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Pitot Tube Calculator

Flow speed from dynamic pressure: v = √(2ΔP/ρ)

Parameters

Paⓘ
kg/m³ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Velocity:
91.29;m/s91.29;m/s
Speed in km/h:
328.63;km/h328.63;km/h

Examples

Air ΔP=500 Pa

ρ=1.2 kg/m³.

    Water probe

    ΔP=10 kPa.

      Visualization

      Pitot Tube — Velocity from Stagnation Pressure

      A Pitot tube (Henri Pitot, 1732; improved by Henri Darcy) measures fluid velocity by sensing stagnation (total) pressure where the flow is brought to rest at the probe tip. From Bernoulli along a streamline: P₀ = P + ½ρv², where P₀ is stagnation pressure, P is static pressure, and v is approach velocity.

      Dynamic pressure q = ½ρv² = P₀ − P = ΔP. Solving gives v = √(2ΔP/ρ). Units check: √(Pa/(kg/m³)) = √(m²/s²) = m/s. For air at ρ = 1.2 kg/m³ and ΔP = 500 Pa, v ≈ √(1000/1.2) ≈ 29 m/s (~105 km/h).

      A Pitot-static probe has two ports: forward-facing (stagnation) and side ports (static pressure in undisturbed flow). Aircraft pitot tubes feed airspeed indicators; calibration accounts for altitude (density) and compressibility at high Mach number.

      The probe must point directly into the flow — misalignment causes underestimation. Blockage, ice formation (aviation hazard), and turbulence can cause errors. In pipes, velocity varies across the section — traverse measurements at several radii are needed for average flow.

      Relation to other formulas: Torricelli v = √(2gh) is the same with ΔP = ρgh. Venturi measures volume flow from ΔP; Pitot measures point velocity. Dynamic pressure appears in drag formulas (pressure drag scales with ρv²).

      Compressible corrections at high subsonic/supersonic speeds use isentropic relations. For incompressible water or low-speed air, v = √(2ΔP/ρ) is standard in hydraulics labs and wind tunnels.

      Key Concepts

      • P₀ = P + ½ρv² (Bernoulli stagnation)
      • v = √(2ΔP/ρ); q = ½ρv²
      • Pitot-static: stagnation vs static ports
      • ΔP = dynamic pressure (Pa)
      • Must align probe with flow vector
      • Local v, not average — traverse for Q

      Real-World Applications

      • Aircraft airspeed and altitude instruments
      • Wind tunnel velocity calibration
      • River, pipe, and duct flow profiling
      • Formula 1 and aerospace aerodynamic testing
      • Class 12 Bernoulli and Pitot demonstrations
      • Industrial anemometry and HVAC traverse

      Explore Further

      More fluid mechanics tools

      Physics Equations

      Bernoulli (Pitot):
      v=2ΔPρv = \sqrt{\frac{2\Delta P}{\rho}}
      Stagnation:
      P0=P+12ρv2P_0 = P + \frac{1}{2}\rho v^2

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Stagnation Pressure

      Equation:

      P0=P+12ρv2P_0 = P + \frac{1}{2}\rho v^2

      Explanation:

      Flow stops at stagnation point; KE → pressure.

      2

      Step 2: Pitot Relation

      Equation:

      v=2ΔPρv = \sqrt{\frac{2\Delta P}{\rho}}

      Explanation:

      ΔP = P₀ − P (dynamic pressure).

      3

      Step 3: Substitute

      Calculation:

      v=2×50001.2=91.2871 m/sv = \sqrt{\frac{2 \times 5000}{1.2}} = 91.2871 \text{ m/s}

      Result:

      v=91.2871m/sv = 91.2871 m/s
      4

      Step 4: Check Units

      ΔP in Pa, ρ in kg/m³ → v in m/s.

      Explanation:

      √(Pa/(kg/m³)) = √(m²/s²) = m/s.

      5

      Step 5: Applications

      Aircraft airspeed, pipe velocity.

      Explanation:

      Correct for compressibility at high Mach.

      6

      Step 6: Bernoulli Link

      Same as Torricelli with ΔP = ρgh.

      Explanation:

      Pitot measures local flow speed.

      Frequently Asked Questions (FAQ)

      Pitot vs Venturi?

      Pitot: point velocity from ΔP; Venturi: integrated Q in pipe.

      Compressibility?

      High-speed air needs isentropic corrections.

      Water hammer?

      Different phenomenon — pressure transients.

      Two holes?

      Pitot-static: stagnation + static ports.

      Turbulent profile?

      Pitot gives local v; traverse for average.

      Practice MCQs

      1. Stagnation pressure is:
      2. v from Pitot scales as:
      3. Pitot measures:
      4. ΔP = 0 means:
      5. Bernoulli assumes:
      6. Pitot hole misaligned:

      Related Calculators

      These tools connect to the same physics concepts used in this calculator.

      Hydrostatic PressureCalculate pressure at depth in a static fluid using P = ρgh.Continuity EquationFind velocity from A₁v₁ = A₂v₂ for incompressible pipe flow.Torricelli's LawEfflux speed v = √(2gh) and flow rate from a tank hole.Stokes' LawViscous drag and terminal velocity of a sphere in fluid.Projectile MotionCalculate and visualize the path of objects under the influence of gravity.Related Mechanics topic.Ideal Gas LawCalculate pressure, volume, temperature, and moles for ideal gases.Related Thermodynamics topic.Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.