Pitot Tubes

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How can wasps endanger a commercial airline flight?

Big Ideas: 
  • Pitot tubes are used to measure speed of fluid.
  • Pitot tubes are applied to determine the air speed of aircraft.
  • Bernoulli's equation forms the basic explanation of how a Pitot tube measures fluid speed.

On November 21, 2013, an A330 flight had to make an emergency landing, shortly after takeoff at Brisbane Airport 1 . The problem was with a Pitot tube used to measure air speed of the aircraft, which is the speed of the aircraft relative to the air.   Fig. 1 shows a picture of the underside of the airplane where there are multiple Pitot tubes installed.  The Captain's Pitot tube was giving false readings of air speed causing the emergency landing.  The malfunction was due to blockage of the Pitot tube by a nest of a mud-dauber wasp 2.   Why would such a blockage cause a malfunction?  In this article we discuss what a Pitot tube is and how it works.

Fig. 1.  The underside of the A330 involved in an emergency landing.  Multiple Pitot tubes are installed underneath.  The Captain's Pitot tube was giving false readings of air speed.  The cause of malfunction was a blockage by a nest of a mud-dauber wasp.   Photo credit: Australian Transport Safety Bureau 3

What is a Pitot tube?

Pitot tubes are named after Henri Pitot, a French engineer in the 18th century.  The basic design of a Pitot tube is shown in Fig. 2.  A Pitot tube has a tube into which fluid enters and is quickly decelerated to zero velocity at the entrance of the tube because the  tube is not open on both ends.  Pitot tubes are used to determine the speed at which fluid flows relative to the Pitot tube.  Notice that a Pitot tube can generally be used to measure the speed of liquids and gases, but in the following we will discuss the example of air.  The pink and dashed stream line in Fig. 2 shows air travelling outside the tube with speed $ v_{1} $ relative to the Pitot tube.  The pressure outside the Pitot tube is $ P_{1} $, which is the atmospheric pressure surrounding the Pitot tube.  The air along the stream line shown in Fig. 2 is decelerated to zero velocity, relative to the Pitot tube, at the entrance of the Pitot tube and the pressure in the tube is $ P_{2} $.  Often a Pitot tube will have another tube around it that has slits in it, as shown in grey in Fig. 2.  Since the streaming air is not entering this outer tube, the pressure inside the outer tube is just the atmospheric pressure, $ P_{1} $, at the airplane's current elevation .   As we will see it is the difference in pressure between $ P_{1} $ and $ P_{2} $ that will be useful to determine the air speed, $ v_{1} $.

 

Fig. 2.  A cartoon drawing of a Pitot tube.  Fluid along a stream line, shown in pink and dashed, enters the inside tube at speed $ v_{1} $.  The fluid is quickly decelerated to zero speed, $ v_{2} = 0 $,  at the entrance of the tube.  The pressure of the fluid outside the Pitot tube is $ P_{1} $.  In the case of our airplane example, $ P_{1} $ is the atmospheric pressure at the airplane's current elevation.  The pressure inside the inner tube into which the fluid decelerates is $ P_{2} $.  The pressure in the outer tube is the atmospheric pressure, $ P_{1} $, because no fluid flows directly into it.  Bernoulli's equation relates the speeds $ v_{1} $ and $ v_{2} $ and  the pressures $ P_{1} $ and $ P_{2} $.  From this relation we can find the speed $ v_{1} $ of the fluid relative to the Pitot tube.

 

 

Fig. 3.  A Pitot tube installed on a Kamov Ka-26 helicopter.  The small holes are to measure the atmospheric pressure outside of the Pitot tube.  Photo credit:  Zátonyi Sándor 4 .

How does a Pitot tube work?

The basic principle of how a Pitot tube can be used to measure the relative speed of a fluid entering the tube involves Bernoulli's equation.  Bernoulli's equation relates the pressure and velocity of fluid along a stream line.  A stream line indicates the path of travel of fluid.  For the pink and dashed stream line in Fig. 2, Bernoulli's equation states that

$  P_{1} + \frac{1}{2} \rho v_{1}^{2} + \rho g y_{1} = P_{2} + \frac{1}{2} \rho v_{2}^{2} + \rho g y_{2} $    (Eq. 1)

where $ y_{1} $ and $ y_{2} $ are vertical height positions along the stream line and $ \rho $ is the density of the fluid.  Here $ y_{1} = y_{2} $ because there is no height differences involved along the stream line.  The speed of the fluid inside the Pitot tube, relative to the Pitot tube, is $ v_{2} = 0 $ so that Eq. 1 becomes

$ P_{1} + \frac{1}{2} \rho v_{1}^{2} = P_{2} $.    (Eq. 2)

We can now solve for the speed $ v_{1} $ of the fluid outside of the Pitot tube from Eq. 2 which gives

$  v_{1} = \sqrt{\frac{2}{\rho}(P_{2} - P_{1})} $.    (Eq. 3)

The speed of the fluid relative to the Pitot tube, $ v_{1} $, can be determined from the difference in pressure outside and inside the Pitot tube.  This difference in pressure can be measured with a pressure measurement device. 

A Pitot tube on an aircraft can become blocked by ice, dirt, or in the case of the incident mentioned in the introduction, a nest from an insect.  In this case, the pressure reading $ P_{2} $ inside the Pitot tube is affected, resulting in incorrect air speed measurements (measurements of $ v_{1} $).  Correct air speed readings are critical for maintaining lift of the airplane and for flight safety, which makes properly functioning Pitot tubes an essential part of the aircraft.

Pitot tubes are not only used for air speed, they are also used on boats for water speed, and various industrial applications where the speed of fluid needs to be measured.  Bernoulli's equation as used in this article still applies even though the fluid is different. 

Comments

Dear Gunnar, Thank you very

Dear Gunnar,
Thank you very much for the additional information. I would have assumed that there is a back-up system in modern airplanes or at least a system that tells the pilot that something is wrong.

Thanks again,
Georg

Dear Ladies & Sirs! I like

Dear Ladies & Sirs!
I like the way You present the troubles of the Pitot tube! It is a wounderful equipment when it works but has led to terrible accidents for instance outside the shores of Brazil in 2009 with the Air France Airbus af 477 when it. is supposed that the Pitot tubes were jammed with ice from a thunderstorm. Now in the latest Airbus accidents with an Airbus flight QZ8105 from Air Asia over the Java Sea it. is presumably the same cause again. The worst thing seems to be that the automatic control system of the Airbus is directly guided by Pitot tubes that can give completely misleading guidance. Pitot made his pioneering work I think for ships in the 18th century. Now I have read there is a firm that delivers complentary laser-speed system. The finesse with that is that You don't have to remove the Pitot tubes but could give a correction to frozen Pitot tubes which in the worst cases otherwise might lead to airplane disasters.
Yours sincerely!
Gunnar (W Bergman)
BT MEDIA
technical journalist
energy technology
& technical physics

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