Calculation Method

The physics behind the numbers.

Overview

DuctStatic sums modeled losses from straight-duct friction, fitting coefficients, and entered published pressure drops at the assigned airflows. The highest path sum is the critical path. Friction and fitting calculations use a total-pressure loss method; the full sum is only on a consistent basis if the published inputs and system boundaries are consistent too.

All calculations are performed internally in SI units (Pa, m, kg/m³) and converted to English (imperial) or SI for display.

Air Properties

Every pressure loss calculation depends on air density and viscosity. DuctStatic computes both from your site conditions:

• Air pressure at altitude. Calculated from the standard atmosphere model (ISA troposphere formula).
• Air density. From the ideal gas law using the dry-air specific gas constant (287.058 J/kg·K).
• Dynamic viscosity. From Sutherland's formula, which accurately models how viscosity changes with temperature.

The engine has nominal 20°C air-property constants, while the interface starts with sea-level altitude and 70°F. Enter and verify the project conditions rather than treating either default as project data. The density model is dry air; it does not include humidity.

Velocity Pressure

Velocity pressure is the kinetic energy of the airstream:

Pv = ½ρV²

Where ρ is air density (kg/m³) and V is air velocity (m/s). It serves as the reference quantity for fitting loss calculations.

Friction Loss (Straight Runs)

Straight duct friction loss follows the Darcy-Weisbach equation:

ΔP = f × (L/Dh) × Pv

Where f is the Darcy friction factor, L is the duct length, and Dh is the hydraulic diameter.

Hydraulic Diameter

For round duct, Dh equals the inside diameter. For rectangular duct:

Dh = 2WH / (W + H)

Friction Factor

DuctStatic solves the Colebrook-White equation iteratively using Newton-Raphson:

1/√f = -2.0 × log₁₀(ε/Dh/3.7 + 2.51/(Re√f))

Where ε is the absolute roughness of the duct material and Re is the Reynolds number. The Swamee-Jain approximation provides the initial guess. For laminar flow (Re < 2300), f = 64/Re.

The turbulent correlation and the laminar rule do not resolve transitional-flow uncertainty. Roughness and actual internal dimensions still require design judgment.

Fitting Loss (Dynamic Losses)

Fitting losses use the loss coefficient method:

ΔP = Co × Pv

Co (also written ζ or C) is referenced to a specified duct section. For a two-port passive fitting it expresses total-pressure loss relative to that velocity pressure. Junction path coefficients can be negative because of energy exchange between streams; that is not a source of net energy.

Where the Coefficients Come From

Loss coefficients in DuctStatic are calculated from the original experimental research that forms the basis of published HVAC standards. The primary source is I.E. Idelchik's Handbook of Hydraulic Resistance (4th Ed., 2007), supplemented by Rozell (1974) for vaned rectangular elbows.

Coefficients are computed dynamically from the geometry you enter, not looked up from a fixed table. Co updates in real time as you change duct dimensions, angles, or area ratios, giving you the correct value for your actual geometry rather than the nearest tabulated size.

Fitting Types and Their Bases

• Smooth radius elbows (round and rectangular). Idelchik Diagram 6.1. Co is a function of R/D ratio, bend angle, and Reynolds number.
• Mitered elbows. Idelchik Diagram 6.7. Function of deflection angle.
• Vaned elbows. Rozell (1974) empirical test data. Tabulated by vane geometry.
• Gradual expansions and contractions. Idelchik Diagrams 5.2, 5.23.
• Converging tees (round). Idelchik Diagrams 7.9, 7.10.
• Diverging tees. Idelchik Diagrams 7.18-7.20.
• 45° converging and diverging wyes. Idelchik Diagrams 7.11/7.12, 7.22-7.23.

Critical Path

After calculating every path in the system, DuctStatic identifies the one with the highest total pressure loss. This is the critical path, the branch that is hardest to serve. Your fan must be able to deliver the design airflow against at least this much resistance.

All other paths have excess pressure available, which is balanced by dampers during system commissioning.

Adjusted loss and fan selection

Adjusted loss = modeled critical loss × (1 + safety factor % / 100)

When both inlet and outlet ductwork are modeled, add the critical inlet and outlet losses before applying the factor. This is not automatically fan static pressure or equipment external static pressure. Define the system boundary, check terminal static/total ratings, and reconcile fan outlet velocity pressure with the chosen fan curve. See fan pressure and modeled duct losses.

Sound Analysis (Preliminary)

A screening-level octave-band estimate of duct-borne noise.

Run Calculate, then open the Sound (Prelim) tab in the results panel. Each diffuser gets a row with its Target NC, its own Terminal NC, the combined Predicted NC, the controlling band, and PASS/FAIL. Fan sound data and target-NC values live in the components' properties panels.

The sound model estimates the noise criterion (NC) each room gets by spreading a fan sound-power spectrum down the duct system in octave bands, applying attenuation per band, and estimating the resulting room sound pressure. This is a preliminary estimate for screening layout and silencer choices early in design. It points the general direction for good duct design, not the exact answer, and does not replace the judgement of an acoustical engineer or a field measurement.

Fan sound-power spectrum (Lw)

The fan is the dominant source. Its contribution is supplied per octave band in two ways:

• User-entered 8-band spectrum. If the fan manufacturer provides an octave-band sound-power spectrum, use it directly. Use data for the selected fan at its operating point and the relevant inlet or outlet sound path.
• Assumed spectrum. When all you know is an overall sound-power level (or a single dBA), a default relative spectrum is assumed and scaled to that Lw. An assumed spectrum is less reliable than measured octave-band data.

Duct, elbow, and branch attenuation

Losses are applied per octave band and summed down the path from fan to terminal:

• Unlined straight duct. ASHRAE per-foot attenuation for the duct cross-section (round vs. rectangular), low at low frequencies and rising through mid-band. Large ducts attenuate less than small ones.
• Elbows. The ASHRAE radiused-elbow rule is size-dependent: attenuation grows with the product of frequency and duct width, and a 45° bend is roughly half a 90° bend.
• Lined & flexible duct. The unlined profile plus the absorption contribution of lining (or a reduced flexible-duct profile), per octave band, per unit length.
• Branch (sound-power split). At each tee, downstream sound power divides in proportion to the downstream cross-sectional areas. A branch carrying less area loses more.
• End reflection. A modest low-frequency loss where the sound leaves the duct into the room.

Silencer (attenuator) insertion

A silencer's rated insertion loss per octave band is subtracted from the Lw before the room estimate. Insertion loss is strongly band-dependent, so it's evaluated spectrum-wise rather than as a single number.

Room sound-pressure level (Lp)

The remaining octave-band sound power is converted to a room sound-pressure level using the AHRI 885 space-effect convention — a nominal ~2,500 ft³ room, listener ~7 ft from the diffuser, absorbing more at high frequencies than low (per-band corrections from about −4 dB at 63 Hz to −11 dB at 8 kHz). The tangent method then turns each band's Lp into NC contributions, and the room NC is the lowest NC curve that none of the bands exceed.

Diffuser self-noise

A diffuser is its own noise source: airflow tearing over the vanes and neck generates noise at the room, so the duct run never attenuates it. With a quiet fan or a heavily-attenuated run, the diffuser usually sets the room NC, not the leftover fan noise. Each terminal picks between two models in the Self-noise section of its properties; self-noise is always modeled.

• Rated NC (manufacturer). Enter the diffuser's catalog NC at its operating CFM. The rating is converted back to a neck sound power through the same room-absorption model used for the fan path, so both sources share a single room correction. Catalog NC ratings are optimistic: expect on the order of 5 NC higher in the field, and substantially more when airflow into the device is disturbed — a balancing damper or a close-fitting inlet plenum right at the collar can add up to ~20 NC points.
• Auto-estimate (CFM & neck). With no rating, NC is estimated from neck velocity (CFM ÷ neck area): about NC 30 at 400 fpm, rising roughly +6 NC per doubling of velocity, snapped to the NC-5 grid.

Fan residual and diffuser self-noise are independent sources at the same point, so they combine by sound-power addition, then a single room-absorption term converts the sum to room pressure. The Sound tab shows both the diffuser's own NC (Terminal NC*, marked rated or est.) and the combined Predicted NC.

NC compliance

Achieved NC is compared with the per-terminal Target NC:

• PASS if the achieved NC is at or below the target across all bands.
• FAIL if any band pushes the achieved NC above the target. The controlling band is shown.

The predicted room spectrum is clamped to an NC 15 acoustic floor. This is an implementation floor, not a measurement of ambient or structure-borne noise. Those sources are not predicted by the duct-path model.

References

• Beranek, L.L. "Revised Criteria for Noise in Buildings." Noise Control, 1957. Origin of the NC (noise criterion) curves used here.
• ASHRAE. ASHRAE Handbook — HVAC Applications, Chapter: Noise and Vibration Control. Straight/round-duct and elbow attenuation data.
• Air-terminal (diffuser/louver) sound: manufacturer octave-band and NC ratings at operating CFM.
• Silencer insertion loss: manufacturer octave-band data.
• Room-Lp conversion and the tangent method: standard acoustics practice for predicting LW→LP in rooms.

Applicability and sources

The loss-coefficient library is built from Idelchik (4th Ed., 2007), with Rozell (1974) for vaned rectangular elbows. Coefficients are computed from the geometry you enter rather than looked up from a fixed table. Applicability limits apply:

• Source range. Each coefficient is valid within the geometry, angle, area-ratio and Reynolds ranges of its source diagram. Outside those ranges the value is an approximation and must be reviewed.
• Sparse regions. Some multi-port tables are sparse. Where a point falls in an unavailable region the engine flags it rather than silently fabricating a value; a result may carry a warning. Verification covers interpolation policy, not absent source data.
• Clamping. Interpolation is bounded to published ranges. It does not extrapolate beyond the source table, and geometry outside the supported domain should not be relied on without engineering review.
• Manufacturer data. Where a fitting or terminal uses a manufacturer pressure drop, the basis (static or total, at what airflow) must come from that manufacturer; DuctStatic does not assume a basis for you.

Review Idelchik diagrams 5-2 / 5.23 (transitions) and their neighbors directly before relying on a borderline geometry. This scope note is what Verification checks; it is not a certification of every Idelchik dataset.

Sources

• Idelchik, I.E. Handbook of Hydraulic Resistance, 4th Ed. Begell House, 2007.
• Rozell, T.C. "Pressure Losses in Duct Fittings." ASHRAE Transactions, 1974.
• Colebrook, C.F. "Turbulent Flow in Pipes." Journal of the Institution of Civil Engineers, 1939.
• Sutherland, W. "The Viscosity of Gases and Molecular Force." Philosophical Magazine, 1893.