Pitot Tube

Fluid velocity measurement in ducts using stagnation pressure. Theory, formulas, worked examples and interactive graphs.

Conceptual context

The Pitot tube is a pressure measurement instrument used to calculate the flow velocity of a fluid. Its operation is fundamentally based on the conversion of the fluid's kinetic energy into pressure energy. It is a critical tool in modern aviation, used to measure the airspeed of aircraft, as well as in hydraulic and industrial engineering for monitoring flow rates in pipes and open channels.

By combining a measurement of total pressure with static pressure, the Pitot tube allows for the local speed of a fluid to be determined in a simple, reliable, and robust way. It is grounded in the physical principle that any moving fluid forced to come to a halt will experience a local increase in pressure proportional to the square of its original velocity—a phenomenon that can be quantified with great mathematical precision.

🟢 Essential level

The basic idea of the Pitot tube is to measure the force with which the fluid "hits" the tube's frontal inlet. This "impact" creates a pressure signature that tells us how much kinetic energy the fluid possessed before encountering the probe.

• Stagnation Point: When a fluid moves toward an open tube oriented head-on to the stream, the fluid entering hits the air or liquid already inside the tube and comes to a complete stop. This specific point in space where the velocity relative to the probe is zero is called the stagnation point.
• Stagnation Pressure: Upon stopping, the energy the fluid carried due to its movement (kinetic energy) is transformed into extra potential energy in the form of pressure.

This is why at the tube's mouth, the measured pressure is higher than the surrounding ambient pressure.

• Deducing Velocity: The faster the fluid moves, the greater the pressure spike at the stagnation point. By measuring this pressure difference, we can back-calculate the fluid's original speed using established physical laws.

Key concepts every student should remember:

1. Static Pressure: The actual pressure of the moving fluid, equivalent to what a sensor would feel if it were traveling exactly at the same speed as the flow.
2. Total Pressure (or Stagnation Pressure): The maximum pressure achieved when the fluid is forced to convert all its motion into pressure.

🔵 Formal level

Basic formulas

Before reading the velocity, identify the two pressures: the stagnation pressure at the front opening and the static pressure at the side. Their difference is the dynamic pressure, from which the velocity follows. If the tube is not aligned with the flow, the reading is biased.

The operating principle is derived directly from the Bernoulli Equation. If Bernoulli is applied between a point in the undisturbed free stream and the stagnation point at the tube inlet, assuming incompressible and steady flow, the result links static pressure, stagnation pressure, and kinetic energy.

At the stagnation point, the local velocity becomes zero, so free-stream kinetic energy is converted into pressure rise. This reading is organized with the pressure difference between total and static pressure:

Pressure difference (Pitot)

From this point, we can solve for the fluid velocity $v$ based on the measured pressure difference between the stagnation point and the free stream:

Ideal flow velocity (Pitot)

Real student questions

• Why does the Pitot tube have a tiny hole in the back? This is a drain hole. It allows rainwater, condensation, or melting ice to exit the system via gravity, preventing the formation of liquid plugs that would ruin the pressure readings.
• Can it be used to measure a river's speed? Yes. By submerging an L-shaped tube into the water, the water rises in the vertical section. The reached height above the river surface can be used to estimate speed with a simplified hydrostatic-energy relation.
• What is "indicated airspeed" vs "true airspeed"? Airspeed indicators are calibrated for the air density at sea level. At high altitudes where the air is much thinner (less dense), the "true airspeed" is higher than the "indicated airspeed" because more speed is required to generate the same impact pressure.

Final synthesis

The Pitot tube is the purest practical application of the conservation of energy in fluids. It allows us to "feel" the velocity of a stream through the pressure it generates when it is brought to a halt. Its mechanical simplicity and extreme robustness make it the global gold standard for aerial navigation and industrial diagnostics. It teaches us that, in many instances in physics, the best way to understand motion is by forcing it to reveal itself through its own moment of stopping.