The Pitot Tube and a Math Lesson

Accident investigators think icing of Pitot tubes used to determine aircraft air speed might have caused the crash of Air France flight 447 on 31 May 2009. Although journalists and others have talked about Pitot tubes, no account I’ve seen or read has described what a Pitot tube is or how it works. To non engineers, it’s just some sort of sensor.

Pitot tubes, and similar devices sense pressure changes, not airspeed. Pressure–along with other variables–lets you calculate fluid velocity. The “modern” Pitot tube dates to the early 1700’s when Henri Pitot discovered the relationship between pressure and the square of the velocity of a fluid.

The Pitot tube relies on two pressures; first, the total pressure of a fluid as it comes to a stop at the tube entrance–often called the stagnation point–and the static pressure of the ambient atmosphere outside the fluid flow. A similar device, the Prandtl tube makes the static measurement perpendicular to the fluid flow, as shown in the two diagrams below. Instrument manufacturers offer use the name “Pitot” to cover all types of pressure-to-velocity sensors.

Figures from Sears, F.W. and M. W. Zemansky, “University Physics, Part 1″ 3rd edition, Addison Wesley Publishing Company, 1963., pg. 329.

Subtracting the static pressure (p₁ or p_a) from the total pressure (p₂) yields the dynamic pressure (p_d):   p₂ - p₁ = p_d and p₂ = p₁ + p_d.

p_d  equals  1/2 * ρ * V²

You might look at this equation:

p₂ = p₁ + (1/2 * ρ * V²)

and say, “Wait a minute, pressure in grams per square centimeter, for example, has no unit of time, so where does the velocity come from?” Here’s where the math lesson comes in. In the US we continue to use old measurements while the rest of the world uses pascals (Pa) or kilopascal (kPa) as a unit of pressure. A pascal = kg/m*sec², so that set of basic units introduces time and the other units work out.  By knowing the density of air and the pressures from a Pitot tube, you can calculate velocity. You can find the equations and their derivations in many places, but when in doubt about units, always fall back on the International System of Units (SI) that expresses things in length, mass, and time.

(I hate most physics textbooks because they show many equations but lack worked-out examples that include measurement units. A few realistic examples would point students in the right direction.)

OK, you can see that blocking air flow or a pressure inlet can cause false velocity readings. So, how would you solve the problem? –Jon Titus