MECHANICS OF FLUIDS

CLASS PROJECT 2

ANALYSIS OF FLUID FLOW USING PITOT TUBE

Group 3 Team Leader: Theodore Christian

Abby Bishop, Luke Reher, Reihle Saldana, Nathan Harris November 11th, 2016

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ABSTRACT Pitot tubes are used in many applications, including aircraft design and fluid analysis along

pipelines. While simple in nature, a Pitot tube does an impressive job in measuring important information

regarding the pressure difference between two points of flow. In this experiment we illustrate how a Pitot

tube can be paired with a water manometer to accurately record and measure changing air pressures at

different flow velocities. This was accomplished by first depositing an initial amount of water into the

manometer and marking its starting point at zero velocity; then we proceeded to accelerate to up to 10 m/s

and recorded the increase in air pressure as a function of changing water height inside the manometer. We

concluded that an inlet air velocity of 5 m/s, 7 m/s, and 10 m/s yielded a 0.2 cm, 0.4 cm and 0.8 cm change

in the water level respectively. We then compared our observations to solutions of theoretical calculations

to ensure that the fabricated Pitot tube accurately measured pressure imposed by fluid flow. Although a

margin of error was present from a few design flaws in the model, the results clearly match the theoretical

trend, and the specific areas of error are further discussed in this report. INTRODUCTION

A pitot tube is a device, invented by Henry Pitot, for measuring the velocity of a flowing fluid [1].

Pitot tubes are typically used to measure the speed of an airplane and other high-speed vehicles. [2] A

pitot tube gives the speed of the object it is attached to by measuring the airflow around it and the object it

is attached to. Pitot tubes, though designed by Henry Pitot were based off of the work done by Daniel

Bernoulli, who theorized that there is a relationship between velocity and pressure. This is true and the

relationship is stated in equation (1).

𝑃1 +1

2𝜌𝑉1

2 + 𝜌𝑔ℎ1 = 𝑃2 +1

2𝜌𝑉2

2 + 𝜌𝑔ℎ2 (1)

Where P is the pressure, ρ is the density of the fluid, V is the velocity of the fluid, g is the

acceleration due to gravity and h is the height from a datum to the center of where the measurements are

being taken. In the classical setup of the Pitot tube, where the fluid measured is air, ρ is the density of air

and V is the air velocity. The subscripts 1 and 2 help to differentiate between the static port and the

stagnation port on the Pitot tube. The stagnation port describes the area of flow where the velocity of fluid

flow is maximum. The static ports measure areas of no direct change in flow speed, and these ports

measure a total pressure equal to the pressure around the Pitot tube. In the case of the experiment, this

pressure is the atmospheric pressure.

Figure 1: A pitot tube, with many static pressure holes towards the left of the picture, and the stagnation

pressure hole on the right side of the picture.

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However, a pitot tube alone cannot measure the pressure difference between its two types of

ports; this is where a manometer comes into play. A manometer is a device used to calculate the

pressure difference between two points, using a liquid of a known density. A manometer shows the

pressure difference between two points through the use of a bent tube. This bend can be in the shape of

a u, or an angled u, or one side can be angled and the other straight. [3] The density of the liquid must be

known because it is used in the calculation for the pressure, given by:

Figure 2: The setup of a manometer, where ρ is the density of the fluid, g is the acceleration due to

gravity, and h is the height difference on each side of the tube, as shown.

When using a manometer to calculate the pressure, the height differences shown in the manometer can

be small, and in those cases it is best to use a manometer that is angled on at least one side so that the

visible difference between the two sides is larger than it would be if they were both straight up and down.

Figure 3 helps to illustrate this point. [4] At first glance this may seem to make the height difference

between the two sides of the manometer difficult to calculate, however it is quite simple once basic

trigonometric functions are applied. If the angle at which the tube is slanted is known, the relationship

between L and h is given by (2), rearranged for h results in (3).

Figure 3: This figure illustrates the benefit to having the lower pressure side of the manometer slanted.

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The use and operation of a Pitot tube and a water manometer together is quite simple. Referring back to

(1), the way to find the velocity is to simplify the equation as much as possible. Since the height difference

between the two openings for airflow is small enough to be assumed as 0, the last term on each side of

the equation is the same, so that term gets cancelled out. Due to the right angle of the Pitot tube V2

equals zero, so that term also cancels out. Rearranging the equation results in (4), and knowing what the

pressure difference is through the use of the water manometer, equation (5) results.

𝑉 = √2(𝑃2 − 𝑃1)

𝜌 (4)

𝑉 = √2(𝑔𝜌𝑤𝑎𝑡𝑒𝑟(𝐿 sin(𝜃)))

𝜌𝑎𝑖𝑟

(5)

OBJECTIVE

To design a water manometer that will be 3D printed along with a pitot tube which will then be calibrated to calculate the velocity at which an object is traveling. MATERIALS AND METHODS Discussion of Model Design:

Understanding the design of both the Pitot tube and water manometer is crucial in analyzing the

results from the experiment. A pitot tube is designed very simply by encasing two nonintersecting, hollow

channels inside an airtight plastic body, and connecting the outlets of these channels into the inlet ports on

the water manometer. The Pitot tube used in the experiment was originally designed by Dr. Steve Tung,

and was delivered to the group as a Solidworks part file. The file was then exported as a stereolithography

file with the extension of “.stl” in order for the model to be printed. While the exact shape of the Pitot tube does not require specific design, there are several key

elements in the design that ensure successful capture of air pressure data. The Pitot tube must have a

channel facing parallel to the fluid flow. This channel opening is called the stagnation port, and it is used to

measure the stagnation pressure imposed by the air flowing into the tube. The stagnation pressure will

change depending on the flow rate of the fluid being studied, and this will be compared to the static

pressure, or atmospheric pressure, being measured in tandem. The atmospheric pressure is measured

through three holes facing in a perpendicular direction to the fluid flow cut along the top of the Pitot tube

called static ports. This ensures that the rate of the fluid flow will not affect the pressure measured inside

the Pitot tube through the channel connecting to the static ports. Two separate channels link the static and

stagnation ports to the bottom of the Pitot tube, following a sequence of two short bends. An isometric view

of the Pitot tube design is shown below in Figure 4, and design of the internal channels with dimensions is

given in Figure 5. The only modification to the given design was an addition of the group number and names

of the team members, which helped set the Pitot tube apart from other groups, even if the part was printed

with the same color of material.

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Figure 4: Isometric view of Pitot tube design

Figure 5: Internal side view of the Pitot tube design. Dimensions all in millimeters.

The Pitot tube also has an important external feature which greatly aids the design of the tube in

connection with the water manometer. This feature is a small lip located at the bottom of the tube along the

same face as the static and stagnation port outlets. The lip is extruded 2.5mm from the face of the Pitot

tube, and is designed to help secure the water manometer to the Pitot tube for repeatable results during

testing. The water manometer was designed using Solidworks software, and the first goal of the design

was to mate the Pitot tube to the water manometer and align the outlet ports with the manometer’s inlets.

The team designed the manometer to accept the profile of the Pitot tube’s lip, and a tolerance of 0.01 inches

was used in order to account for the material thickness and spreading during printing. The channels were

originally bent at 45 degrees from the normal in hopes of a more accurate measurement, however this was

changed to 42.7 degrees in order to achieve a more square looking design. The exact angle is arbitrary, as

long as the value of the angle is known and properly used when calculating the measured height values.

The sides of the manometer are parallel with one another for increased accuracy of both channel measures.

It is important to note that both channels intersect at the base of the manometer, forming what is called a

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U Tube. If the channels did not intersect, then no pressure difference could be developed, and it would be

impossible to measure the effect of flow rate on pressure given the provided Pitot tube. At first, the manometer was designed to have a face without walls. Instead of a 3D printed wall, the

wall of the manometer was cut out of a thin plastic sheet, repurposed from some packaging materials.

However, upon application of the super glue, the plastic was not properly aligned to the glue face, and after

realignment of the face glue had smeared into the channels through which water would be flowing, turning

the surface completely opaque. The clear plastic face was then attempted to be forcibly removed from the

3D printed part, leaving the manometer in unusable condition. This original print compared to the original

3D design of the manometer is pictured in Figure 6 below; Figure 7 shows the extent of the damage the

super glue did to the part after the failed clear plate alignment.

Figure 6: A comparison of the manometer model design (left) with the manometer 3D print before gluing

(center), and the design of the panel end used to insert into the 3D print (right)

Figure 7: A close up view of the glue damage (left) and the overall damage of removing the plastic face

(right)

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After conducting this failed experiment, the manometer was tested with water to see whether or not

the water could be viewed through the 3D printed wall on the opposite side; it was found that water could

indeed be seen clearly, and this eliminated the need for having to hand make a clear plastic wall for the

manometer. Instead, the walls of the redesigned manometer were chosen to be 0.01 inches in order for the

liquid to be seen through the plastic and still maintain water tightness around the part’s channels. Then a

scale, measured in centimeters, was added to the side of the manometer, making it easy to read the

measurements during the execution of the experiment. Lastly, before moving to the second print of the

design, the fit between the insert on the Pitot tube and the receiving channel was tested. The fit was near

perfect, and provided a very snug area to attach the Pitot tube to the water manometer. Discussion of Model Fabrication: The models that are required for the project need to be both sturdy and, in the case of the water

manometer, water tight. They also require a low printing cost and high speed production time. This builds

an impressive case for using 3D printing techniques, and the MEEG department’s uPrint SE plus 3D printer

was used to create the models out of red ABS filament (printer number P55451). In order to print the models,

the files were imported into Catalyst EX 4.5 as .stl files and oriented for printing. Both the water manometer

and the Pitot tube were laid on the flattest side possible, so as to limit the support material used in the

printing. After the prints were finished, they were then put inside the chemical bath over the course of two

days and 12 total hours. The support material inside of both the water manometer and the Pitot tube took

an abnormally long time to evacuate from the channels, which is most likely due to the age of the material

solvent inside the chemical bath. The solvent was very white and completely opaque each time the prints

were put into the bath. Eventually, both prints were cleared out enough to be used in the experiment,

however traces of support material can still be seen along both channels. This did not affect the results of

the experiment, as the measure of pressure imposed on the fluid does not depend on the diameter of the

tube, but rather on the height of the water inside of the tube. Because the pressure operates this way

independent of the tube shape, the water manometer could be used without further post processing for the

experiment. The water manometer required more post processing than a usual 3D print, as the team wanted to

ensure the part did not leak water. This water tight effect was accomplished with the application of super

glue. The super glue bonded with the plastic, sealing up the crevasses where water had the potential to

leak out. These crevasses occur most in the thinnest areas of the print, and along the layers lines of the 3D

print. Because the process of 3D printing is additive, potential for water leakage is created with each

successive layer of 3D printing material added to the base. The superglue helped to minimize any risks of

leakage strengthened the parts at the thinnest corners, which proved to be the weakest parts of the design.

Figure 8 depicts an image of this post processing process after applying the super glue.

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Figure 8: The water manometer and Pitot tube after post processing. Materials:

After printing the models, the experiment was performed and the results recorded. Several materials

were necessary in order to generate results of the experiment. Items included in conducting the experiment

are listed below:

● 4oz water ● Concentrated Cherry Kool-Aid® mix (dye)

● Gel pen ● Truck with open bed

● Pitot tube ● Water Manometer ● Camera

The team chose to use a cherry Kool-Aid® mix due to its solubility in water, however the effects that this

solution has on the liquid’s density were not considered. As such, it is unknown the precise density of the

fluid inside the manometer, and the analysis assumes the liquid’s density is equivalent to that of regular

water. Experimental Procedure: The experiment was performed in average weather conditions in the afternoon. The general procedure can

be described as follows:

1. Mix together the 4oz of water and Cherry Kool-Aid®.

2. Insert this mixture into the water manometer using an empty gel pen.

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3. Set up the experiment in the back of a truck bed. Position one team member with a camera

recording the data, and other team member holding the Pitot tube assembly steady.

4. The initial readings of the Pitot tube should be read and recorded on camera to establish a baseline

for the experiment.

5. Start the car and proceed to move, in a safe, empty area, up to speeds of 10-11 mph. The teammate

that is driving the car should honk the horn whenever the speed has been reached and constantly

maintained in order to make analysis of the video data later easy.

6. Data is then taken for 15mph and 22mph velocity.

7. At the end of the experiment, park the vehicle and safely step out of the truck bed. Save the video

recordings for later analysis.

RESULTS AND DISCUSSION

We conducted this experiment as a three person team, one individual driving and two team

members observing and videotaping the process of the water level changing as we increased our velocity.

We attempted to be as consistent as possible in our data recording method by driving on an empty street

that was straight and relatively flat. By using this method to conduct this experiment we recorded the

following data:

Velocity (m/s) Height (cm)

0 0

5 0.2

7 0.4

10 0.8

Table 1: Experimental data To keep units consistent, we reported velocity in meters per second rather than miles per hour. The

following pictures were taken during the experiment.

Figure 9: Water manometer and pitot tube at a velocity of zero.

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Figure 10: Water manometer and pitot tube at a velocity of 5 m/s, approximately 11 mph. The change in

height is about 0.2 cm. It is important to note that we recorded only a 0.2 cm height change in at 11 mph. We found that speeds

lower than that were extremely difficult determine.

Figure 11: Water manometer and pitot tube at a velocity of approximately 7 m/s, or just over 15 mph. The

height changes by 0.4 cm.

Figure 12: Experiment at 10 m/s, ~22 mph. The height of the water changes by about 0.8 cm.

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As we conducted our experiment our results we gathered from our change in water level was

comparable to our theoretical solutions. In reference to the illustrations above, we recorded a change in

about 0.2 cm on our manometer, and calculated a change of 0.230 cm when driving at 5 m/s. As we

accelerated to 7 m/s, we recorded a change of 0.4 cm and calculated a change of .451 cm. Lastly as we

continued to accelerate to our final data point, 10 m/s, we observed the water level change of 0.8cm and

calculated a change of .921 cm in our theoretical solution. The change in height is consistently lower than

what it theoretically should be. Therefore if we were using this Pitot tube and water manometer to measure

velocity, we would obtain values that are lower than what the actual velocity would be. The following graph

shows the theoretical and experimental values for each velocity.

Figure 13: Graph of theoretical and experimental data, shows the experimental height to be lower than the

theoretical

While our data was consistent and accurate it wasn’t very precise and recorded an average 12.6%

of error. This error is due in part to some design flaws in our model. First and the most hindering flaw was

the material our model was printed out of. Being red rather than some other lighter/translucent color or

material meant that the water level was fairly hard to see. This translated to us not being able to be very

precise in our observations for where the water level dropped to. If the model had been transparent it also

would’ve in turn allowed us to use even more data mark on the manometer and record much slighter

changes in water level. Because of this issue we were forced to mix an additive into the water to make the

water level visible. We decided to use a Kool-Aid® drink mix as we concluded that it would it have little

effect on the density and behavior of the water, but is not as precise as a dye or food coloring. Another

cause for inaccuracy was the method by which we decided to conduct the experiment. To explain further,

as we were traveling down the road we held the pitot tube against the top of the vehicle, so every time the

vehicle hit an irregularity in the road surface it translated to the manometer and altered our water level

instead of only undergoing a change due to the increase in air pressure inside the manometer. The last

factor that could improve results of this experiment is concluded when we refer to how small our maximum

change in water level height is, which was recorded to be .8 cm at 10 m/s. If we traveled at a higher speed

it would be much easier to observe a change of say 2-3 cm rather than trying to approximate how many

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millimeters the water level changed. Of course this was aided by a slanted water manometer design,

however we still encountered a high level of difficulty when differentiating between two measurements.

CONCLUSIONS

The main conclusions that may be drawn from this work are as follows. The water manometer we designed does accurately measure wind speed. Kool Aid should be avoided as a water dye as it could affect the density. To better see the fluid a more neutral colored 3D printed material should be used. Overall the test went well though vibrations made it difficult to analyze the footage.

The height measured at 7 m/s was 0.4 cm. Driving at 5 m/s produced a 0.2 cm change on our manometer. Driving at 7 m/s, we recorded a change of 0.4 cm. Lastly at our final data point, driving at 10 m/s, we observed the water level change of 0.8cm. The average error throughout the test was 12.6%.

REFERENCES

[1] Encyclopaedia Britannica, 2016, “Pitot tube.” from https://www.britannica.com/technology/pitot-tube [2] Benson, Tom, “Pitot Tube.” from https://www.grc.nasa.gov/WWW/k-

12/VirtualAero/BottleRocket/airplane/pitot.html [3] D’Angelo, R. and Thomas, Dave, 2001, “Manometer Basics.” from

http://www.sensorsmag.com/sensors/pressure/manometer-basics-1073] [4] Encyclopedia of Chemical Engineering Equipment, “Pressure Measurement.” from

http://encyclopedia.che.engin.umich.edu/Pages/ProcessParameters/PressureMeasurement/PressureMea

surement.htm]