Pipe Flow — validation & limitations

What it calculates

• Darcy-Weisbach pressure drop with Colebrook-White friction factor (Swamee-Jain explicit form) — laminar (f = 64/Re) and turbulent, with the indeterminate transitional band checked at the turbulent value
• Reynolds number and automatic flow-regime classification (Laminar / Transitional / Turbulent)
• Interactive Moody diagram with the operating point overlaid on the full ε/D family of curves
• Pump & system curve intersection — locate the true operating flow rate and head for a centrifugal pump
• Water-hammer surge pressure via Joukowsky (rapid closure) and Michaud (gradual closure), with wave-speed calculation and closing-time chart
• Series and parallel pipe network solver — given total flow find ΔP, or given ΔP find flow in each branch
• Compressible isothermal gas flow at constant mass flux, solved for the self-consistent outlet pressure, with outlet Mach-number warnings (Ma > 0.3, and near the isothermal choking limit 1/√γ) and a choked-flow refusal

Validation evidence — independent reference cases (2)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Turbulent Darcy-Weisbach pressure drop and velocity

  Conservative

  Source: F. M. White, Fluid Mechanics, 5th ed., Sec. 6.6 worked example and Eq. 6.48 (Colebrook-White); Darcy-Weisbach; hand-derived water case

  Inputs: Case W: oil rho 900, mu 0.009, Q 12000 L/min, D 200 mm, L 500 m, eps 0.26 mm. Case S: water, D 100 mm, L 100 m, Q 1000 L/min, eps 0.045 mm

  Quantity	Reference value	Tolerance
  velocity (case W)	6.3662 m/s	1e-6 relative
  pressure drop (case W)	1036104 Pa; head loss 117.39 m	-0.5 % to +1.5 % vs Colebrook
  pressure drop (case S)	0.41494 bar	-0.5 % to +1.5 % vs Colebrook
  friction factor (W / S)	0.0227243 / 0.0184621	-0.5 % to +1.5 % vs Colebrook

  Conservative simplification: The engine uses the explicit Swamee-Jain fit for the friction factor, which reads about 0.6 % (case S) and 0.8 % (case W) above the implicit Colebrook value, giving a slightly higher pressure drop.

  tests/golden/REF-pipeflow-darcy-turbulent.golden.test.ts

• Water hammer wave speed and surge pressure

  Agrees

  Source: Wylie & Streeter, Fluid Transients in Systems (Prentice Hall, 1993), Ch. 1-2 (Korteweg wave speed, Joukowsky surge); Michaud estimate; hand derivation

  Inputs: Water K 2.2 GPa, rho 1000; steel E 200 GPa; D 500 mm, e 10 mm, L 1000 m, v0 2 m/s; closure 0, 1, 10 s

  Quantity	Reference value	Tolerance
  wave speed	1191.37 m/s	1e-6 relative
  rapid-closure surge (tc 1 s)	23.827 bar (2L/a = 1.6787 s)	1e-6 relative
  gradual-closure surge (tc 10 s)	4.000 bar	1e-6 relative

  tests/golden/REF-pipeflow-hammer.golden.test.ts

Limitations

Conservative simplifications

• Turbulent Darcy-Weisbach pressure drop and velocity — The engine uses the explicit Swamee-Jain fit for the friction factor, which reads about 0.6 % (case S) and 0.8 % (case W) above the implicit Colebrook value, giving a slightly higher pressure drop.

Not checked by this tool

• Pipe wall pressure rating for the operating and surge pressure — Check the wall with /dn (Barlow screen) or /pipestress (ASME B31.3 section 304)
• Two-phase, slurry and non-Newtonian flow — Single-phase Newtonian flow only; use a method for the actual flow type
• Cavitation and flashing at valves, orifices and high points — Not checked; compare local pressures with the vapour pressure (pump NPSH in /pumps)
• Heat loss or gain along the line — One temperature for the whole line; split long or heated lines into segments
• Control-valve sizing and authority — Fittings are fixed losses; size control valves per IEC 60534
• Pipe supports, thermal expansion and anchors — Use /pipestress