hvac duct size derived

{
  "input": {
    "body": {
      "airflow": 1000,
      "friction_rate": 0.08
    },
    "type": "http",
    "method": "POST",
    "bodyType": "json"
  },
  "output": {
    "type": "json",
    "example": {
      "notes": [
        "The rectangular size has the same friction loss and airflow as the round duct (ASHRAE equivalent diameter); its velocity is lower because its area is larger.",
        "Galvanized steel (ε = 0.0003 ft) and standard air (0.075 lb/ft³, 70 °F, sea level). Fittings and transitions are not included.",
        "For design guidance; the engineer of record is responsible for final selections."
      ],
      "round": {
        "area": 1.1112,
        "diameter": 14.27,
        "velocity": 900,
        "friction_rate": 0.08,
        "standard_sizes": [
          {
            "best_fit": true,
            "diameter": 14,
            "velocity": 935,
            "friction_rate": 0.088
          },
          {
            "best_fit": false,
            "diameter": 16,
            "velocity": 716,
            "friction_rate": 0.0457
          }
        ]
      },
      "steps": [
        {
          "step": "Round diameter at the friction rate (equal friction)",
          "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
          "calculation": "Iterated the diameter (bisection) until the Darcy-Weisbach friction loss at 1,000 CFM equals 0.0800 in. w.g./100 ft → D = 14.27 in"
        },
        {
          "step": "Square equivalent",
          "reference": "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design (Huebscher equivalent diameter)",
          "calculation": "For W = H = S: De = 1.30·S^1.25 / (2S)^0.25 = 1.09317·S → S = 14.27 / 1.09317 = 13.06 in"
        },
        {
          "step": "Round duct: Reynolds number",
          "reference": null,
          "calculation": "Re = D·V / ν = 1.1895 ft × 14.998 ft/s / 1.56×10⁻⁴ ft²/s = 114,361"
        }
      ],
      "units": "IP",
      "checks": {
        "friction": "Typical design range (0.04-0.15 in. w.g./100 ft; about 0.3-1.2 Pa/m).",
        "velocity": "Normal design range (400-2,500 FPM; about 2-12.7 m/s).",
        "aspect_ratio": null
      },
      "airflow": 1000,
      "velocity": 900,
      "next_calls": [
        {
          "why": "What cooling load does 1000 CFM carry from 80/67 to 55/54 °F?",
          "tool": "hvac_coil_load",
          "price": "$0.002",
          "arguments": {
            "units": "IP",
            "airflow": 1000,
            "leaving": {
              "dry_bulb": 55,
              "wet_bulb": 54
            },
            "entering": {
              "dry_bulb": 80,
              "wet_bulb": 67
            }
          }
        }
      ],
      "references": [
        "ASHRAE Handbook—Fundamentals (2021), Ch. 21 Duct Design",
        "SMACNA HVAC Duct Design Manual (standard sizes, aspect ratio guidance)"
      ],
      "solved_for": "size",
      "inputs_used": {
        "airflow": 1000,
        "friction_rate": 0.08
      },
      "rectangular": {
        "area": 1.184,
        "basis": "equal_friction",
        "width": 13.06,
        "height": 13.06,
        "velocity": 845,
        "aspect_ratio": 1,
        "friction_rate": 0.08,
        "standard_sizes": [
          {
            "width": 14,
            "height": 14,
            "best_fit": false,
            "velocity": 735,
            "aspect_ratio": 1,
            "friction_rate": 0.0568,
            "equivalent_diameter": 15.3
          },
          {
            "width": 16,
            "height": 12,
            "best_fit": false,
            "velocity": 750,
            "aspect_ratio": 1.33,
            "friction_rate": 0.0605,
            "equivalent_diameter": 15.11
          }
        ],
        "equivalent_diameter": 14.27
      },
      "unit_labels": {
        "area": "ft²",
        "load": "MBH (1,000 BTU/h)",
        "grains": "gr / lb dry air",
        "length": "in",
        "airflow": "CFM",
        "density": "lb / ft³",
        "enthalpy": "BTU / lb dry air",
        "pressure": "psia",
        "velocity": "FPM",
        "elevation": "ft",
        "condensate": "gal / h",
        "temperature": "°F",
        "friction_rate": "in. w.g. / 100 ft",
        "humidity_ratio": "lb water / lb dry air",
        "specific_volume": "ft³ / lb dry air",
        "relative_humidity": "%",
        "velocity_pressure": "in. w.g."
      },
      "friction_rate": 0.08,
      "primary_shape": "round",
      "friction_factor": 0.01885,
      "reynolds_number": 114361,
      "velocity_pressure": 0.0505
    }
  }
}