × (50 / 0.1) × (1000 × 1.273²) / 2 = 0.02 × 500 × (1000 × 1.621) / 2 = 0.02 × 500 × 810.5 = 8,105 Pa ≈ 8.1 kPa. This pressure drop must be supplied by the pump or the available static head in the system.
Frequently asked questions
What is the Darcy-Weisbach equation and when should I use it for pipe flow?
The Darcy-Weisbach equation is the most accurate and broadly applicable method for calculating pressure drop due to friction in full-flowing pipes. Unlike the older Hazen-Williams equation, it works for any fluid (not just water), any flow regime, and any pipe material when the correct friction factor is used. It is the industry standard in mechanical and civil engineering for sizing pumps, designing distribution networks, and checking pressure adequacy. Use it whenever you need reliable results, especially for non-water fluids or high-velocity flows where friction losses are significant.
How does pipe diameter affect pressure drop in a fluid system?
Pipe diameter has a dramatic effect on pressure drop because ΔP scales with 1/D⁵ when flow rate is held constant — a relationship that emerges from combining the 1/D (L/D term) and the 1/D⁴ velocity dependence. In practice, halving the pipe diameter increases pressure drop by a factor of 32. This is why slightly larger pipes can save enormous pumping energy costs over the life of a system. Engineers balance the capital cost of larger pipe against operating energy costs to find an economically optimal diameter.
Why does this calculator use a fixed friction factor of 0.02 instead of computing it from roughness?
A friction factor of 0.02 is a reasonable approximation for turbulent flow in smooth commercial steel or PVC pipes at moderate Reynolds numbers (roughly 10⁵–10⁶), which covers many common engineering situations. The exact friction factor depends on both the Reynolds number and the relative roughness (ε/D), and requires solving the implicit Colebrook-White equation or reading the Moody chart. For preliminary design or quick estimates, f = 0.02 gives acceptable accuracy. For final design — especially with rough pipes, viscous fluids, or very high velocities — you should compute f properly using the Colebrook-White equation or Swamee-Jain approximation.