Air Velocity Pressure (the 4005 Rule)

Hold a tube in a moving airstream with its open end facing upstream and the air that runs into it has to stop. All the energy it was carrying as motion turns into pressure, and the difference between what that tube reads and what a hole in the duct wall reads is the velocity pressure — the part of the total pressure that exists only because the air is moving. That is what a pitot tube measures, and the whole reason a balancer carries one: static pressure tells you what the fan is fighting, velocity pressure tells you how fast the air is going, and only the second one converts into cfm.

The physics is $\mathrm{VP} = \tfrac{1}{2}\rho V^2$, the same Bernoulli term that appears in every fluids course. The trade does not write it that way. It writes $V = 4005\sqrt{\mathrm{VP}}$, with V in feet per minute and VP in inches of water gauge, and 4005 is what $\tfrac{1}{2}\rho V^2$ collapses to once you substitute standard air and both unit conversions and never mention any of them again. Work it backwards and the constant confesses: 4005 has a density of 0.0751 lb/ft³ — 1.2035 kg/m³ — packed inside it, which is dry air at about sea level and room temperature. The general form it came from is $V = 1096.7\sqrt{\mathrm{VP}/\rho}$ with ρ in lb/ft³, and $1096.7/\sqrt{0.075}$ is 4005 to four figures.

Which means 4005 is wrong everywhere the air is not standard, and it is wrong in a direction that flatters the report. Thinner air produces less velocity pressure at the same speed, so a traverse worked with 4005 in thin air returns a velocity that is too low, and every cfm on the sheet is short by the same fraction. In Calgary, at about 1 045 m, the air is roughly 12 % thinner and the constant should be nearer 4265 — the 4005 answer is about 6 % low. In Denver it is worse. Hot air does the same thing: 200 °C air in an oven exhaust is 40 % less dense than the 4005 assumes. The rule of thumb is fine on a rooftop unit at sea level in shirtsleeve weather and nowhere else, and the fix is not difficult — find the actual density and use the 1096.7 form.

Two field notes about the reading rather than the arithmetic. First, velocity goes as the SQUARE ROOT of the pressure, which is a mixed blessing: it halves your percentage error at high readings and doubles the pain at low ones. At 0.01 in w.g. a few thousandths of manometer drift is tens of percent of velocity, which is why pitot traverses have a practical floor around 600 fpm and why anything slower wants a hot-wire anemometer. Second, one reading is not a traverse. Duct velocity is not uniform across the cross-section, so the standard is a log-Tchebycheff or equal-area grid of points averaged as VELOCITIES, not as pressures — averaging the pressures first and taking one square root at the end always reads high, because the square root is concave and Jensen's inequality does not care how busy you are.