Development and Investigation of Lab Apparatus for Fluid DynamicsINTRODUCTION College students do not typically enter undergraduate school with a formal teaching of fluid dynamics.1 This is unfortunate since many professions make use of it such as civil and environmental engineers, architects, city service planners, farmers, waste disposal managers and nearly all jobs related to the oil industry. Since it is a new topic to these students, it is important that they are able to get as much help as possible, especially with the drop rate of science majors.2 With this in mind, the main goal for this project is to complete an apparatus that is capable of being used during in-class lectures as a visual, interactive, learning tool for students in fluid dynamics. To achieve this, an analysis of the fluid flow in a system is done to determine its effectiveness as a teaching tool and ease of use. The system is a pipe flow apparatus that displays various levels of flow rate, and the effects of perturbations and pipe bends. Then, a diagnostic tool is created and used on a large varied population to test if there is a significant increase in a participants understanding when the apparatus is used as a teaching tool versus no visual demonstration. The primary impact is to create a reliable, beneficial teaching mechanism for undergraduate students in the field of introductory fluid dynamics.

THEORYA. FluidsAn accurate description of the behavior of a fluid in motion is very complex and nearly impossible to describe numerically.3,4,5,6 It would be better off to instead, start off with a definition of what a fluid is and then explore its properties. Fluid is a substance that has no fixed shape and has little resistance to any outside pressures acting on it1,8 Obviously, this model does not work for the higher level analysis, especially when determining the chaotic effects, effects of temperatures, or any shift in initial conditions.9,10,11 B. Fluid Dynamics Using An Ideal Fluid and its Issues For simplicity sake, most introductory fluid dynamic courses begin with what is called the ideal fluid.1,6. An Ideal fluid must have steady flow, which is to say that the flow rate of the fluid is constant. An ideal fluid must be incompressible. Incompressible flow is when the fluid does not change in volume regardless of the pressure applied to it. It must have nonviscous flow, such that no drag force occurs due to the flow of the fluid. Lastly, it must have irrotational flow, which means no object or section of fluid rotates about some axis of its own center of mass.10,11 Keeping in mind the objective of this system, the steady flow assumption, immediately becomes a topic of interest. When discussing a system with steady flow, there must also be a discussion of its counterpart, unsteady flow. This is known as turbulent flow.8,10 A simplistic example of laminar and turbulent flow can be found in Figure 1.

Figure 1 Smooth laminar flow is shown above while the unsteady, 'turbulent' flow is characterized below.Turbulent flow may not necessarily be an ideal fluid, due to its unsteady flow, but it can still be looked at as a simplistic model because the other three conditions are met. Turbulent flow is a major topic among both physics and engineers, especially when discussing a shift from laminar to turbulent flow or vice a versa.13,14 With the setup proposed in this project, it will be easy to view both just laminar and turbulent flow conditions, but also the transition phases. Physicists and engineers differentiate between laminar and turbulent flow through the variable known as Reynolds number. This can be calculated in a pipe from,

,

where isdensity, is the velocity of the fluid based on cross section of pipe, is the hydraulic diameter, is the dynamic viscosity, and is the kinematic viscosity. The fluid is determined to be laminar if its associated Reynolds number is less than 2300 and turbulent if it is greater than 4000.3,5 Anything in-between is considered to be in a transient state.3,5 However, to minimize the need for participants having a mathematical background, this experiment approaches Reynolds number in only a qualitative sense.

The shift from liquid fluid, water, to a gas fluid, air, forces another acknowledgment to one more of the four assumptions of an ideal fluid, namely incompressibility. It is generally accepted that gases are compressible, in fact an ideal gas will compress so predictably that there is an ideal gas law.15 This apparently creates a problem since a gas cant be an ideal fluid and this problem allows for a potential discussion point on fluids in general. In physics, it is known that while the actual transition points are no longer completely predictable we will see a similar process as that of ideal fluids. The ideas of chaotic motion are just more relevant for the non-ideal fluid. As for nonviscous flow, the proposed system does not need to worry about it as the fluids create a minimal drag force and any drag that does occur will not be visible to the casual observer. This system also does not have to worry about irrotational flow as there are no solid objects being released into the flow. This may happen when exploring future possibilities for advanced lab students, but it will be addressed at that time.C. Determining Effectiveness as a Teaching ToolThere are many ways to try and test the effectiveness of a new teaching tool or method, but the diagnostics tool that will be used in this experiment is the implementation of pre and posttests. These tests were created around the experiments defined objectives. These objectives are that the student needs to be able to define laminar and turbulent flow, distinguish what happens to fluid flow at and around pipe bends, and describe the relationship between Reynolds number and the type of fluid flow. These objectives are to be analyzed by scoring the pre and post tests and determining the average gain or improvement achieved by the demonstration. Gain is calculated through the equation,

,where the post score, pre score, and gain are in percentages.13 It is recommended that a total gain of at least 30% be acquired before concluding positive results.14 The data should also be separated into like groups to determine if specific demographics display a trend or see if learning objectives are not being correctly met. The gain percentage will also have an associated standard error, which has the function,

,

where SE is the standard error, is the population, is a specific gain score for a participant, is the average gain score, and is the standard deviation. EXPERIMENTA. Fluid Flow ApparatusThe apparatus consists of a clear PVC pipe system eight feet in length and two feet wide and one and a half inch inner diameter. The pipe is rated to withstand up to forty pounds per square inch of pressure which goes greatly beyond the projected maximum pressure of this apparatus. Figure 2 below shows the pipe layout of the apparatus. The pipe is connected by clear PVC couplings and schedule 90(90 PSI limit) rounded right angles turns. At the couplings, the pipe is dry-fitted or not glued down so the pipe sections can be removed and perturbations may be added to the pipe system. It also allows for the system to be stored safely and cleaned easily if necessary.

Figure 2: The pipe system lays flat on a wooden table. There is a flow meter attached to the pipe at the center of the first turn.A flow meter is attached to a section of piping in the system to allow for a numerical approach to fluid flow if deemed necessary. At one foot in the pipe system, a syringe is inserted with tracer dye from the top of the pipe to show the differences of the fluid flow visually which can be seen in Figure 2. The purpose of the tracer dye is to see the flow of a specific section of water down the pipe.

Figure 3: The syringe can be replaced with different sizes but for safety reasons, all syringes are blunt tipped. At the connect point from a reservoir to pipe exit, a valve is connected so the flow and pressure can be adjusted. The flow of the pipe comes from a five hundred gallon per minute cartage bilge pump which stays in a five gallon bucket reservoir. The pump power source comes from a Web-Tronics HY3002D-3 DC Power Supply as seen in Figure 4. The voltage to the pump can be varied using the power supply and this in turn adjusts the work and flow rate of the pump.

Figure 4 From left to right, there is a multimeter to check power supply accuracy, the power supply, and a removable exit section for the pipe system.The resulting apparatus allows for a voltage range of 3.5 volts to 16 volts with flow velocity ranging from nearly one gallon per minute to over eight gallons per minute with variable pressure and pipe perturbation options. B. Procedure Students participating in non-fluid dynamics courses were encouraged to attend a mock lecture involving the use of the fluid flow apparatus. Upon arrival, students are assigned a number and asked not to give or write any personal information while attending the lecture. If confidentiality forms are required for that lecture by IRB standards, they are passed out as the participant enters and collected before the lecture begins. When the forms are filled out, a pre-quiz is passed out to the participants and they are asked to answer it to the best of their ability and write only their number and not their name on the quiz. An example of the pre-quiz can be found in Appendix A. After the pre-quiz has been completed or a time limit of eight minutes has passed, quizzes are collected and a mock lecture on fluid dynamics takes place with the use of the fluid flow apparatus. To see an outline of the lecture refer to Appendix B or an audio copy of a mock lecture is available upon request. This mock lecture takes approximately fifteen minutes, but the time can vary within a three minute window. At the completion of the mock lecture, participants are then given a post-quiz and asked to write once again, their given number. This quiz is similar to the pre-quiz in material, but written differently so participants do not recall information from the pre-quiz. This quiz is then collected at the end of an eight minute time period and the participants are thanked and asked to exit. The pre/post quizzes are then used for analysis to determine the effectiveness of the fluid flow apparatus as a teaching tool in a class room setting. ANALYSISThe collected data is organized and displayed in Appendix B. The participants Pre and Post quizzes were graded with a three point scale for each problem. If the student displayed complete control of the learning objective that problem receives a two, partial control receives a one, and no indication of knowing acquiring or possessing the objective yielded a one. The data was then scored to determine the percent gain each participant had between the pretest and posttest. The average gain calculated for the experiment is 89% with a population of 18 and a standard error of 6%. When separating the data between those with some experience in physics, three semesters or more, and those with less you see the following results. Those with some experience in physics had an average gain of 95%, while those with little to no physics experience had an average gain of 87%. The standard errors for these are 5% and 9%, respectively. The most missed objective on both the pre quiz and the post quiz was that the student will be able to describe Reynolds number and its relationship to types of flow. In the pre quiz, it was obvious that Reynolds number was a new term and concept to the general population, especially those with little to no physics experience. The pre quiz question testing this objective was not answered the most, and most attempts at answering it assumed that Reynolds number had some relationship to friction or buoyancy. In the post test, nearly all were able to address this objective correctly and most mistakes came from the participants trying to incorrectly relate Reynolds number to other variables. This seems to be from the demonstrations brief explanation of Reynolds number as a ratio. CONCLUSIONThe current data suggests that a demonstration or lecture based around the use of the fluid flow apparatus described is beneficial to the learning of students in an introductory physics course. It successfully has a net gain of over 80% in achieving the learning objectives tested and there has not been a single case of a negative gain occurring among the population. However, a higher population with a more varied demographic background is greatly desired to solidify the current assertion. Suggested changes would be to develop a larger system so that the effects on the fluid flow would be more notable and visible from a larger distance. It would also be interesting to see if this apparatus could be introduced to higher level physics courses to test and display head loss, pressure relationships to fluid flow, video analysis of turbulent flow and the effects of both free flowing and stationary perturbations in the pipe system. Even if these possible experiments were to not happen, it is recommended that this apparatus be used as a teaching demonstration for introductory level physics courses.

Works Cited1) National Human Genome Research Institute. USA Government, n.d. Web. 19 Nov. 2013.< http://www.genime.gov/12011721>.2) United States. National Center for Education Statistics. STEM Attrition. By US Department of Education. N.p., n.d. Web. 14 Mar. 2014.Brodkey, Robet S., and Harry C. Hershey. Basic Concepts in Transport Phenomena. 3) Columbus: Brodkey, n.d. Print. Vol. 1 of Transport Phenomena.4) Thomson, William J. Transport Phenomena. N.p.: PTR PH, 2000. Print.5) Holden, Arun V., ed. Chaos. N.p.: Manchester U.P., 1986. Print.6) Halliday, and Resnick. Physics Part I & II. N.p.: Wiley, n.d. Print.7) Tiplet, Paul A., and Gene Mosca. Physics for Scientists and Engineers. 6th ed. Vol. 1 & 2. N.p.: Freeman, n.d. Print.8) Halliday, Resnick, and Walker. Fundamentals of Physics. 6th ed. N.p.: Wiley, n.d. Print.9) Batchelor, G. Introduction to Fluid Mechanics. N.p.: Cambridge University Press, 2000. Print. Cambridge Mathematical Library.10) Fluid Dynamics, Vol. 41, No. 6, 2006, pp. 916922. Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2006, pp. 6876. Original Russian Text Copyright 2006 by Pavelyev, Reshmin, and Trifonov.11) Effect of temperature on turbulent and laminar flow efficacy analysis of nanofluids Tesfai, Waka and Singh, Pawan K. and Masharqa, Salim J. S. and Chiesa, Matteo and Shatilla, Youssef, Journal of Applied Physics, 111, 064319 (2012)12) Dong, Ming, Yong-ming Zhang, and Heng Zhou. "A New Method For Computing Laminar-Turbulent Transition And Turbulence In Compressible Boundary LayersPSE+DNS." Applied Mathematics & Mechanics 29.12 (2008): 1527-1534. Academic Search Complete. Web. 20 Nov. 2013.13) Williams, Richard, and Donald W. Zimmerman. "Are Simple Gain Scores Obsolete?" Applied Psychological Measurement 20 (Mar. 1996): 59-69. Sage Journals. Web. 3 Apr. 2014.14) "Pre- and Post- Testing." OME Falculty Development. Boston University Medical Campus, n.d. Web. 3 Apr. 2014.

Appendix APre-Quiz: Water Flow DemonstrationMajor:Age:Gender:1) How many physics classes have you taken?

2) What are the similarities and differences between laminar and turbulent flow?

3) What is Reynolds number?

4) If Reynolds number is very high, what can be said about the fluid associated with it?

5) Water is flowing smoothly and slowly down a pipe with a ninety degree turn. From your personal experience, how should the turn in the pipe affect the water?

Post-Quiz: Water Flow Demonstration1) Water is flowing slowly and smoothly down a straight pipe. From a physics standpoint, how would you describe the flow of the fluid?

2) How is Reynolds number useful in describing fluid flow? Explain.

3) Water is flowing slowly and smoothly down a pipe with a ninety degree turn. In terms of physics, describe the fluid flow before the turn, at the turn, and after the turn.

Appendix BScript*Set up for laminar flow*Pass out physical numbers and confidentiality forms.Please fill out the consent form handed to you when you entered. Please keep in mind that if at any time you feel uncomfortable, you can stop and leave at any timeCollect forms and pass out pre-quiz.Do not write down your name, just your number.Begin the quiz and when you are finished with it bring it to the front. (Will wait maximum of ten minutes or until everyone is done.)Collect pre quizand begin mock lecture.

IntroductionFirst, I would like to thank you all for participating in this survey. As you may or may not already know the purpose of this experiment is to determine how effective a lesson based around the use of this demonstration is in helping students learn about fluid flow. Before we begin, I would like to cover what a fluid is in terms of physics. A fluid is defined as something that gives little to no resistance to any outside pressure or force. It also will take the shape of any container it is in.It is important to note that this means a fluid doesnt have to be just a liquid. It can be a gas as well. Water, tea, air, helium, all of these are fluids. Now if you all would stand up and get near the apparatus. We will begin the demonstration. Also, please keep hold of your numbers.Apparatus The apparatus in front of you makes use of this power supply here. Using this we can change how fast the pump in this bucket puts out water. This will let me change the speed or rate of fluid flow of the water in the pipes. We can then use this needle to inject dye into the water so we can watch how the water acts.

Run the apparatus at a low speed and display laminar flow (one to two dye injections for laminar flow)

Laminar flow*Point out the front of the pipe after the needle as the location to look*What you see in the pipe now is called laminar flow. The fluid is moving in a smooth, steady progression and, as you can see from the dye, it flows together. Laminar flow can usually only happen at very low fluid speeds so it isnt seen in nature that often, but its easy to study because of its predictability. Apparatus 2 Increase velocity of fluid. Before dye injection, ask So, with an increased fluid flow, what do you think the dye will look like?

*Have them look at both straight sections of the pipe and not look at the speed of the dye, but the way the dye acts.*Inject dye (again one to two injections).What is different?* Revert to laminar flow (low Reynoldss number, low velocity)*Turbulent flowThis is called turbulent flow or turbulence. It is the opposite of laminar flow in the sense that it is unsteady and disjointed. This is more common in nature and it happens, as you see now, at a higher fluid speed. Turbulent flow is nearly impossible to work with in physics, unlike laminar flow because of its unpredictable nature.

Introduce Reynoldss numberIn physics we have something called Reynolds number which allows us to predict or state if a fluid is in laminar or turbulent flow. It is a ratio of the fluids resistance to change over the fluids viscosity or stickyness1. So, a low Reynoldss number means that the fluid will have laminar or smooth, steady flow and a high Reynoldss number means it will be turbulent or unsteady and disjointed. This number is useful because it allows us to guess what type of flow we will have for nearly any situation before we go ahead and cause or observe the flow of a fluid.

Apparatus 3/ Perturbations & BendsOkay, so we are back at laminar flow but there is one more condition where the fluid can become turbulent even with a low fluid speed. If we look here at the bend in the pipe we see that the smooth lines of dye suddenly become turbulent. (Inject dye again)Look how its smooth, steady, laminar flow before the pipe bend. Then it hits that pipe bend and you see the unsteady, turbulent flow. This is because the fluid there is receiving a sudden force causing it to change directions and so Reynolds number goes up briefly. Since that force is temporary though, the fluid goes back to laminar flow! This is why Reynolds is important; we can predict what type of flow we will have for a fluid. (inject dye again for fun)ConclusionTo recap, laminar flow is smooth and steady and turbulent is unsteady. Fluid with laminar flow will have a low Reynolds number, and fluid with turbulent flow will have a high Reynolds number. Alright, that concludes the demonstration. If would please return to your seats, we will now take a post quiz.Pass out post quizRemember to write the number you were given on your quiz and not your name.Wait until they finish or until ten minutes have expired and collect the quiz and number they were given upon entering.If you have any questions about the experiment or the apparatus feel free to come up and ask me a question, but that is it for the survey and demonstration!

Sourceshttp://www.grc.nasa.gov/WWW/BGH/reynolds.html

Demographics

Gain Scoring