Pipe pressure loss with Darcy–Weisbach
A pressure-loss calculation accounts for energy dissipated through a defined pipe segment. Start with actual inside diameter and fluid properties at the operating temperature. Nominal DN and outside diameter are not flow areas.
Worked numbers are illustrative. Use your own operating conditions and documented material/process data.
Required inputs
- Flow Q, pipe length L and inside diameter D.
- Density ρ and dynamic viscosity μ at the operating condition.
- Roughness for friction calculation, or a documented Darcy friction factor; fitting loss coefficients K and their local diameters.
Governing equations
A = πD²/4; v = Q/A
Re = ρvD/μ
hf = fD(L/D)v²/(2g)
hm = ΣK v²/(2g); Δp = ρg(hf + hm)
Variables and units
- D, L and head: m; Q: m³/s; v: m/s; μ: Pa·s; ρ: kg/m³.
- fD: Darcy friction factor, four times the Fanning factor; K is dimensionless.
Assumptions
- Steady incompressible liquid in a full pipe.
- Example fD = 0.020 is supplied only to make arithmetic independently reproducible; it is not a default for every pipe.
Calculation workflow
- Convert flow and diameter to SI, then calculate velocity and Reynolds number.
- Use the appropriate flow-regime friction treatment; transition is uncertain.
- Calculate straight-pipe and fitting losses separately, then convert head to pressure.
Worked example
- Q = 25 m³/h, D = 0.080 m, L = 30 m, ρ = 1000 kg/m³, μ = 0.001 Pa·s; g = 9.81 m/s².
- v = 1.381553 m/s; Re = 110524.266.
- With entered fD = 0.020 and ΣK = 2, hf = 0.729621 m and hm = 0.194566 m.
- Total loss = 0.924187 m; Δp = 9066.276 Pa = 9.066276 kPa.
Limitations
- Compressible gas, two-phase flow, water hammer and network balancing are outside this example.
- A friction factor must not be selected solely from nominal diameter; roughness and Reynolds number matter.
Common mistakes
- Using a Fanning factor in a Darcy equation.
- Adding fitting K values evaluated at different velocity bases without adjustment.
- Equating pressure loss with static elevation head.
Practical interpretation
This is the dissipative loss, not the entire pump head requirement. Static lift, pressure differences and endpoint velocity differences belong in the energy balance. Where diameter changes, each segment and fitting must use its own velocity basis.
Related formulas
The governing equations, units and calculation steps above provide the formula basis for this guide. The related workspace also shows its calculation trace.
Pipe area and velocity references →Related workspace
Open Fluid Systems →Sources and reference basis
Equations and worked examples are independently explained here. References reviewed 2026-10-17; no copyrighted standard tables are reproduced.