피트 정압관: 풍량 측정 장치
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Overview
출처: 데이비드 구오, 공학, 기술 및 항공 대학 (CETA), 서던 뉴 햄프셔 대학 (SNHU), 맨체스터, 뉴햄프셔
피토 정적 튜브는 공기 흐름에서 알 수 없는 속도를 측정하는 데 널리 사용되며, 예를 들어 비행기 공기 속도를 측정하는 데 사용됩니다. 베르누이의 원칙에 따르면, 공기 속도는 압력의 변화와 직접적으로 관련이 있습니다. 따라서 피토 정적 튜브는 침체 압력과 정적 압력을 감지합니다. 기압계 또는 압력 트랜스듀서에 연결되어 압력 판독값을 얻을 수 있으며, 이를 통해 공기 속도 예측을 가능하게 합니다.
이 실험에서는 풍동이 피토 정적 튜브 예측과 비교하여 특정 비행 속도를 생성하는 데 사용됩니다. 유동 방향에 대한 정렬 불량으로 인한 피토 정적 튜브의 감도도 조사됩니다. 이 실험에서는 피토 정적 튜브를 사용하여 공기 흐름 속도를 측정하는 방법을 보여 줍니다. 목표는 얻은 압력 측정에 따라 공기 흐름 속도를 예측하는 것입니다.
Principles
베르누렐리의 원칙은 유체의 속도 증가가 압력의 감소와 동시에 발생하고 그 반대의 경우도 마찬가지라고 명시되어 있습니다. 특히 유체 속도가 0으로 감소하면 유체의 압력이 최대로 증가합니다. 이를 정체 압력 또는 총 압력으로 알려져 있습니다. 베르누이방정식의 한 가지 특별한 형태는 다음과 같습니다.
정체 압력 = 정적 압력 + 동적 압력
여기서 정체 압력, Po는유동 속도가 0으로 감소하면 압력, 정압, Ps,주변 유체가 주어진 지점에 가해지는 압력, 그리고 동적 압력, Pd,또한 램 압력이라고도 하며, 유체 밀도, θ,및 유량, V,주어진 지점에 대해 직접 관련이 있다. 이 방정식은 액체 흐름 및 저속 공기 흐름(일반적으로 100m/s 미만)과 같은 비압축성 흐름에만 적용됩니다.
위의 방정식에서, 우리는 다음과 같이 압력 차등 및 유체 밀도 측면에서 흐름 속도, V를 표현 할 수 있습니다 :
18세기에, 프랑스 엔지니어 헨리 피토피토피토 피토 튜브를 발명 [1], 그리고 19세기 중반에, 프랑스 과학자 헨리 다르시 현대 형태로 수정 [2]. 20세기 초, 독일의 공기역학주의자 루드비히 프란틀(Ludwig Prandtl)은 정적 압력 측정과 피토 튜브를 피토 정적 튜브에 결합하여 오늘날 널리 사용되고 있습니다.
피토 정적 튜브의 회로도가 도 1에 표시됩니다. 튜브에는 2개의 개구부가 있습니다: 한 개구부는 정체 압력을 감지하기 위해 직접 흐름을 직면하고, 다른 개구부는 정적 압력을 측정하는 흐름에 수직입니다.
그림 1. 피토 정적 튜브의 회로도.
압력 차동은 일반적으로 압력 변환기로 측정되는 유속을 결정하는 데 필요합니다. 이 실험에서 액체 컬럼 기마계는 압력의 변화를 측정하기 위해 좋은 시각적 개체를 제공하는 데 사용됩니다. 압력 차동은 다음과 같이 결정됩니다.
Δh가 기마계의 높이 차이인 경우, θL은 기마계내의 액체밀도이며, g는 중력으로 인한 가속이다. 방정식 2와 3을 결합하면 유동 속도가 다음과 같은 것으로 예측됩니다.
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.