Pipe Pressure Drop Calculator
Calculates pressure drop along a circular pipe using the Darcy-Weisbach equation. Use it when sizing pumps, designing piping networks, or checking if flow velocities are practical.
About this calculator
The Darcy-Weisbach equation gives the head loss (and hence pressure drop) due to friction in a pipe: ΔP = f × (L / D) × (v² / (2g)) × ρ, where f is the dimensionless Darcy friction factor, L is pipe length (m), D is internal diameter (m), v is mean flow velocity (m/s), and g is gravitational acceleration (9.81 m/s²). In this calculator the result is expressed in pascals by multiplying head loss (m) by fluid density (assumed 1000 kg/m³ for water, embedded in the ×1000 factor). The friction factor f depends on the Reynolds number and pipe roughness; for turbulent flow it is found from the Moody chart or the Colebrook-White equation. A longer pipe, smaller diameter, higher velocity, or rougher wall all increase pressure drop, requiring a more powerful pump.
How to use
Consider a 50 m steel pipe with diameter 0.05 m carrying water at 2 m/s. The friction factor for this condition is f = 0.02. Apply the formula: ΔP = 0.02 × (50 / 0.05) × (2² / (2 × 9.81)) × 1000. Step by step: L/D = 1000; v²/2g = 4/19.62 ≈ 0.204 m; head loss = 0.02 × 1000 × 0.204 = 4.08 m. Multiply by 1000 to convert to Pa: ΔP ≈ 4,080 Pa (about 0.04 bar). This pressure loss must be overcome by the pump.
Frequently asked questions
What is the Darcy-Weisbach equation and when should I use it?
The Darcy-Weisbach equation calculates frictional head loss in a pipe: h_f = f × (L/D) × (v²/2g). It is the preferred method for pressure-drop calculations in engineering because it works for any fluid (not just water), any flow regime, and any pipe material. You should use it whenever you need to size a pump, select pipe diameter, or evaluate whether an existing system can deliver the required flow rate. The Hazen-Williams formula is an alternative but is limited to water and a specific velocity range.
How do I find the Darcy friction factor for my pipe?
The friction factor f depends on whether flow is laminar or turbulent. For laminar flow (Reynolds number Re < 2300), f = 64 / Re, which is exact. For turbulent flow, f is read from the Moody chart using both Re and the relative roughness (pipe wall roughness divided by diameter). The Colebrook-White equation gives f implicitly for turbulent flow, while the explicit Swamee-Jain approximation is accurate to within 3% and is convenient for calculators. Typical f values range from about 0.008 for smooth pipes at high Re to 0.05 for rough pipes at moderate Re.
Why does pipe diameter have such a large effect on pressure drop?
Pipe diameter appears in two places in the Darcy-Weisbach equation: in the L/D ratio (directly) and through velocity, since flow velocity v = Q / (π D²/4) — so for the same flow rate, halving the diameter quadruples the velocity. Combined, reducing diameter by half can increase pressure drop by a factor of roughly 32. This is why even a modest increase in pipe diameter can dramatically reduce pumping costs in long distribution systems, making pipe sizing one of the most important decisions in fluid system design.