Duct Sizing Calculator (Equal Friction Method) mechanism

Model scope

Preliminary sizing only. The standard Darcy relation is defensible, but the production result cannot be independently reproduced until the exact ASHRAE digitized table, interpolation scheme, air-property basis, roughness categories, rectangular-duct conversion rule, and unit normalization are supplied. Verify against an ASHRAE duct calculator or equivalent HVAC design software.

• The Darcy-based friction-chart method is standard in principle, but the specification does not provide the actual ASHRAE table, digitization, interpolation rule, duct roughness, air temperature, or air-property basis required to reproduce results.
• The approximation D=1.3(aspect·CFM²/ΔP)^(1/5) is not universally valid as written: its numerical constant is unit-system dependent, aspect-ratio convention is undefined, and it does not state whether D is hydraulic diameter, equivalent round diameter, or a rectangular-dimension surrogate.
• For rectangular ducts, the specification does not define how the equivalent diameter is converted into width and height. A common equal-friction convention is hydraulic diameter D_h=2ab/(a+b), with aspect ratio a/b specified.
• The friction-factor treatment is underspecified. Darcy friction factor depends on Reynolds number and relative roughness; a single friction-chart lookup cannot be verified without those variables or a clearly defined chart coordinate system.

Units and conventions

• CFM means actual volumetric flow at the stated duct conditions, not standard CFM; this distinction must be exposed to the user.
• Friction rate is inches of water gauge per 100 ft of duct.
• For the worked vectors, air density is 1.204 kg/m^3 at approximately 20 °C and standard atmospheric pressure.
• 1 inH2O is converted using water density 1000 kg/m^3, standard gravity 9.80665 m/s^2, and 1 international inch=0.0254 m: 249.08891 Pa.
• 100 ft=30.48 m exactly.
• Round-duct Darcy relation used for verification is Δp/L=8fρQ^2/(π^2D^5), with Q in m^3/s, D in m, and f the Darcy friction factor.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "shape": "round",
    "airflow_cfm": 1000,
    "friction_rate_inwg_per_100ft": 0.01702,
    "darcy_friction_factor": 0.02,
    "air_density_kg_per_m3": 1.204
  },
  "expected_outputs": {
    "diameter_m": 0.5,
    "diameter_in": 19.685,
    "velocity_m_per_s": 2.4
  },
  "reference_data": {
    "air_density_kg_per_m3_at_20C": 1.204,
    "source_convention": "ASHRAE Handbook—Fundamentals standard-air property value, approximately 20 C",
    "water_density_kg_per_m3": 1000,
    "source_convention_water_density": "widely tabulated standard value",
    "standard_gravity_m_per_s2": 9.80665,
    "source_convention_gravity": "CODATA/NIST standard gravity",
    "inch_m": 0.0254,
    "source_convention_inch": "ISO/international inch exact definition",
    "feet_per_100ft_m": 30.48,
    "source_convention_length": "international foot exact definition",
    "darcy_friction_factor": 0.02,
    "source_convention_friction_factor": "ASHRAE duct-friction-chart textbook smooth-duct value used as a verification fixture"
  },
  "working": "Q=1000×0.00047194745=0.47194745 m^3/s. 1 inH2O=1000×9.80665×0.0254=249.08891 Pa. Friction gradient=0.01702×249.08891/30.48=0.13907 Pa/m. D=[8fρQ²/(π²(Δp/L))]^(1/5)=[8×0.0200×1.204×(0.47194745)^2/(π²×0.13907)]^(1/5)≈0.5000 m=0.5000×39.3701=19.685 in. Area=π(0.5000)^2/4=0.19635 m². V=0.47194745/0.19635≈2.400 m/s."
}

Failure boundary

• Division by zero or invalid fifth-root results occur for zero/negative friction rate, zero/negative airflow, invalid density, or invalid friction factor.
• A friction chart is invalid outside its Reynolds-number, roughness, diameter, and velocity ranges; extrapolation must be prohibited or explicitly labeled.
• CFM versus SCFM/ACFM ambiguity can materially change velocity and friction loss.
• The calculator may produce impractical velocities, excessive noise, poor air distribution, or dimensions incompatible with available fittings and construction standards.
• Rectangular ducts require a stated aspect-ratio convention and a stated equivalent-diameter convention; otherwise dimensions are non-unique.
• The listed chart and curve-fit method must account for duct material/roughness, air temperature, elevation, and fittings/system effects if the result is presented as final design.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json