Darcy–Weisbach head loss
h_f = f(L/D)V²/(2g)
Major head loss for steady fully developed internal flow.
Darcy–Weisbach Pressure Loss Calculator
Estimate straight-pipe major loss from volumetric flow, pipe geometry, density, dynamic viscosity, and absolute roughness.
Access: Free to use, no installation, and No account required.
Inputs
This route calculates straight-pipe major loss only. Fittings, valves, entrances, exits, elevation, pumps, and network interactions require additional terms.
Results
Darcy–Weisbach major loss
Major head loss scales with friction factor, pipe length-to-diameter ratio, and velocity squared. The workbench engine uses 64/Re in laminar flow and a turbulent explicit friction-factor approximation.
Engineering reference
Darcy–Weisbach Pressure Loss Calculator: background and worked detail
Use the Darcy–Weisbach Pressure Loss Calculator to estimate pipe velocity, Reynolds number, Darcy friction factor, straight-pipe head loss, and pressure loss from flow rate, pipe geometry, fluid properties, and roughness.
Head loss and friction factor
Pressure loss
Δp = ρgh_f
Head loss converts to pressure loss through fluid density and gravity.
Laminar friction factor
f = 64/Re
The implemented laminar circular-pipe relationship.
Choosing a friction-factor correlation
Darcy–Weisbach major loss scales with friction factor, length-to-diameter ratio, and velocity squared. The workbench engine uses 64/Re for laminar flow and an explicit turbulent friction-factor approximation using relative roughness and Reynolds number.
This route covers straight-pipe major loss only. Fittings, valves, entrances, exits, elevation, pumps, parallel branches, transients, cavitation, and compressibility require additional modeling.
2 L/s of water through 50 mm pipe over 20 m
Use 2 L/s, 20 m length, 50 mm inside diameter, 998 kg/m³ density, 1.002 mPa·s viscosity, and 0.0015 mm roughness.
- Flow rate and diameter give mean velocity of about 1.02 m/s.
- Reynolds number is about 50,700, so the engine uses its turbulent friction-factor expression.
- The resulting head and pressure loss represent straight-pipe major loss only.
Result: Use the full Internal Pipe Flow Workbench to add fittings, networks, pump/head interactions, and water-hammer checks.
Assumptions and model boundaries
Assumptions
- Steady one-dimensional internal flow.
- Constant diameter, fluid density, viscosity, and roughness along the entered length.
- The calculated friction factor follows the formulas implemented in the shared engine.
Limitations
- Does not include minor losses, elevation change, pump work, compressibility, heat transfer, transient flow, cavitation, or pipe-network interactions.
- Turbulent friction factor is an explicit approximation, not an iterative Colebrook solve.
Validation checks
Length scaling
Case: Double pipe length without changing flow or diameter.
Expected: Major head loss and pressure loss should double.
Zero-flow limit
Case: Reduce flow toward zero.
Expected: Velocity and pressure loss should approach zero, although friction-factor evaluation at exactly zero flow is undefined.
Darcy–Weisbach Pressure Loss Calculator FAQ
What is the difference between head loss and pressure loss?
Head loss is energy loss per unit weight expressed as fluid height; pressure loss is the corresponding pressure drop Δp = ρgh.
Do fittings count in pipe length?
This focused calculator does not add fitting losses. Use K factors or equivalent-length methods in the full workbench.
Why does pipe diameter matter so much?
At fixed volumetric flow, reducing diameter sharply increases velocity; Darcy–Weisbach loss then rises with V² and also with L/D.
Where this calculation comes from
Shared with the Fluid Mechanics Workbench, which solves multi-branch networks and pump curves.
Open the source workbench →Read calculation and source methodology →