Pitot tube (thing)

A Pitot tube (invented by the French scientist Henri Pitot) is a device to measure fluid velocity. It is commonly used in air speed indicators in airplanes and wind tunnels; in anemometers, and in devices to measure the flow in rivers and canals.

A conceptual schematic of the Pitot tube is given below:

          
          
        →
        →       _____________
        →      =___________PT|
        →                  | |
        →                  | |
        v                  | |
                           | |
                           | |
                 PS        | |
         _______ ↓ ________| |_________
         ///////| |////////| |/////////
                | |        | |
                |~|   ↑    | |
                | |   | h  | |
                | |   ↓    | | 
                | |        |~|
                | |________| |
                |____________|

The Pitot tube consists of a pipe with its opening perpendicular to the flow. At the tip of the tube (the stagnation point), the streaming fluid is brought from a velocity v to zero velocity. The pressure in the tube is called the total pressure P_T, and it is the sum of the static pressure and dynamic pressure.

The other end of the Pitot tube has an opening parallel to the flow. This opening is called the static pressure hole or tap. The dimensions of the hole are such that the fluid in the hole remains at rest. As a result, the tap measures the static pressure P_S.

The pressure difference between both ends of the Pitot tube (P_T - P_S) yields the dynamic pressure, and this is a function of the fluid velocity. In this example, the pressure difference is measured by a u-tube manometer containing a liquid, although modern Pitot tubes generally have a different configuration and use a pressure transducer (a u-tube manometer would not work properly in an airplane).

The height differential between the two legs of the manometer is proportional to the dynamic pressure:

P_T - P_S = ρ_L g h

where ρ_L is the density of the liquid inside the manometer and g is the gravitational acceleration.

The fluid velocity follows directly from Bernoulli's equation:

P_T + 0 + 0 = P_S + ½ ρ v² + 0

Note that the height difference between the two openings of the Pitot tube is neglected (no potential energy difference). The fluid velocity can be calculated with:

v = √(2(P_T-P_S) / ρ)

where ρ is the density of the flowing fluid. These values are tabulated in the literature. For airplane use, the air density is also a function of altitude so this has to be taken into account.

The Pitot tube is based on the assumptions of Bernoulli's Equation, and the velocity calculation has to be adjusted if the conditions do not meet the assumptions anymore. For instance, for supersonic speed, a correction has to be made for the shock wave. In spite of the restrictions of Bernoulli's equation, the Pitot tube is surprisingly accurate for velocity measurements over a wide range.