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    "Geometric pipe inlet: h = K v² / (2g); flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]; K is reported, not an input",
    "Require kind flush|reentrant|rounded; rounded needs 0 < rᵢ/D ≤ 1; default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible; from a large reservoir",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not Darcy f, not orifice C_d, not Q=Av"
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    "Geometric pipe inlet: h = K v² / (2g); flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]; K is reported, not an input",
    "Require kind flush|reentrant|rounded; rounded needs 0 < rᵢ/D ≤ 1; default g=9.80665; default ρ=1000 for Δp; incompressible; from a large reservoir",
    "Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not Darcy f, not orifice C_d, not Q=Av"
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    "v_m_s ≤ 0, h ≤ 0, or ri_d ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "ri_d > 1 → VALUE_OUT_OF_RANGE",
    "K, k, rd, n_miters, θ, f, Q, C_d, v1/v2 → MIXED_INPUT_ENCODING",
    "minor, circular, mitered, or unknown kind → INVALID_MODE"
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    {
      "title": "ISO 80000-4 — Mechanics",
      "section": "Length, speed, pressure",
      "url": "https://www.iso.org/standard/31895.html",
      "supports": "h is a head; v is a speed; Δp is a pressure",
      "kind": "standard"
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    {
      "title": "White — Fluid Mechanics",
      "section": "Entrance loss coefficients",
      "supports": "Flush sharp inlet K=0.5; thin-walled reentrant / inward-projecting K=0.8. Not a catalog K input",
      "kind": "reference"
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    {
      "title": "Swamee — rounded pipe inlet",
      "section": "K = 0.5 / [1 + 36 (r/D)^1.2]",
      "supports": "Flush-mounted rounded entrance; r/D=0 recovers K=0.5. Not Idelchik circular-arc B1, not mitered n",
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