Calculation Method

The physics behind the numbers.

Overview

DuctStatic uses the total pressure loss method, which is the standard approach for HVAC duct system design. For each segment of duct, total pressure loss is the sum of friction loss (straight runs) and dynamic loss (fittings and transitions). The path from fan to terminal with the highest total loss is the critical path, and that number determines the required fan static pressure.

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

Air Properties

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

At sea level and 68°F (20°C), air density is 1.204 kg/m³ and viscosity is 1.825×10⁻⁵ Pa·s. These are the defaults if no site conditions are entered.

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.

This is the same equation used in fluid mechanics and hydraulics engineering worldwide. It accounts for both smooth-pipe and fully rough turbulent behavior, and everything in between.

Fitting Loss (Dynamic Losses)

Fitting losses use the loss coefficient method:

ΔP = Co × Pv

Co (also written ζ or C) is a dimensionless coefficient that captures how much velocity pressure a fitting converts to heat through turbulence and flow separation. Co = 1.0 means the fitting dissipates energy equal to the full velocity pressure. Co = 0.1 is a low-loss fitting.

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

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.

Fan Static Pressure

The required fan static pressure is the critical path loss multiplied by the safety factor:

Fan SP = Critical Path Loss × (1 + SF)

For systems where the fan has both supply and return ductwork attached (dual-inlet), the critical supply path loss and critical return path loss are summed before applying the safety factor.

Sources

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