๐ Pitot Tube Calculator
Compute flow velocity from pitot tube differential pressure. Includes Bernoulli incompressible and isentropic compressibility corrections.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Fluid Mechanics
๐ Solver Telemetry
โ ACTIVE
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๐ฆ Fortran Code
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Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ฌ Pitot-Static Probe Schematic
๐ Configuration
Key Equations:
Bernoulli: V = โ(2ฮP/ฯ)
Isentropic: Pt/Ps = (1+(ฮณโ1)/2 Mยฒ)ฮณ/(ฮณโ1)
V = Mยทa; a = โ(ฮณRT)
Correction = Vcomp/Vincomp
Bernoulli: V = โ(2ฮP/ฯ)
Isentropic: Pt/Ps = (1+(ฮณโ1)/2 Mยฒ)ฮณ/(ฮณโ1)
V = Mยทa; a = โ(ฮณRT)
Correction = Vcomp/Vincomp
๐ Results
Configure inputs and click Compute to view results.
๐ Methodology
Bernoulli vs Compressible
For M < 0.3, Bernoulli's incompressible equation gives less than 2% error. Above M = 0.3, the isentropic pressure-Mach relation must be used to avoid significant velocity underestimation.
Correction Factor
The ratio Vcomp/Vincomp quantifies how much the incompressible assumption over- or under-estimates the true velocity. The chart shows this divergence as ฮP increases.
Assumptions
- Steady, one-dimensional flow at probe location.
- Perfect gas with constant ฮณ.
- No probe interference or alignment error.
- Subsonic isentropic relation (no normal shock for M > 1).
๐ Calculation Methodology: Pitot-Static Tube Velocity Measurement
Mathematical Model & Theory
A Pitot-static tube measures stagnation pressure $P_0$ and static pressure $P_\infty$. Applying Bernoulli's equation yields local flow velocity $V$:
$$V = C \sqrt{\frac{2(P_0 - P_\infty)}{\rho}}$$
$$\text{Compressible: } V = \sqrt{\frac{2\gamma R T}{\gamma-1}\left[\left(\frac{P_0}{P_\infty}\right)^{\frac{\gamma-1}{\gamma}} - 1\right]}$$
Assumptions
- Steady, frictionless streamline along probe stagnation point.
- Instrument coefficient $C pprox 0.98 - 1.00$.
Academic References
- ISO 3966: Measurement of fluid flow in closed conduits.
- White, F. M.: Fluid Mechanics, Ch. 6.
Worked Engineering Example
Problem Statement:
A pitot tube in air ($\rho = 1.20\text{ kg/m}^3$) reads $\Delta P = 450\text{ Pa}$ with $C = 0.995$. Calculate airspeed.
Step-by-step Solution:
1. $V = 0.995 \times \sqrt{2 \times 450 / 1.20} = 0.995 \times \sqrt{750} \approx 27.25\text{ m/s}$.
2. $V = 27.25 \times 3.6 = 98.1\text{ km/h}$.
Final Result:
Airspeed is $V = \mathbf{27.25\text{ m/s}}$ ($98.1\text{ km/h}$).
A pitot tube in air ($\rho = 1.20\text{ kg/m}^3$) reads $\Delta P = 450\text{ Pa}$ with $C = 0.995$. Calculate airspeed.
Step-by-step Solution:
1. $V = 0.995 \times \sqrt{2 \times 450 / 1.20} = 0.995 \times \sqrt{750} \approx 27.25\text{ m/s}$.
2. $V = 27.25 \times 3.6 = 98.1\text{ km/h}$.
Final Result:
Airspeed is $V = \mathbf{27.25\text{ m/s}}$ ($98.1\text{ km/h}$).