Calculate the local air velocity from a 0.5-inch-water total-minus-static pressure reading. Then estimate flow in a 12-inch circular duct using an explicitly assumed mean-to-local velocity ratio of 0.90.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Solve for | Local velocity | |
| Fluid density | 0.075 | lbm/ft³ |
| Probe velocity coefficient | 1 | dimensionless |
| Total minus static pressure | 0.5 | in H₂O (conventional) |
| Circular duct inside diameter | 12 | in |
| Mean / local velocity ratio | 0.90 | dimensionless |
2. Step-by-step Math
Convert pressure and density
ΔP = 0.5 × 249.08891 ≈ 125 Pa ρ = 0.075 × 0.45359237 / 0.3048³ ρ = 1.201384753047 kg/m³
The calculator uses conventional inches of water with 249.08891 Pa per inch. The air density is a specified input, not an automatic temperature or pressure correction.
Calculate the local velocity
Vlocal = C √(2ΔP/ρ) Vlocal = 1 × √(2 × 124.544455 / 1.201384753047) Vlocal = 14.399126202 m/s = 47.241227697 ft/s
C = 1 is the assumed probe velocity coefficient. Use a calibrated coefficient for a real probe.
Apply the supplied profile ratio
Vmean = 0.90 × Vlocal Vmean = 12.959213582 m/s = 42.517104927 ft/s
The mean/local ratio is independent of the probe coefficient. This 0.90 ratio is a benchmark assumption, not a universal correction for a centerline reading.
Estimate duct flow
D = 12 in = 1 ft ≈ 0.305 m A = π × 1² / 4 ≈ 0.785 ft² Q = Vmean × A × 60 Q = 42.517104927 × 0.785398163397 × 60 Q = 2,003.571367 ft³/min = 3,404.089383 m³/h
The calculator displays estimated duct flow in m³/h. The ft³/min result is actual flow at the entered density conditions, not standard flow.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Local velocity | 14.4 m/s / 47.2 ft/s | __________ |
| Estimated mean velocity | 13 m/s | __________ |
| Estimated duct flow | 3,400 m³/h | __________ |
| Actual flow in US units | 2,000 ft³/min | __________ |
Second check
Select Differential pressure and enter a local velocity of 47.241227697 ft/s. With the same density and coefficient, the calculator returns 124.544455 Pa, equivalent to 0.5 conventional in H₂O. Setting duct diameter to zero omits the flow estimate without changing local velocity.
4. Assumptions and Method
This uses the incompressible pitot relation. A single local measurement does not establish mean duct flow; use a justified profile ratio or a traverse. Probe alignment, calibration, density, compressibility and pressure-tap errors affect real measurements.
Equation definitions and implementation: Pitot-Tube Velocity Calculator. See also calculation methodology and other worked examples.