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Subsonic pitot impact pressure
Impact pressure, the pitot total pressure minus the local static pressure p, for isentropic deceleration of a subsonic calorically perfect gas.
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- qc [Pa]
A pitot tube brings the flow to rest, and in isentropic flow the total pressure is pt = p[1 + (γ−1)M²/2]^(γ/(γ−1)). The impact pressure is qc = pt − p. At low Mach number it reduces to the dynamic pressure ½ρV², and it exceeds it by about M²/4 relative: 6 % at Mach 0.5, 27 % at Mach 1. This subsonic form holds until a shock forms ahead of the tube.
Impact pressure, the pitot total pressure minus the local static pressure p, for isentropic deceleration of a subsonic calorically perfect gas. At appreciable Mach number it exceeds the incompressible dynamic pressure ½ρV² by a factor that grows with M².
Calculator
- Dynamic pressure, ½γpM²14,000 Pa
- Compressibility factor, qc/q1.064
- Pitot total pressure, p + qc94,900 Pa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The impact pressure is 14.897 kPa, 6.407 % more than the incompressible dynamic pressure of 14 kPa.
- The pitot total pressure is 94.897 kPa, 1.186 times the static pressure.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Pa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| M Mach number | 0.05 to 0.95 | 140.1 | 63,000 | 62,850 | +10% | +22.6 % |
| p Static pressure | 5,000 to 110,000 Pa | 931.1 | 20,480 | 19,550 | +10% | +10 % |
| γ Heat-capacity ratio | 1.1 to 1.67 | 11,710 | 17,760 | 6,044 | +10% | +9.96 % |
Sweep of Mach number
| Mach number | Impact pressure (Pa) |
|---|---|
| 0.05 | 140.1 |
| 0.1625 | 1,489 |
| 0.275 | 4,316 |
| 0.3875 | 8,729 |
| 0.5 | 14,900 |
| 0.6125 | 23,050 |
| 0.725 | 33,510 |
| 0.8375 | 46,660 |
| 0.95 | 63,000 |
Sweep one variable
Variables and how each one contributes
Impact pressure
What the equation gives you. Everything else feeds it.
Static pressure
The static pressure, in Pa. Scales the impact pressure in direct proportion. Raising it by 10 % (to 88,000) moves the result by +10 %, from 14,900 to 16,390 Pa.
Heat-capacity ratio
The heat-capacity ratio cp/cv of the gas, about 1.4 for air. A lower γ (hotter, more complex gas) changes the compressible-flow exponents and the sizes of the shock and expansion effects. Raising it by 10 % (to 1.54) moves the result by +9.96 %, from 14,900 to 16,380 Pa.
Mach number
The flight Mach number (subsonic). Raises the impact pressure with roughly the square of M, a little faster at higher M. Raising it by 10 % (to 0.55) moves the result by +22.6 %, from 14,900 to 18,260 Pa.
Worked example with the values above
- Temperature ratio: 1 + (γ − 1)M²/2 = 1 + 0.2 × 0.25 = 1.05.
- Pressure ratio: 1.05^3.5 = 1.186213.
- qc = p × (ratio − 1) = 80,000 × 0.186213 = 14,897.01 Pa.
Assumptions and limits
- Calorically perfect gas with a constant heat-capacity ratio, and isentropic deceleration to the pitot tube.
- Subsonic flow for the pitot and calibrated-airspeed formulas; a shock forms ahead of the probe above Mach 1.
Common mistakes
- Using the incompressible ½ρV² formula at high Mach number, where it underestimates impact pressure.
- Confusing true, equivalent and calibrated airspeed.
- Treating a recovery temperature as a static temperature.
Statistics and uncertainty
Air-data conversions are exact for the stated models, so errors come from the instrument: pitot and static ports carry position errors of 1 % to 2 % in speed, and a poorly designed temperature probe can have a recovery factor that differs from 0.9 by several per cent.
Where it is used
- Converting instrument readings to speed, Mach number and static temperature.
- Understanding what the airspeed indicator and temperature probes really measure.
Maths you need
- Stagnation point: where the flow is brought to rest
- Dynamic pressure: q = ½ρV²
- Speed of sound: a = √(γRT)