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Darcy–Weisbach Calculator

Major head loss h_f = f(L/D)(v²/2g)

Parameters

ⓘ
mⓘ
mⓘ
m/sⓘ
m/s²ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Head Loss h_f:
4.08;m4.08;m
L/D ratio:
1000.00;1000.00;

Examples

Water pipe 100 m

f=0.02, D=0.1 m, v=2 m/s.

    Long pipeline

    L=500 m.

      Visualization

      Darcy–Weisbach Equation — Pipe Head Loss

      The Darcy–Weisbach equation is the standard engineering formula for head loss due to friction in straight, full, steady pipe flow: h_f = f(L/D)(v²/2g), where f is the Darcy friction factor (dimensionless), L is pipe length (m), D is internal diameter (m), v is average velocity (m/s), and g ≈ 9.81 m/s².

      Head loss h_f has dimensions of length (meters of fluid column) and represents energy dissipated per unit weight of fluid. Pressure drop along the pipe is ΔP = ρgh_f (Pa). Pump must supply head at least equal to total system head loss to maintain flow.

      Friction factor f is not constant — it depends on Reynolds number Re = ρvD/μ and relative roughness ε/D (pipe wall roughness height ε). Laminar flow (Re < 2300): f = 64/Re exactly, independent of roughness. Turbulent flow: f from Moody chart or Colebrook equation (iterative). Smooth pipe turbulent f can be as low as ~0.008; rough old pipes may have f > 0.04.

      The v² dependence is critical: doubling flow velocity quadruples friction head loss. Doubling pipe length doubles h_f. Halving diameter (for same v) multiplies h_f by 2 (L/D effect) and also increases v for fixed Q — combined effect is very strong.

      Total system head loss = major losses (straight pipe, Darcy–Weisbach) + minor losses (elbows, tees, valves) often modeled as K(v²/2g). Non-circular ducts use hydraulic diameter D_h = 4A/P. Link to Hagen–Poiseuille: laminar limit gives Q ∝ D⁴ΔP/L.

      Used in water distribution networks, fire protection hydraulics, oil pipelines, HVAC duct design, and pump curve matching. The Moody diagram is one of the most used charts in mechanical and civil engineering.

      Key Concepts

      • h_f = f(L/D)(v²/2g) — major loss
      • ΔP = ρgh_f; h_f in meters of fluid
      • f = f(Re, ε/D) from Moody chart
      • Laminar: f = 64/Re (Re < 2300)
      • h_f ∝ v² — strong velocity effect
      • Minor losses: K(v²/2g) fittings

      Real-World Applications

      • Municipal water supply and distribution
      • Pump selection and system curve analysis
      • Fire sprinkler and standpipe hydraulics
      • Oil, gas, and slurry pipeline design
      • Class 12 pipe friction and Reynolds number labs
      • Building plumbing pressure-loss calculations

      Explore Further

      More fluid mechanics tools

      Physics Equations

      Darcy–Weisbach:
      hf=fLDv22gh_f = f\frac{L}{D}\frac{v^2}{2g}
      Pressure Drop:
      ΔP=ρghf\Delta P = \rho g h_f

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Darcy–Weisbach

      Equation:

      hf=fLDv22gh_f = f\frac{L}{D}\frac{v^2}{2g}

      Explanation:

      Major head loss in pipe flow; h_f in meters of fluid.

      2

      Step 2: Friction Factor f

      Result:

      f=0.02f = 0.02

      Explanation:

      Depends on Re and roughness (Moody chart).

      3

      Step 3: L/D Ratio

      Calculation:

      L/D=100/0.1=1000.0000L/D = 100/0.1 = 1000.0000
      4

      Step 4: Velocity Head

      Calculation:

      v22g=222×9.81=0.2039 m\frac{v^2}{2g} = \frac{2^2}{2 \times 9.81} = 0.2039 \text{ m}

      Explanation:

      Kinetic energy per unit weight.

      5

      Step 5: Head Loss

      Calculation:

      hf=0.02×1000.0000×0.2039=4.0775 mh_f = 0.02 \times 1000.0000 \times 0.2039 = 4.0775 \text{ m}

      Result:

      hf=4.0775mh_f = 4.0775 m
      6

      Step 6: Pressure Drop

      Equation:

      ΔP=ρghf\Delta P = \rho g h_f

      Explanation:

      Multiply by ρg for Pa if density known.

      Frequently Asked Questions (FAQ)

      Darcy f vs Fanning?

      Fanning f_F = Darcy f/4 — check which definition.

      Smooth vs rough pipe?

      Roughness ε increases f at high Re.

      Non-circular duct?

      Use hydraulic diameter D_h = 4A/P.

      Link to Poiseuille?

      Laminar limit gives Hagen–Poiseuille Q relation.

      Negative h_f?

      Head loss always positive — energy dissipated.

      Practice MCQs

      1. Doubling flow velocity multiplies h_f by:
      2. Darcy f depends on:
      3. Laminar pipe flow f =
      4. Smaller diameter D at same v:
      5. h_f has units of:
      6. Pressure drop from h_f:

      Related Calculators

      These tools connect to the same physics concepts used in this calculator.

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