Calculate pipe friction head loss and pressure drop with the Darcy–Weisbach equation. Uses the Colebrook–White equation for turbulent friction factor.
The Darcy–Weisbach equation is the fundamental relationship for calculating pressure loss due to friction in pipes: ΔP = f (L/D) ρV²/2. The friction factor f depends on the Reynolds number and relative roughness of the pipe wall, making the equation universally applicable to any incompressible, steady, fully-developed flow in a round conduit.
For laminar flow (Re < 2 300), the friction factor is simply f = 64/Re, a result derived analytically from the Navier–Stokes equations. For turbulent flow, the implicit Colebrook–White equation 1/√f = −2 log₁₀(ε/D/3.7 + 2.51/(Re√f)) must be solved iteratively — this calculator performs that iteration automatically with high precision.
This tool covers the full design workflow: select a pipe material to set wall roughness, choose a fluid, enter the velocity and dimensions, and get head loss, pressure drop, pumping power, and flow rate instantly. The velocity sweep table shows how pressure drop scales with speed (roughly proportional to V² in turbulent flow).
Pressure-drop calculations are essential for pump selection, piping design, and energy-cost estimation. The Darcy–Weisbach equation with the Colebrook friction factor is the most accurate general-purpose method for Newtonian fluids in circular pipes. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Darcy–Weisbach: ΔP = f (L / D) (ρV² / 2) Head loss: h_L = f (L / D) (V² / 2g) Laminar friction: f = 64 / Re Turbulent friction (Colebrook–White): 1/√f = −2 log₁₀( ε/(3.7D) + 2.51/(Re√f) ) Where: • f = Darcy friction factor • L = pipe length (m), D = diameter (m) • ρ = fluid density (kg/m³) • V = mean velocity (m/s) • ε = absolute roughness (m)
Result: ΔP ≈ 39.3 kPa, h_L ≈ 4.01 m
Re = 998 × 2 × 0.1 / 0.001002 ≈ 199 200. Using Colebrook with ε/D = 4.5×10⁻⁴ gives f ≈ 0.0197. ΔP = 0.0197 × (100/0.1) × (998 × 4/2) ≈ 39 300 Pa.
Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.
Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes
Use this for repeatability, keep assumptions explicit. ## Practical Notes
Track units and conversion paths before applying the result. ## Practical Notes
Use this note as a quick practical validation checkpoint. ## Practical Notes
Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes
Use as a sanity check against edge-case outputs. ## Practical Notes
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Head loss (meters) is the energy loss per unit weight of fluid: h_L = ΔP/(ρg). Pressure drop (pascals) is the actual decrease in pressure. They convey the same information in different units.
Use the Colebrook–White equation, which this calculator solves iteratively. Alternatively, read f from a Moody chart using the Re and ε/D values. Explicit approximations like Swamee–Jain also work.
At very high Re the viscous sublayer becomes thinner than the roughness protrusions, so roughness elements directly disturb the flow. In this "fully rough" regime, f depends only on ε/D, not Re.
Yes — replace D with the hydraulic diameter D_h = 4A/P (cross-sectional area divided by wetted perimeter). The Darcy–Weisbach equation then gives reasonable estimates for rectangular, annular, and other shapes.
Minor losses from fittings, valves, and bends are usually expressed as K-factors: ΔP_minor = K ρV²/2. Add them to the friction loss for total system pressure drop.
Yes, for short pipe runs where density change is small (< 10%). For long gas pipelines with significant expansion, compressible-flow equations like Weymouth or Panhandle are preferred.