Duct sizing and airflow

duct velocityequivalent round ductair changes per hourACHvelocity pressureCFM

Duct velocity, equivalent round diameter, velocity pressure and air changes per hour — sizing ductwork and proving the room turns over.

Round Duct Air Velocity

v = \frac{4 \dot{V}}{\pi d^{2}}

Air velocity in a round duct from the volume flow and the duct diameter, the check that keeps branches quiet and mains efficient.

Equivalent Round Duct Diameter

D_e = 1.30 \frac{(ab)^{0.625}}{(a+b)^{0.25}}

Huebscher's equation for the round duct that has the same friction loss and airflow as a given rectangular duct of sides a and b.

Air Changes per Hour (ACH)

\mathrm{ACH} = \frac{3600 \, \dot{V}}{V_{room}}

How many times per hour a ventilation rate replaces the air in a room, the ventilation yardstick behind BTU/hr = 60 × CFM ÷ room volume.

Volumetric Flow Rate (Q = Av)

Q = A v

Flow through a duct or pipe: cross-sectional area times average flow velocity.

Dynamic Pressure (q = ½ρv²)

q = \tfrac{1}{2} \rho v^{2}

The kinetic energy per unit volume of a moving fluid — the pressure of motion itself.

How they fit together

Every duct calculation starts from Q = A × v, and the rest of this set is that identity dressed for the field. Equivalent round diameter converts a rectangular duct to the round duct with the same friction loss at the same flow — not the same area, which is the point people miss. Velocity pressure is what a pitot tube actually reads, and air changes per hour restates the flow as a room turnover so it can be checked against a code or an IAQ target.

Use velocity to check noise and comfort, equivalent round to look up friction on a duct chart, and ACH to argue about ventilation. The mistake is treating ACH as if it meant the room's air was replaced that many times per hour: real rooms mix, so at 6 ACH roughly 63% of the original air is displaced in the first hour, not 100%. The second mistake is sizing rectangular duct by matching cross-sectional area to the round duct it replaces — a flat, wide duct has far more wetted perimeter for the same area, so it loses more pressure and the fan runs out of static long before the drawing says it should.