Pipe Flow Calculator — Darcy–Weisbach Head Loss & Flow Rate
Enter pipe diameter, length, flow velocity and material to calculate volumetric flow rate, Reynolds number, flow regime, Darcy friction factor and head loss using the Darcy–Weisbach equation.
mm
m
m/s
Fluid
Pipe material / roughness
Flow rate through the pipe cross-section at the entered velocity
- 1
Pipe diameter (m)
50 mm ÷ 1 000 = 0.05 - 2
Cross-sectional area
π × (0.05 ÷ 2)² = 0.0019635A = π(D/2)² for a circular pipe. - 3
Flow rate (m³/s)
1.5 m/s × 0.0019635 m² = 0.00294524 - 4
Flow rate (L/s)
0.00294524 × 1 000 = 2.945
2.95 L/s
Flow rateHow does this calculator work?
Flow rate Q = v × π(D/2)². The Reynolds number Re = vD/ν determines laminar (Re < 2 300, f = 64/Re) or turbulent (Re > 4 000, Swamee–Jain f) flow. Head loss h_f = f·(L/D)·v²/(2g) in metres; pressure drop ΔP = ρgh_f in Pa. Enter pipe diameter, length, velocity and material to get all values.
Formula
How this is calculated
The flow rate through a circular pipe is Q = v × A where A = π(D/2)² is the cross-sectional area and v is the mean flow velocity. Given diameter in millimetres and velocity in m/s, the calculator first computes Q in L/s and m³/h.
The Reynolds number Re = vD/ν (where ν is the kinematic viscosity of the fluid) determines the flow regime. Below Re ≈ 2 300 the flow is laminar — smooth, layered and governed by Hagen–Poiseuille theory, which gives a friction factor f = 64/Re. Above Re ≈ 4 000 the flow is turbulent and f depends on both Re and the relative pipe roughness ε/D. This calculator uses the Swamee–Jain explicit approximation f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]², which is accurate to within ~3% of the implicit Colebrook–White equation for the valid range (ε/D ∈ [10⁻⁶, 10⁻²], Re ∈ [5 000, 10⁸]). The transition zone (2 300–4 000) uses the turbulent formula as a conservative estimate.
The Darcy–Weisbach equation h_f = f × (L/D) × v²/(2g) gives the head loss in metres of fluid — the energy lost per unit weight of fluid to pipe friction. Multiplying by fluid density and g converts this to pressure drop ΔP = ρgh_f in Pa (shown in kPa). Real installations also have minor losses from bends, valves and fittings that are not included here; for long straight runs they are typically small compared to the major friction loss.
Frequently asked questions
The Darcy–Weisbach equation h_f = f(L/D)(v²/2g) calculates the pressure head lost to friction as a fluid flows through a straight pipe. It is the standard method for pipe flow analysis in civil, mechanical and chemical engineering because it applies to all flow regimes and fluids.
The Swamee–Jain equation is an explicit formula for the Darcy friction factor in turbulent flow: f = 0.25 / [log₁₀(ε/3.7D + 5.74/Re⁰·⁹)]². It avoids the iterative solution required by the Colebrook–White equation and is accurate to within about 3% across a wide range of Reynolds numbers and relative roughnesses.
Water distribution mains are typically designed for 0.5–2 m/s; pump suction lines are kept below 1.5 m/s to avoid cavitation; discharge lines run at 1.5–3 m/s. Velocities above 3–4 m/s risk erosion in metal pipes and water hammer on sudden valve closure.
Also known as
TG we-Calculate Editorial Team. (2026). Pipe Flow Calculator — Darcy–Weisbach Head Loss & Flow Rate [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/pipe-flow-calculator
TG we-Calculate Editorial Team. "Pipe Flow Calculator — Darcy–Weisbach Head Loss & Flow Rate." TG we-Calculate. 2026. https://we-calculate.com/calculator/pipe-flow-calculator.
TG we-Calculate Editorial Team, "Pipe Flow Calculator — Darcy–Weisbach Head Loss & Flow Rate," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/pipe-flow-calculator
@misc{wecalculate_pipe_flow_calculator, title = {Pipe Flow Calculator — Darcy–Weisbach Head Loss & Flow Rate}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/pipe-flow-calculator}}, year = {2026}, note = {TG we-Calculate} }
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