ピトースタティックチューブ:空気の流速を測定する装置
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Overview
出典:デビッド・グオ、工学・技術・航空学部(CETA)、南ニューハンプシャー大学(SNHU)、マンチェスター、ニューハンプシャー州
ピトースタティックチューブは、空気の流れの未知の速度を測定するために広く使用され、例えば、飛行機の対気速度を測定するために使用されます。ベルヌーイの原理では、対気速度は圧力の変動に直接関係しています。従って、ピトー静電気管は停滞圧力および静的圧力を感知する。それは圧力の読書を得るために圧力の変圧器に接続され、対速度の予測を可能にする。
この実験では、風洞を利用して特定の対気速度を生成し、ピトー静電気管予測と比較します。流れ方向に対するずさんによるピトー静電気管の感度も調べられる。この実験では、ピトー静的チューブを用いて気流速度を測定する方法を示します。目標は、得られた圧力測定値に基づいて気流速度を予測することです。
Principles
ベルヌーイの原理は、流体の速度の増加は圧力の低下と同時に起こり、その逆も同様であると述べています。具体的には、流体の速度がゼロに減少した場合、流体の圧力は最大値まで増加します。これは、停滞圧力または総圧力と呼ばれます。ベルヌーイの方程式の1つの特別な形態は次のとおりです。
停滞圧力=静圧+動的圧力
ここで、停滞圧力、P oは、流速がゼロに減少した場合の圧力である、静圧、Psは、周囲の流体が所定の点に及ぼす圧力であり、動的圧力、Pdはラム圧とも呼ばれ、所定の点の流体密度、ε、および流速Vに直接関連します。 この方程式は、液体流れや低速気流(一般に100m/s未満)などの非圧縮性流れに適用されます。
上記の方程式から、圧力差と流体密度の観点から、流速Vを次のように表現できます。
18世紀には、フランスのエンジニアアンリ・ピトがピトー管[1]を発明し、19世紀半ばにフランスの科学者ヘンリー・ダーシーが現代の形に変更しました[2]。20世紀初頭、ドイツの空力学者ルートヴィヒ・プラントルは、静的圧力測定とピトー管を組み合わせてピトー静的チューブに組み込み、現在広く使用されています。
ピトー静的チューブの概略図を図 1 に示します。管内には2つの開口部があり、一方の開口部は停滞圧力を感知するために流れに直接面し、もう一方の開口部は静圧を測定するために流れに垂直である。
図 1.ピトー静的チューブの回路図。
圧力差は、通常、圧力トランスデューサによって測定される流速を決定するために必要です。この実験では、液体カラムの圧計を使用して、圧力の変化を測定するための良好な視覚を提供します。圧力差は次のように決定されます。
Δhはマノメーターの高さの差であり、εLはマノメーター内の液体の密度であり、gは重力による加速度である。方程式 2 と 3 を組み合わせると、流量速度は次のように予測されます。
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.