Velocity Pressure ↔ Air Velocity

Convert between velocity pressure and air velocity using Pitot-tube formulas. Imperial (4005 constant) and SI, with optional density correction.

Why velocity pressure?

A Pitot tube measures two pressures: total pressure (TP = SP + VP) and static pressure (SP). The difference is velocity pressure (VP). Because VP varies as the square of velocity, it is much easier to measure accurately than velocity itself — a Pitot tube can resolve a 10 fpm change at 1000 fpm when a mechanical anemometer would average over the same range.

The standard ACGIH Industrial Ventilation Manual (IV Manual) codifies the imperial relationship as V = 4005 × √VP, where V is in feet per minute (fpm) and VP is in inches of water column (in H₂O). This constant absorbs standard air density (0.075 lb/ft³ at 70 °F, 14.7 psia) and the unit conversion factor into a single number, making field calculations fast without a calculator.

In SI, the canonical formula is V = √(2 VP / ρ), derived directly from Bernoulli's equation. VP is in Pa, ρ is the air density in kg/m³, and V is in m/s. The SI formula makes the physics explicit and requires no memorization of special constants.

When to apply density correction

The 4005 constant and the SI standard density (1.204 kg/m³) assume sea-level, near-room-temperature air. Any significant deviation from those conditions introduces systematic error. Density correction is important in three scenarios:

  • High altitude (≥ 500 m / 1640 ft): Atmospheric pressure drops roughly 1.2 kPa per 100 m. At 1500 m (Denver, Colorado), air density is about 85% of sea-level, inflating the uncorrected velocity reading by approximately 8%.
  • Hot ducts (T > 40 °C / 104 °F): Process exhaust, furnace ventilation, and dryer ducts can run at 80–200 °C. Air at 100 °C (373 K) has a density of ≈ 0.946 kg/m³ vs 1.204 at 20 °C — a 21% reduction that directly translates to a velocity error if not corrected.
  • Pressurized ducts or cold environments: Supply air ducts under positive static pressure, cold storage ventilation, and outdoor systems in winter all shift density enough to matter in precision measurements.

psia vs psig — disambiguation

When entering pressure in psi, the distinction between absolute and gauge pressure matters. Atmospheric pressure at sea level is approximately 14.696 psi. Gauge pressure (psig) is measured relative to that ambient baseline — a gauge reading of 0 psig means you are at atmospheric pressure, not vacuum.

Absolute pressure (psia) includes that 14.696 psi offset, so 14.696 psia = 0 psig = atmospheric. For the density formula ρ = (P × M) / (R × T), you must use absolute pressure. Plugging in gauge pressure directly would give a density close to zero for near-atmospheric ducts, producing a wildly wrong result.

The ACGIH standard condition of 14.7 psia is essentially sea-level atmospheric (14.696 psia rounded). In this tool, selecting 'psi' reveals a gauge/absolute toggle. When psig is selected, 14.696 psi is added automatically before the density calculation.

Frequently Asked Questions

What is the 4005 constant?
The ACGIH formula V (fpm) = 4005 × √VP (in H₂O) is derived from the Bernoulli equation V = √(2 VP / ρ) expressed in imperial units. At standard ACGIH conditions (70 °F, 14.7 psia), air density is 0.075 lb/ft³. Converting that density and the in-H₂O-to-lb/ft² unit factor into the radical produces 4005. It is not an empirical constant — it is an exact unit conversion baked into a single number for convenience.
How accurate is V = 4005 × √VP?
Very accurate under standard conditions. Because VP is proportional to V², a ±5% error in measuring VP propagates to only ±2.5% in velocity (the square-root relationship halves the relative error). The main limitation is the assumption of standard air density. At significantly non-standard conditions (high altitude, hot ducts, pressurized systems), use the density-corrected SI formula or apply the correction factor √(ρ_standard / ρ_actual) to the result.
What is the difference between total pressure and velocity pressure?
Total pressure (TP) is the sum of static pressure (SP) and velocity pressure (VP): TP = SP + VP. Static pressure is the pressure exerted perpendicular to flow — it is what inflates a duct balloon or what a wall tap measures. Velocity pressure is the kinetic component created by the air moving; it acts in the direction of flow. A Pitot tube measures TP at the forward-facing port and SP at the side ports, allowing direct subtraction to get VP. This is why Pitot tubes can accurately measure duct velocity even in the presence of significant static pressure.
Why does air density matter?
Air density ρ appears directly in the Bernoulli equation: VP = ½ ρ V². For a given true velocity, denser air creates a higher VP reading. Conversely, if you observe a given VP and assume standard density when the air is actually lighter (high altitude or hot duct), you will underestimate the actual velocity. In occupational hygiene, this matters most when estimating capture velocities at exhaust hoods, verifying that a local exhaust ventilation (LEV) system meets design specifications, or sizing replacement air fans. A 10–15% velocity error can translate to significant contaminant exposure above the OEL.

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