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Darcy-Weisbach Equation

Understand the Darcy-Weisbach equation for straight-pipe friction loss, including pressure loss, head loss, variables, and applicability.

Referencefluids & pipingPublishedLast reviewed: 2026-05-16

Use the Darcy-Weisbach equation when you need a transparent straight-pipe friction-loss check and you already have a Darcy friction factor from a suitable source or method.

What This Means

Darcy-Weisbach estimates major loss caused by wall friction in a constant-diameter pipe. The result can be expressed as head loss, which is energy per unit weight of fluid, or as pressure loss, which depends on fluid density.

The equation is useful because it separates geometry, velocity, fluid density, and friction factor. It does not choose the friction factor for you. That choice depends on Reynolds number, roughness, and the friction-factor method being used.

Key Formula

h_f = f (L / D) V^2 / (2 g)
Delta p = rho g h_f
Delta p = f (L / D) rho V^2 / 2
  • h_f is head loss.
  • Delta p is pressure loss.
  • f is the Darcy friction factor.
  • L is straight pipe length.
  • D is inside pipe diameter.
  • V is average pipe velocity.
  • rho is fluid density.
  • g is gravitational acceleration.

Use This When

  • The pipe is full, circular, and constant in diameter.
  • Flow is steady or represented by a steady design condition.
  • Density is reasonably constant over the pipe length.
  • You are estimating straight-pipe major loss, not a complete system curve.
  • The Darcy friction factor is known, selected, or computed separately.

Assumptions

  • The velocity is cross-sectional average velocity.
  • The entered diameter is actual inside diameter.
  • The friction factor is a Darcy friction factor, not a Fanning friction factor.
  • The loss is for wall friction in straight pipe.
  • Fluid properties represent the operating condition being checked.

Limitations

  • Fittings, valves, entrances, exits, and other local losses require additional loss terms.
  • Elevation changes, pump work, and velocity changes belong in a broader energy balance.
  • Compressible gas flow and flashing liquids require methods that account for density or phase changes.
  • A pressure-loss result is only as reliable as the friction factor and fluid properties supplied.

Common Mistakes

  • Entering nominal pipe size instead of inside diameter.
  • Mixing Darcy and Fanning friction factors.
  • Treating a straight-pipe result as total system pressure drop.
  • Using a turbulent friction factor method without checking Reynolds number and roughness assumptions.
  • Comparing head loss between fluids without accounting for density when pressure loss matters.

Sources

This reference is based on Crane TP-410 for practical piping-flow equations and pressure-drop context, Frank M. White's Fluid Mechanics for head-loss formulation and pipe-flow assumptions, and a White worked example used to check the arithmetic form.