{ "schemaVersion": 1, "engineVersion": "pressure-2026-09-08", "generatedAt": "2026-09-08T20:40:04.583Z", "engineSources": [ { "file": "static/js/fittings.js", "sha256": "21e7d7e9af1b61d94514e375d87ee13cf2b3b2d097b170f95f1df981fdb7666e" }, { "file": "static/js/duct-calc.js", "sha256": "5d8178d6445c09cdbe26c1097340e7afa344282f1e54428d417a991604983607" } ], "appVersion": null, "appVersionNote": "Engine identifier is separate from the application/deployment version; app.js is not executed by this suite.", "projectFixture": "/static/verification/benchmark-cold-round-project.json", "scope": "Bounded numerical equation verification; not third-party certification or a general engineering validation.", "assumptions": { "roughness_mm": 0.09144, "pressurePaPerInWG": 249.089, "cfmReference": "actual site volumetric flow, exact 0.3048^3 / 60 m³/s per CFM", "airModel": "Dry ideal gas; altitude pressure lapse model (101325 Pa, 288.15 K, 0.0065 K/m, g=9.80665, M=0.0289644, R=8.31447); rho=P/(287.058 T); mu=1.458e-6 T^1.5/(T+110.4).", "toleranceRationale": "Absolute 1e-9 plus relative 2e-6 accommodates the production rounded CFM conversion and numerical solver roundoff; it is NOT an engineering accuracy allowance." }, "limitations": [ "Not third-party certification, laboratory measurements, or validation of all Idelchik/ASHRAE datasets.", "Material roughness and air-model constants are declared assumptions, not independently measured properties.", "No transitional-flow, full input-domain, compressibility, humidity, acoustic, fan-curve, system-effect or balancing validation.", "Inlet/outlet aggregation is not covered: CALC.calcSystem exposes sections/paths, not a two-sided fan-pressure aggregation API.", "Other empirical standards and the legacy validate.js suite require a separate source-by-source audit; this suite does not supersede them." ], "sources": [ { "id": 1, "title": "SMACNA Duct Design Fundamentals, Patrick J. Brooks, P.E. (Utah ASHRAE presentation)", "url": "https://utahashrae.org/images/meeting/011119/Slides/smacna_duct_design_fundamentals.pdf", "supports": "Pressure Losses slides: Darcy-Weisbach, Colebrook, hydraulic diameter, Co × Pv. Supports equations, not these generated benchmark numbers or application certification." } ], "cases": [ { "id": "round-friction", "title": "Round galvanized duct friction", "conditions": { "altitude_ft": 0, "temperature_f": 70 }, "input": { "cfm": 2000, "length_ft": 100, "material": "galv_spiral", "ductType": "round", "diameter_in": 16, "fittings": [] }, "method": "Independent SI Darcy-Weisbach and bisected Colebrook equation; independent evaluation of declared air-property model", "limitations": [ "Turbulent, steady dry-air model at this one geometry and flow; imposed roughness 0.09144 mm." ], "checks": [ { "quantity": "T_K", "unit": "K", "expected": 294.2611111111111, "actual": 294.26111111111106, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 5.684341886080802e-14, "allowedError": 0.0005885232222222223, "pass": true }, { "quantity": "P", "unit": "Pa", "expected": 101325, "actual": 101325, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.202650001, "pass": true }, { "quantity": "rho", "unit": "kg/m³", "expected": 1.199538211942537, "actual": 1.1995382119425373, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.220446049250313e-16, "allowedError": 0.0000024000764238850743, "pass": true }, { "quantity": "mu", "unit": "Pa·s", "expected": 0.00001818717979073799, "actual": 0.000018187179790737986, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 3.3881317890172014e-21, "allowedError": 1.036374359581476e-9, "pass": true }, { "quantity": "A_m2", "unit": "m²", "expected": 0.1297171146489594, "actual": 0.1297171146489594, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 2.6043422929791885e-7, "pass": true }, { "quantity": "Dh_mm", "unit": "mm", "expected": 406.4, "actual": 406.4, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.0008128009999999999, "pass": true }, { "quantity": "Q_m3s", "unit": "m³/s", "expected": 0.9438948864000002, "actual": 0.943894, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 8.864000001773675e-7, "allowedError": 0.0000018887897728000004, "pass": true }, { "quantity": "V_ms", "unit": "m/s", "expected": 7.276563998161457, "actual": 7.276557164830307, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.0000068333311498136595, "allowedError": 0.000014554127996322913, "pass": true }, { "quantity": "Re", "unit": "dimensionless", "expected": 195042.286589926, "actual": 195042.10342812983, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.1831617961579468, "allowedError": 0.390084574179852, "pass": true }, { "quantity": "f", "unit": "Darcy dimensionless", "expected": 0.01731595579862731, "actual": 0.017315957939510834, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.14088352254449e-9, "allowedError": 3.563191159725462e-8, "pass": true }, { "quantity": "Pv_Pa", "unit": "Pa", "expected": 31.75680470599498, "actual": 31.756745061178844, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00005964481613673911, "allowedError": 0.00006351460941198996, "pass": true }, { "quantity": "frictionLoss_Pa", "unit": "Pa", "expected": 41.24245699459867, "actual": 41.24238463313559, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00007236146307576519, "allowedError": 0.00008248591398919734, "pass": true }, { "quantity": "frictionLoss_inWG", "unit": "in.w.g.", "expected": 0.16557317663404916, "actual": 0.16557288612959864, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.9050445052303253e-7, "allowedError": 3.3214635326809834e-7, "pass": true } ], "pass": true }, { "id": "rectangular-friction", "title": "Rectangular hydraulic-diameter friction", "conditions": { "altitude_ft": 0, "temperature_f": 70 }, "input": { "cfm": 2000, "length_ft": 100, "material": "galv_spiral", "ductType": "rectangular", "width_in": 20, "height_in": 12, "fittings": [] }, "method": "Independent SI Darcy-Weisbach and bisected Colebrook equation; independent evaluation of declared air-property model", "limitations": [ "Turbulent, steady dry-air model at this one geometry and flow; imposed roughness 0.09144 mm.", "Hydraulic-diameter approximation only; not an empirical aspect-ratio correction or equivalent-round chart validation." ], "checks": [ { "quantity": "T_K", "unit": "K", "expected": 294.2611111111111, "actual": 294.26111111111106, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 5.684341886080802e-14, "allowedError": 0.0005885232222222223, "pass": true }, { "quantity": "P", "unit": "Pa", "expected": 101325, "actual": 101325, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.202650001, "pass": true }, { "quantity": "rho", "unit": "kg/m³", "expected": 1.199538211942537, "actual": 1.1995382119425373, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.220446049250313e-16, "allowedError": 0.0000024000764238850743, "pass": true }, { "quantity": "mu", "unit": "Pa·s", "expected": 0.00001818717979073799, "actual": 0.000018187179790737986, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 3.3881317890172014e-21, "allowedError": 1.036374359581476e-9, "pass": true }, { "quantity": "A_m2", "unit": "m²", "expected": 0.1548384, "actual": 0.1548384, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 3.1067679999999996e-7, "pass": true }, { "quantity": "Dh_mm", "unit": "mm", "expected": 381, "actual": 380.99999999999994, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 5.684341886080802e-14, "allowedError": 0.000762001, "pass": true }, { "quantity": "Q_m3s", "unit": "m³/s", "expected": 0.9438948864000002, "actual": 0.943894, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 8.864000001773675e-7, "allowedError": 0.0000018887897728000004, "pass": true }, { "quantity": "V_ms", "unit": "m/s", "expected": 6.096000000000002, "actual": 6.0959942753218845, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.0000057246781173248, "allowedError": 0.000012193000000000003, "pass": true }, { "quantity": "Re", "unit": "dimensionless", "expected": 153185.85367256665, "actual": 153185.7098176283, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.14385493836016394, "allowedError": 0.30637170834513333, "pass": true }, { "quantity": "f", "unit": "Darcy dimensionless", "expected": 0.017987504914763766, "actual": 0.017987507303597394, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.388833627436915e-9, "allowedError": 3.6975009829527534e-8, "pass": true }, { "quantity": "Pv_Pa", "unit": "Pa", "expected": 22.288149297125216, "actual": 22.288107436094823, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.000041861030393164356, "allowedError": 0.00004457729859425043, "pass": true }, { "quantity": "frictionLoss_Pa", "unit": "Pa", "expected": 32.07265560184227, "actual": 32.07259962320953, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00005597863274431347, "allowedError": 0.00006414631120368455, "pass": true }, { "quantity": "frictionLoss_inWG", "unit": "in.w.g.", "expected": 0.12875982320312127, "actual": 0.12875959846966156, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.2473345970275282e-7, "allowedError": 2.5851964640624256e-7, "pass": true } ], "pass": true }, { "id": "cold-zero-f", "title": "Explicit 0°F dry-air conditions and round friction", "conditions": { "altitude_ft": 0, "temperature_f": 0 }, "input": { "cfm": 2000, "length_ft": 100, "material": "galv_spiral", "ductType": "round", "diameter_in": 16, "fittings": [] }, "method": "Independent SI Darcy-Weisbach and bisected Colebrook equation; independent evaluation of declared air-property model", "limitations": [ "Turbulent, steady dry-air model at this one geometry and flow; imposed roughness 0.09144 mm." ], "checks": [ { "quantity": "T_K", "unit": "K", "expected": 255.37222222222223, "actual": 255.3722222222222, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.842170943040401e-14, "allowedError": 0.0005107454444444444, "pass": true }, { "quantity": "P", "unit": "Pa", "expected": 101325, "actual": 101325, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.202650001, "pass": true }, { "quantity": "rho", "unit": "kg/m³", "expected": 1.382207680987673, "actual": 1.3822076809876733, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.220446049250313e-16, "allowedError": 0.000002765415361975346, "pass": true }, { "quantity": "mu", "unit": "Pa·s", "expected": 0.00001626699325789448, "actual": 0.000016266993257894478, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 3.3881317890172014e-21, "allowedError": 1.032533986515789e-9, "pass": true }, { "quantity": "A_m2", "unit": "m²", "expected": 0.1297171146489594, "actual": 0.1297171146489594, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 2.6043422929791885e-7, "pass": true }, { "quantity": "Dh_mm", "unit": "mm", "expected": 406.4, "actual": 406.4, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.0008128009999999999, "pass": true }, { "quantity": "Q_m3s", "unit": "m³/s", "expected": 0.9438948864000002, "actual": 0.943894, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 8.864000001773675e-7, "allowedError": 0.0000018887897728000004, "pass": true }, { "quantity": "V_ms", "unit": "m/s", "expected": 7.276563998161457, "actual": 7.276557164830307, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.0000068333311498136595, "allowedError": 0.000014554127996322913, "pass": true }, { "quantity": "Re", "unit": "dimensionless", "expected": 251273.14064359805, "actual": 251272.90467610312, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.2359674949257169, "allowedError": 0.502546282287196, "pass": true }, { "quantity": "f", "unit": "Darcy dimensionless", "expected": 0.01677610298221889, "actual": 0.0167761048469064, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 1.8646875085681636e-9, "allowedError": 3.455220596443778e-8, "pass": true }, { "quantity": "Pv_Pa", "unit": "Pa", "expected": 36.59283126726643, "actual": 36.592762539549234, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00006872771719912407, "allowedError": 0.00007318666253453287, "pass": true }, { "quantity": "frictionLoss_Pa", "unit": "Pa", "expected": 46.04138293129658, "actual": 46.041301575107006, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00008135618957538782, "allowedError": 0.00009208376586259316, "pass": true }, { "quantity": "frictionLoss_inWG", "unit": "in.w.g.", "expected": 0.18483908535220978, "actual": 0.18483875873726663, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 3.2661494314689676e-7, "allowedError": 3.7067817070441956e-7, "pass": true } ], "pass": true }, { "id": "high-altitude", "title": "5000 ft, 95°F dry-air conditions and round friction", "conditions": { "altitude_ft": 5000, "temperature_f": 95 }, "input": { "cfm": 2000, "length_ft": 100, "material": "galv_spiral", "ductType": "round", "diameter_in": 16, "fittings": [] }, "method": "Independent SI Darcy-Weisbach and bisected Colebrook equation; independent evaluation of declared air-property model", "limitations": [ "Turbulent, steady dry-air model at this one geometry and flow; imposed roughness 0.09144 mm." ], "checks": [ { "quantity": "T_K", "unit": "K", "expected": 308.15000000000003, "actual": 308.15, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 5.684341886080802e-14, "allowedError": 0.0006163010000000001, "pass": true }, { "quantity": "P", "unit": "Pa", "expected": 84307.55510568082, "actual": 84307.55510568082, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.16861511121136163, "pass": true }, { "quantity": "rho", "unit": "kg/m³", "expected": 0.9530916578638883, "actual": 0.9530916578638884, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 1.1102230246251565e-16, "allowedError": 0.0000019071833157277765, "pass": true }, { "quantity": "mu", "unit": "Pa·s", "expected": 0.000018843146984498333, "actual": 0.000018843146984498333, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 1.0376862939689968e-9, "pass": true }, { "quantity": "A_m2", "unit": "m²", "expected": 0.1297171146489594, "actual": 0.1297171146489594, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 2.6043422929791885e-7, "pass": true }, { "quantity": "Dh_mm", "unit": "mm", "expected": 406.4, "actual": 406.4, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0, "allowedError": 0.0008128009999999999, "pass": true }, { "quantity": "Q_m3s", "unit": "m³/s", "expected": 0.9438948864000002, "actual": 0.943894, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 8.864000001773675e-7, "allowedError": 0.0000018887897728000004, "pass": true }, { "quantity": "V_ms", "unit": "m/s", "expected": 7.276563998161457, "actual": 7.276557164830307, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.0000068333311498136595, "allowedError": 0.000014554127996322913, "pass": true }, { "quantity": "Re", "unit": "dimensionless", "expected": 149575.78305725762, "actual": 149575.64259249187, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.1404647657473106, "allowedError": 0.29915156711451524, "pass": true }, { "quantity": "f", "unit": "Darcy dimensionless", "expected": 0.01796449085520778, "actual": 0.017964493306927988, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.4517202087959156e-9, "allowedError": 3.692898171041556e-8, "pass": true }, { "quantity": "Pv_Pa", "unit": "Pa", "expected": 25.23233136248469, "actual": 25.23228397176705, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00004739071763992797, "allowedError": 0.00005046566272496938, "pass": true }, { "quantity": "frictionLoss_Pa", "unit": "Pa", "expected": 33.996448951269656, "actual": 33.996389739698664, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.0000592115709920904, "allowedError": 0.0000679938979025393, "pass": true }, { "quantity": "frictionLoss_inWG", "unit": "in.w.g.", "expected": 0.13648314036858172, "actual": 0.1364829026560734, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 2.3771250831639001e-7, "allowedError": 2.7396628073716347e-7, "pass": true } ], "pass": true }, { "id": "elbow-imposed-co", "title": "Imposed elbow Co × local velocity pressure", "conditions": { "altitude_ft": 0, "temperature_f": 70 }, "input": { "cfm": 2000, "length_ft": 0, "material": "galv_spiral", "ductType": "round", "diameter_in": 16, "fittings": [ { "id": "elbow_smooth_90_1_5d", "Co_override": 0.35 } ] }, "method": "Δp = 0.35 × independently calculated ρV²/2, using section-local velocity pressure", "coefficientReference": "section-local velocity pressure, not common-duct or downstream velocity pressure", "limitations": [ "Co = 0.35 is deliberately imposed, NOT independently validated empirical elbow data. FittingsLib auto-calculation is not called." ], "checks": [ { "quantity": "Co", "unit": "dimensionless", "expected": 0.35, "actual": 0.35, "tolerance": { "absolute": 0, "relative": 0 }, "absoluteError": 0, "allowedError": 0, "pass": true }, { "quantity": "fittingLoss_Pa", "unit": "Pa", "expected": 11.114881647098242, "actual": 11.114860771412594, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.000020875685647681053, "allowedError": 0.000022230763294196484, "pass": true }, { "quantity": "totalLoss_Pa", "unit": "Pa", "expected": 11.114881647098242, "actual": 11.114860771412594, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.000020875685647681053, "allowedError": 0.000022230763294196484, "pass": true } ], "pass": true }, { "id": "branched-critical-path", "title": "Shared trunk, two branch paths: sum each, then maximum", "conditions": { "altitude_ft": 0, "temperature_f": 70 }, "input": { "sections": [ { "cfm": 2000, "length_ft": 25, "material": "galv_spiral", "ductType": "round", "diameter_in": 16, "fittings": [] }, { "cfm": 1200, "length_ft": 20, "material": "galv_spiral", "ductType": "round", "diameter_in": 14, "fittings": [] }, { "cfm": 800, "length_ft": 80, "material": "galv_spiral", "ductType": "round", "diameter_in": 10, "fittings": [] } ], "paths": [ [ 0, 1 ], [ 0, 2 ] ] }, "method": "Independently calculate each section, sum explicitly supplied paths, select maximum", "limitations": [ "Topology and flows are explicitly supplied to CALC.calcSystem; controller tree-to-path conversion is not tested.", "No junction coefficient included; no empirical tee/wye validation or fan static-pressure conversion." ], "checks": [ { "quantity": "path0_totalLoss_Pa", "unit": "Pa", "expected": 16.47428866512513, "actual": 16.474259840652557, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.000028824472572352988, "allowedError": 0.00003294957733025026, "pass": true }, { "quantity": "path1_totalLoss_Pa", "unit": "Pa", "expected": 71.46642045164283, "actual": 71.4662952115917, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00012524005113334624, "allowedError": 0.00014293384090328565, "pass": true }, { "quantity": "criticalPathIndex", "unit": "zero-based index", "expected": 1, "actual": 1, "tolerance": { "absolute": 0, "relative": 0 }, "absoluteError": 0, "allowedError": 0, "pass": true }, { "quantity": "criticalPathLoss_Pa", "unit": "Pa", "expected": 71.46642045164283, "actual": 71.4662952115917, "tolerance": { "absolute": 1e-9, "relative": 0.000002 }, "absoluteError": 0.00012524005113334624, "allowedError": 0.00014293384090328565, "pass": true } ], "pass": true } ], "summary": { "cases": 6, "checks": 59, "passed": 59, "failed": 0 }, "pass": true }