Take home labs – reflections on uncertainty quantification

I have been using take home labs as part of my undergraduate fluid mechanics class for a while now and have often been frustrated with students approach to uncertainty and possible error in their measurements and resulting calculations. All the take home labs require the students to measure some quantity using multiple techniques and then compare their results from the different tests. Ideally, any differences in their values can be explained by analysis of the uncertainty in their underlying measurements. If it cannot be accounted for in this way then there is a potential problem in the way the students did the test or the analysis. Given this frustration I have come to the point where I see a major goal of the take home labs to be to teach the students about basic error analysis. I typically have 4-5 take home labs during each semester and see the teaching process with regard to uncertainty analysis as a 4 step program.

Step 1. Accepting that you have uncertainty – In the first lab of the semester I ask the student to quantify their uncertainty. This very rarely goes well. I get vague statements in their lab reports like “possible sources of error include human error, timing errors, not being able to hold the camera steady, and errors from measuring the area  of …” They are generally all lumped together regardless of their relative magnitude or their influence on the final result. However, it does force them to think about possible sources of error in their experiments.

Step 2. Quantifying your measurement uncertainty – When I hand back the first graded lab report I talk to the class about quantifying their uncertainty. I explain that what 95% of them did was present a qualitative discussion of possible sources of error. However, being engineers, they need to actually quantify that uncertainty. I then discuss measurement errors, primarily associated with scale resolution. For the second take home lab they are required to provide a table with every measurement they made and an associated uncertainty (that is XXXX ± YY). I can then provide feedback on this when grading and returning the second lab report.

Step 3. Quantifying your calculation uncertainty – Once they have quantified their measurement uncertainty in the second lab we discuss how those uncertainties propagate through their calculations. I tend to keep this fairly easy and only use basic linear error analysis such as is described here. For the third lab they have to present each of their their experimental results with the associated propagated error and state if each of their different sets of results (from each of the different types of experiments they ran) agree within the margin of error/uncertainty. If they do not then, most likely, one or more of three things has happened. (1) they have made a mistake in either their experimental design or analysis such that the resulting calculation is not representative of the quantity they were supposed to measure. (2) their estimates of their uncertainty in their measurements is too small. This sometimes happens when they report that their times are accurate to a hundredth of a second when actually their uncertainty is mostly dominated by their ability to hit start and stop in a timely manner. (3) their experiments were not repeatable. That is, the experimental conditions changed between tests. For example, they may not always turn the hose on to the same flow rate each test.

Step 4. Putting it all together – For the fourth (and possibly fifth) take home lab they need to look at their underlying assumptions when they make their measurements. For example, one lab is to measure the mass flow rate from a compressed air can using at least two different methods. One problem is that the air decompresses as it leaves the can so if you make an assumption about density there is an uncertainty associated with that. Another problem with that lab is that the flow rate decreases over time as the pressure in the can decreases. Therefore, they need to discuss repeatability of the test and its impact on the final results. This is more complex, and we do not go over this in detail in class but the lab does make them aware of other issues with running lab experiments.


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

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Take home lab experiment – flow rate from a hose

I typically use this lab as the 3rd or 4th lab of the semester. The lab is simple enough, they have to use two different methods to measure the flow rate out of a hose. They can use kinematics, conservation of volume, or even momentum (though this is a little more tricky). This is one of the labs where I ask my students to use their estimates of measurement uncertainty, through some basic linear error analysis, to estimate their calculated flow rate uncertainty. If their 2 measurements are not the same (within the bounds of uncertainty they calculated) they have to discuss why not. It is a great experiment for discussing errors because, even though the measurements are simple to make, they often have significant percentage errors that propagate into very large percentage error in their calculated flow rates. For example, measuring the diameter of the hose outlet can be tricky and a 10% error in the measurement becomes a 20% error in the hose area. There are also challenges with repeatability of the experiments as it is hard to get the hose to have the same flow rate each time you turn it on. I do not explicitly ask them to discuss repeatability but rather I discuss it when I return the graded reports and ask them to think about repeatability as part of their next take home lab.

As with all the take home labs I will not publish methods for conducting the tests as I still use them in class and want my students to figure it out on their own.


Introduction

In this class we have looked at a range of different flow analysis techniques (conservation of mass, kinematics, Bernoulli, momentum, etc.). In this 3rd lab you need to use 2 different approaches to calculate the flow rate from a garden hose.

Task

  1. Run a series of experiments to establish the flow rate our of the flow from a regular garden hose. There is a hose in the fluids lab that you could use. You can use buckets, measuring tapes, and stopwatches. If you wish to use anything other than that you will need to check with me first. You are not to use laboratory flow rate measurement devices such as the venturi meter.
  2. Write a brief report (3 page max) that:
    1. Includes photos of you running your 2 experiments.
    2. Describes how the test was run
    3. Includes diagrams showing what you measured
    4. Presents the theory and equations you used in your calculations
    5. Lists what data was collected and estimates of your measurement error (in a table)
    6. Error analysis (see class notes) to estimate your uncertainty in your calculation of flow rate.
    7. A table listing the two calculated flow rates and your uncertainty estimation.
    8. If the two measurements to not agree (within the error range you calculated) then discuss why not.

Due date in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Take home lab – Relative viscosity

I have been trying to think about how to have students measure the viscosity of a fluid in their kitchen. The problem is that you need to make a lot of measurements (not least of which is the fluid layer thickness) that are (1) hard to make and (2) have potentially very large error. However, if the errors are consistent then it should be possible to quantitatively compare the viscosity of two different fluids using the identical test. I think that this may be a way around the problem.

The instructions given below are for one of the first take home labs that I use in a semester. The goal is to find the ratio of the viscosity of two common fluids you can find in a kitchen. There are a number of possible ways to approach this problem as long as you are not too hung up on accuracy beyond order of magnitude. At this stage in the semester the students have been down to the lab to measure the viscosity of a range of fluids including oil, molasses, corn syrup so they have data they can use for comparison. It is also possible to look up a lot of viscosity values at http://en.wikipedia.org/wiki/Viscosity.

The first time I ran this lab I got a range of results. It was the first lab of the semester and so the students were a little unsure how to approach the write up. However, the range of experiments they ran were very impressive. One team even built a simple viscometer using a cup, some string, a pencil, and a pile of pennies. I also had students researching online how to measure viscosity. That was all great. The actual quantitative results were less great. It is actually very hard to do well. It is also hard to get a simple theoretical model for some of the tests they ran. For example, you can place equal volumes of different fluids at the top of a slope and time how long each takes to travel a certain distance. However, the time taken is a function of the  fluid density, the thickness of the slug of fluid flowing down the slope, and the viscosity of the fluid. It is, therefore, hard to control for all these parameters in order to get a viscosity ratio. There was also the age old problem of students not actually reading the instructions and instead of a viscosity ratio giving estimates of the actual viscosity which were obviously way off. I also had students picking non-Newtonian fluids which complicates things a little. In future I may move this lab to later in the semester.

As with all the take home lab write ups I will not publish detailed methods for conducting the tests. I still use them in class and want my students to figure it out on their own.


Instructions to students

On your first visit to the fluids lab you used a viscometer to measure the viscosity of various fluids. In this take home lab you will need to calculate the ratio of the viscosity of 2 common household fluids such as oil, honey, syrup, or molasses. Ideally you would use fluids that you also used in the viscosity lab.

Task

  1. Identify 2 fluids that you will be using to measure viscosity.
  2. Run a series of experiments to establish the ratio of the viscosity of the two fluids you selected. That is, develop an experiment that will allow you to compare the two fluids viscosity’s without necessarily accurately measuring the viscosity of the individual fluids.
  3. Write a brief report that
    1. Is 3 pages max including photos of you running your experiments
    2. Details how you made the measurements including clear diagrams showing your setup
    3. Details of how you used the measurements to calculate the viscosity ratio (include any appropriate free body diagrams)
    4. Compares your measured ratio to that based on tabulated data from textbooks or online (or you can use your results from the first lab).
    5. Quantifies potential sources of error that explains any discrepancy between your measurements and your lab or tabulated data.

Rules

  1. You may not use equipment in the fluids lab or any other scientific lab equipment
  2. You should only use items that are commonly available in your home.
  3. If you need to go to a store to buy something please come and see me first. I may be able to lend you something or I will buy it and then lend it to you. You will need to explain why you need it and it should be cheap.

Due in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Take home lab experiment – Density of oil

This is another early semester take home lab. When I give this to my students they have already been down to the lab and used a U-tube manometer to measure the specific gravity of oil (See post https://teachingfluids.wordpress.com/2014/01/13/measuring-specific-gravity-of-oil-with-a-u-tube-manometer/). This goes a step further and requires them to find 2 more ways to measure the density of common cooking oil. They have to look at the course material covered so far (typically we just finished hydrostatics when I hand this out) and work out what topics will enable them to measure the density of cooking oil. The two main goals are to (1) have them review the course to find possible measurement techniques and (2) to start doing some error quantification. They are required to give 3 different values of density based on three different measurement tecuniques and explain any possible differences. At this stage in the semester I typically only ask for estimates of their direct measurement uncertainty but not their uncertainty in their final calculated density.

In general the students are able to come up with three different methods for doing the measurement. They also, typically, measure densities that are slightly less than that of water. This puts them in the right ball park for the actual density. However, the students sometimes end up measuring some very small quantities (such as the height differences in the U-tube manometer. This in turn leads to large measurement percentage errors and even larger density percentage errors. The analysis of this error propagation is left to later take home labs though I do discuss error propagation in class around the time when I hand back the graded lab reports.

As with all the take home labs I will not publish methods for conducting the tests as I still use them in class and want my students to figure it out on their own.


Introduction

Fluid density is needed for many fluid mechanics calculations (hydrostatic pressure, forces on submerged structures, buoyancy, conservation of mass calculations). You have already measured the specific gravity of cooking oil in the lab. You are now required to measure its density.

Task

  1. Use three different methods to measure the density of cooking oil (you can repeat the approach you used in the lab if you like).
  2. Write a brief report that
    1. Is 3 pages max including photos of you running your experiments
    2. Details how you made the measurements
    3. Details how you used the measurements to calculate the cooking oil density
    4. Has clear diagrams showing your setup
    5. Compares the three different measured values of density.
    6. Quantifies potential sources of error in your measurements including a table of what you measured directly, typical values, and estimated uncertainty.

Rules

  1. You can use tubing from the fluids lab and a scale from the materials lab if you can get permission and access. Otherwise you are limited to household implements.
  2. You can take the density of water to be 1,000 kg/m3.
  3. If you need to go to a store to buy something please come and see me first. I may be able to lend you something or I will buy it and then lend it to you. You will need to explain why you need it and it should be cheap.

Due in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Take home lab – Personal specific gravity

This is a fun take home lab as the students have to measure themselves. It is also a lab in which the student should know roughly the answer before they start. Generally speaking, most people either just float or just don’t and therefore their specific gravity should be approximately S.G.=1. As with all the take home labs the students are required to use more than one method. The fundamental problem is measuring a person’s volume. There are a range of methods for doing this which often have significant uncertainty/error. There is, therefore, the possibility of having significantly different values from the two different measurements that must be reconciled through the error analysis.

When giving this as a take home lab I have generally found that the students are able to find two, and sometimes more, ways of doing the measurements. The students also sometimes borrow methods they learned about in other classes such as their materials lab. Once a team even worked out how to measure their submerged weight. It is a nice introductory take home lab as the measurements are easy to make but have significant uncertainty. Therefore, it is a good platform for discussing error analysis before they get into the more complex take home labs to follow.

As with all the take home labs I will not publish detailed methods for conducting the tests as I still use them in class and want my students to figure it out on their own.


Instructions to students

Introduction

The specific gravity of a fluid is its density divided by the density of water. But specific gravity is not unique to fluids. Your goal is to calculate the specific gravity of one of your team members using at least 2 different approaches.

Task

  1. Run a series of experiments to establish the specific gravity of either a member of your team or the team as a whole (or both if one particular method suits an individual test and the other suits a group test).
  2. Write a brief report that
    • Is 3 pages max including photos of you running your experiments.
    • Describes the experiment(s) you used to establish your result including:
      1. How the test was run.
      2. What data you collected.
      3. How you performed your calculations including diagrams, equations, and relevant theory that has been covered in in this class.
      4. A quantitative discussion of the uncertainties in your measurements and calculations including an analysis of the differences between your two sets of measurements.

Due in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.