{
  "problem": "Steady flow from a reservoir through a single horizontal pipe; Darcy–Weisbach friction with the friction factor from Colebrook–White.",
  "pipe": {
    "L_m": 1000.0,
    "D_m": 0.3,
    "roughness_m": 0.00015
  },
  "fluid": {
    "kinematic_viscosity_m2s": 1e-06,
    "g_ms2": 9.81
  },
  "boundaries": {
    "upstream": {
      "type": "reservoir",
      "head_m": 100.0
    },
    "downstream": {
      "type": "withdrawal",
      "velocity_ms": 1.0,
      "flow_m3s": 0.0706858347
    }
  },
  "output": "Piezometric head h at x = 0 and x = L (and any interior points the solver reports), each row tagged with x.",
  "notes": "Re = 3.0e5 and relative roughness 5.0e-4: fully turbulent. Explicit friction formulas (Swamee–Jain, Haaland) agree with Colebrook–White to about 1 % in this range."
}