PUZZLE #3892: Hydraulic Cipher (diff 3)

hydraulic learn difficulty: 3/7 simulate author: system unsolved

6 buckets of different sizes. Each has a tap at an angle. All open for the same duration. Water heights encode a word.

DATA

Buckets	{'id': 0, 'letter': 'p', 'area_cm2': 41, 'tap_angle_deg': 75, 'water_height_cm': 1.14}, {'id': 1, 'letter': 'i', 'area_cm2': 36, 'tap_angle_deg': 68, 'water_height_cm': 1.18}, {'id': 2, 'letter': 'v', 'area_cm2': 49, 'tap_angle_deg': 17, 'water_height_cm': 0.22}, {'id': 3, 'letter': 'p', 'area_cm2': 38, 'tap_angle_deg': 84, 'water_height_cm': 1.38}, {'id': 4, 'letter': 'p', 'area_cm2': 19, 'tap_angle_deg': 73, 'water_height_cm': 2.39}, {'id': 5, 'letter': 'p', 'area_cm2': 21, 'tap_angle_deg': 63, 'water_height_cm': 1.87}
K	`4`
Open Duration	`14`
N Chars	`6`
Max Height	`2.39`
Hint	`f = K × (θ/90°), K=4. V = f × t. h = V / area. t is the same for every bucket. Sort buckets by water_height_cm ascending and read the letters.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "hydraulic",
  "buckets": [
    {
      "id": 0,
      "letter": "p",
      "area_cm2": 41,
      "tap_angle_deg": 75,
      "water_height_cm": 1.14
    },
    {
      "id": 1,
      "letter": "i",
      "area_cm2": 36,
      "tap_angle_deg": 68,
      "water_height_cm": 1.18
    },
    {
      "id": 2,
      "letter": "v",
      "area_cm2": 49,
      "tap_angle_deg": 17,
      "water_height_cm": 0.22
    },
    {
      "id": 3,
      "letter": "p",
      "area_cm2": 38,
      "tap_angle_deg": 84,
      "water_height_cm": 1.38
    },
    {
      "id": 4,
      "letter": "p",
      "area_cm2": 19,
      "tap_angle_deg": 73,
      "water_height_cm": 2.39
    },
    {
      "id": 5,
      "letter": "p",
      "area_cm2": 21,
      "tap_angle_deg": 63,
      "water_height_cm": 1.87
    }
  ],
  "K": 4,
  "open_duration": 14,
  "n_chars": 6,
  "max_height": 2.39,
  "hint": "f = K \u00d7 (\u03b8/90\u00b0), K=4. V = f \u00d7 t. h = V / area. t is the same for every bucket. Sort buckets by water_height_cm ascending and read the letters.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: hydraulic diff 3