Tubo Pitot-statico: un dispositivo per misurare la velocità del flusso d'aria
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Overview
Fonte: David Guo, College of Engineering, Technology, and Aeronautics (CETA), Southern New Hampshire University (SNHU), Manchester, New Hampshire
Un tubo pitot-statico è ampiamente utilizzato per misurare velocità sconosciute nel flusso d’aria, ad esempio, viene utilizzato per misurare la velocità dell’aereo. Secondo il principio di Bernoulli, la velocità dell’aria è direttamente correlata alle variazioni di pressione. Pertanto, il tubo pitot-statico rileva la pressione di ristagno e la pressione statica. È collegato a un manometro o a un trasduttore di pressione per ottenere letture di pressione, che consente la previsione della velocità dell’aria.
In questo esperimento, una galleria del vento viene utilizzata per generare determinate velocità dell’aria, che viene confrontata con le previsioni del tubo pitot-statico. Viene inoltre studiata la sensibilità del tubo pitot-statico dovuta al disallineamento rispetto alla direzione del flusso. Questo esperimento dimostrerà come viene misurata la velocità del flusso d’aria utilizzando un tubo pitot-statico. L’obiettivo sarà quello di prevedere la velocità del flusso d’aria in base alle misure di pressione ottenute.
Principles
Il principio di Bernoulli afferma che un aumento della velocità di un fluido si verifica contemporaneamente a una diminuzione della pressione e viceversa. In particolare, se la velocità di un fluido diminuisce a zero, la pressione del fluido aumenterà al massimo. Questo è noto come pressione di ristagno o pressione totale. Una forma speciale dell’equazione di Bernoulli è la seguente:
Pressione di ristagno = pressione statica + pressione dinamica
dove la pressione di ristagno, Po, è la pressione se la velocità del flusso è ridotta a zero isentropicamente, la pressione statica, Ps, è la pressione che il fluido circostante sta esercitando su un dato punto, e la pressione dinamica, Pd, chiamata anche pressione ram, è direttamente correlata alla densità del fluido, ρe alla velocità del flusso, V, per un dato punto. Questa equazione si applica solo al flusso incomprimibile, come il flusso di liquido e il flusso d’aria a bassa velocità (generalmente inferiore a 100 m/s).
Dall’equazione di cui sopra, possiamo esprimere la velocità del flusso, V, in termini di differenziale di pressione e densità del fluido come:
Nel 18° secolo, l’ingegnere francese Henri Pitot inventò il tubo di Pitot [1], e a metà del 19° secolo, lo scienziato francese Henry Darcy lo modificò nella sua forma moderna [2]. All’inizio del 20° secolo, l’aerodinamico tedesco Ludwig Prandtl combinò la misurazione della pressione statica e il tubo di Pitot nel tubo pitot-statico, che è ampiamente usato oggi.
Uno schema di un tubo pitot-statico è mostrato nella Figura 1. Ci sono 2 aperture nei tubi: un’apertura affronta il flusso direttamente per percepire la pressione di ristagno e l’altra apertura è perpendicolare al flusso per misurare la pressione statica.
Figura 1. Schema di un tubo pitot-statico.
Il differenziale di pressione è necessario per determinare la velocità del flusso, che viene tipicamente misurata dai trasduttori di pressione. In questo esperimento, un manometro a colonna liquida viene utilizzato per fornire una buona visuale per misurare la variazione di pressione. Il differenziale di pressione è determinato come segue:
dove Δh è la differenza di altezza del manometro, ρL è la densità del liquido nel manometro e g è l’accelerazione dovuta alla gravità. Combinando le equazioni 2 e 3, la velocità del flusso è prevista da:
Procedure
Results
Representative results are shown in Table 1 and Table 2. The results of the experiment are in good agreement with the actual wind speed. The Pitot-static tube accurately predicted the airspeed with a maximum percentage of error of approximately 4.2%. This can be attributed to errors in setting the wind tunnel airspeed, errors reading the manometer and instrument errors of the Pitot-static tube.
Table 1. Calculated airspeed and error based on manometer reading at various wind tunnel speeds.
| Wind tunnel airspeed (mph) | Manometer reading (in. water) | Calculated airspeed (mph) | Percent error (%) |
| 50 | 1.1 | 48.04 | -3.93 |
| 60 | 1.6 | 57.93 | -3.45 |
| 70 | 2.15 | 67.16 | -4.06 |
| 80 | 2.8 | 76.64 | -4.20 |
| 90 | 3.6 | 86.90 | -3.45 |
| 100 | 4.4 | 96.07 | -3.93 |
| 110 | 5.4 | 106.43 | -3.25 |
| 120 | 6.5 | 116.77 | -2.69 |
| 130 | 7.8 | 127.91 | -1.61 |
Table 2. Calculated airspeed and error based on manometer reading at various angles of attach.
| Pitot-Static Tube angle of attack (°) | Manometer readings (in water) | Calculated airspeed (mph) | Percent error (%) |
| 0 | 4.4 | 96.07 | 0.00 |
| 4 | 4.5 | 97.16 | 1.13 |
| 8 | 4.5 | 97.16 | 1.13 |
| 12 | 4.6 | 98.23 | 2.25 |
| 16 | 4.65 | 98.76 | 2.80 |
| 20 | 4.7 | 99.29 | 3.35 |
| 24 | 4.55 | 97.69 | 1.69 |
| 28 | 4.3 | 94.97 | -1.14 |
In Table 2, the percentage error is compared against the zero-angle case in Table 1. The results indicate that the Pitot-static tube is insensitive to misalignment with flow directions. The highest discrepancy occurred at an angle of attack of about 20°. A 3.35% error was obtained with respect to the zero angle reading. As the angle of attack increased, both the stagnation and static pressure measurements decreased. The two pressure readings tend to compensate each other so that the tube yields velocity readings that are accurate to 3 – 4% for angles of attack up to 30°. This is the chief advantage of the Prandtl design over other types of Pitot tubes.
Applications and Summary
Airspeed information is critical to aviation applications, such as for aircraft and drones. A Pitot-static tube is typically connected to a mechanical meter to show the airspeed at the front panel in the cockpit. For commercial aircraft, it is also connected to the onboard flight control system.
Errors in pitot-static system readings can be extremely dangerous. There are typically 1 or 2 redundant Pitot-static systems for commercial aircraft. To prevent ice buildup, the Pitot tube is heated during flight. Many commercial airline incidents and accidents have been traced to a failure of the Pitot-static system. For example, in 2008 Air Caraibes reported two incidents of Pitot tube icing malfunctions on its A330s [3].
In industry, the airspeed in duct and tubing can be measured with Pitot tubes where an anemometer or other flow meters would be difficult to install. The Pitot tube can be easily inserted through a small hole in the duct.
In this demonstration, the use of Pitot-static tubes was examined in a wind tunnel and the measurements were used to predict airspeed in the wind tunnel. The results predicted by the Pitot-static tube correlated well with the wind tunnel settings. The sensitivity of possible misalignment of the Pitot-static tube was also investigated and it was concluded that the Pitot-static tube is not particularly sensitive to misalignment up to and angle of attack of 28°.
References
- Pitot, Henri (1732). "Description d'une machine pour mesurer la vitesse des eaux courantes et le sillage des vaisseaux". Histoire de l'Académie royale des sciences avec les mémoires de mathématique et de physique tirés des registres de cette Académie: 363–376. Retrieved 2009-06-19.
- Darcy, Henry (1858). "Note relative à quelques modifications à introduire dans le tube de Pitot" (PDF). Annales des Ponts et Chaussées: 351–359. Retrieved 2009-07-31.
- Daly, Kieran (11 June 2009). "Air Caraibes Atlantique memo details pitot icing incidents". Flight International. Retrieved 19 February 2012.
Transcript
Unknown speeds in an airflow, for example, the air speed of an aircraft, are typically measured using a pitot-static tube. The pitot-static tube is based on Bernoulli’s principle, where the increase in speed of a fluid is directly related to pressure variations.
The fluid itself exerts pressure on the surroundings, called static pressure. If the speed of the fluid is zero, the static pressure is at its maximum. This pressure is defined as the stagnation pressure, or total pressure.
As the fluid speed increases, it exerts static pressure on the surroundings as well as forces due to the velocity and density of the fluid. These forces are measured as the dynamic pressure, which is directly related to the fluid density and fluid velocity.
According to Bernoulli’s principle, the stagnation pressure is equal to the sum of the static pressure and dynamic pressure. Thus, if we are interested in determining the fluid velocity, we can substitute the equation for dynamic pressure and solve for the velocity as shown. The difference between the stagnation pressure and the static pressure is called the pressure differential, delta P.
So how do we measure the stagnation and static pressures in order to determine delta P and therefore velocity? This is where the pitot-static tube comes in.
A pitot-static tube has two sets of openings. One opening is oriented directly into the airflow, while a second set of openings is perpendicular to the airflow. The opening facing the flow senses the stagnation pressure, and the openings perpendicular to the flow sense the static pressure. The pressure differential, delta P, is then measured using either a pressure transducer or a fluid manometer.
A fluid manometer is a U-shaped tube containing a liquid. At ambient pressure, where delta P equals zero, the fluid in the manometer is level at an initial height. When the manometer experiences a pressure differential, the manometer fluid height changes, and we can read the change in height as delta h.
We can then calculate the pressure differential, delta P, which is equal to the density of the liquid in the manometer, times gravitational acceleration, times delta h. Then, by substituting the calculated pressure differential into our earlier equation, we can calculate the fluid speed.
In this experiment, you will measure different wind speeds in a wind tunnel using a pitot-static tube and a fluid manometer. You will then calculate the percent error in the air speed measurements collected using a misaligned pitot-static tube.
For this experiment, you will need access to an aerodynamic wind tunnel with a test section of 1 ft by 1 ft and a maximum operating air speed of 140 mph. You will also need a pitot-static tube and a manometer filled with colored oil, but marked as water-inch graduations.
Begin by connecting the two leads of the pitot-static tube fitting to the tube ports of the manometer using soft tubing. Now, open the test section and insert the pitot-static tube into the front threaded fittings. Orient the pitot-static tube so that the sensing head is in the center of the test section, pointing upstream. Use a handheld inclinometer to measure the angle of attack, and adjust the pitot tube to reach an angle of zero.Then close the front and top of the test section.
Now, turn on the wind tunnel, set the velocity to 50 mph, and observe the height difference on the manometer. Record the height difference. Next, increase the wind speed to 60 mph and again record the height difference on the manometer.
Repeat this procedure, increasing the wind speed, in increments of 10 mph, until the wind speed reaches 130 mph. Record the height difference on the manometer for each wind speed. Then, stop the wind tunnel and open the test section.
Using the handheld inclinometer, adjust the angle of attack to positive 4°. Then, close the test section and run the wind tunnel at 100 mph. Record the manometer height difference in your notebook. Repeat this procedure for angles of attack up to 28° using 4° increments. Record the manometer height difference for each angle at 100 mph.
Now, let’s take a look at how to analyze the data. First, recall that the stagnation pressure, or the pressure with zero flow speed, is equal to the static pressure plus the dynamic pressure. The dynamic pressure is directly related to the fluid density and flow speed. We can rearrange the equation to express flow speed in terms of the pressure differential and the fluid density.
The pressure differential is measured using the manometer, where the pressure differential is equal to the density of the liquid times g times the height difference in the manometer. Thus, flow velocity is predicted by the equation shown.
The air density, water density, and gravitational acceleration are known. Using the manometer height difference for each wind tunnel air speed at zero angle of attack, calculate the air speed measured by the pitot-static tube. As you can see, the percent error is quite small, showing that the pitot-static tube can predict air speed accurately, with error introduced from wind tunnel air settings, manometer readings, and other instrument errors.
Now, calculate the air speed at various angles of attack when the wind tunnel was operated at 100 mph. As you can see, the calculated air speeds are quite close to what is expected.
The percent difference is calculated by comparing the calculated air speed to the air speed measured at zero angle of attack. All differences are below 4% for the angles measured, showing that the pitot-static tube is generally insensitive to misalignment with the flow direction.
In summary, we learned how pitot-static tubes use Bernoulli’s principle to determine the speed of a fluid. We then generated a range of air speeds in a wind tunnel and used a pitot-static tube to measure the different air speeds. This demonstrated the predictive sensitivity of the pitot-static tube.