{
  "ran": "2026-10-13T08:23:53.373Z",
  "how": "kit/siphon.mjs. Unprimed bowl spills over the trap crest as a weir, Qw = C·b·H^1.5. The air-filled downleg passes at most Qd = Cd·A·sqrt(2gL). The siphon primes when the bowl head reaches H* = min(head where Qw = Qd, throat diameter): either the spill outruns the downleg, or the water over the crest reaches the top of the pipe and leaves no air path. The crest is as wide as the pipe. A bucket of fixed volume is poured at a steady rate over T seconds; the bowl is a tank of area bowlArea (explicit Euler, dt 2 ms). Threshold = longest T that still primes (bisection, 40 steps).",
  "sources": {
    "mechanism": "Kohler, How a Toilet Flushes: the surge fills the trapway and displaces the air, the change in pressure forms a siphon",
    "bucket": "1 US gallon = 3.785 L, rounded to 3.8 L"
  },
  "simplification": "The bowl is treated as a tank spilling over the crest; the momentum of the poured stream pushing water into the trap is left out.",
  "assumptions": {
    "throatDiameter_m": 0.0508,
    "drop_m": 0.15,
    "cd": 0.61,
    "weirC": 1.7,
    "crestWidth_m": 0.0508,
    "bowlArea_m2": 0.03,
    "bucket_L": 3.8
  },
  "derived": {
    "downlegCapacity_L_per_s": 2.121,
    "capacityHead_cm": 8.45,
    "primeHead_cm": 5.08,
    "primedBy": "top of the pipe",
    "thresholdPourTime_s": 3.627,
    "upperBound_s": 3.843
  },
  "ok": true
}