Pitot-static Tube: A Device to Measure Air Flow Speed

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.