Do you remember the scientific method? A technical report is simply a written log of each step in the method and is the fundamental method scientists and engineers use to communicate with each other. This document will serve as a simple outline for writing such a report. We will give some general guidelines about what each section is meant to do as well as how to properly divide up each section. Along the way we will give you tips about how to incorporate the report into one cohesive whole document.

Remember, you will be submitting a group report and an individual report. The group report will contain the abstract, introduction, experimental procedure, and results, and must be a maximum of 5 pages. The individual report will contain the discussion and conclusion, and should reference the results from the group section. This report must be a maximum of 2 pages.

All lab reports are to be emailed to [email protected] as a PDF. The group portion of the lab should have group member last names, group number, and lab number in the filename. For example: Novoselov_Meehan_Huang_Group51_Lab1.PDF

The individual portion should include your name, your group number, and your lab number. For example: Meehan_Group51_Lab1.PDF

Abstract (10%)

The abstract should serve as a brief summary of the lab. Think of this section as the most elemental summary you can give of your activities in the lab. It should be a single paragraph that allows anyone to read it and get the general gist of the lab start to finish. Busy scientists have precious little time, so they often read the abstract to determine whether the paper is worth reading in full or not. The TA should be able to understand the 1) the main point of the lab 2) main setup of the lab and 3) main conclusions of the lab all from the abstract.

Introduction (15%)

What are we observing and why does this phenomenon occur? The introduction is the first foray into the scientific subject. This section serves two main purposes.

• Explain the purpose of the lab
• Explain the scientific concepts in the lab

The best lab reports are the ones which explain the concepts in the lab in their own words. It is best to consult 2-3 external resources for different explanations and perspectives on the topics at hand. Here is where you will want to include explanations for each of the topics and perhaps a reason why it is important to understand and explore these topics in the fluids lab. This is also where you will want to include any equations and illustrative figures to demonstrate further your understanding of the concepts. This section is very important, as any topics introduced here should be tied to the results as well as corroborate and explain them.

Objective and Purpose of the Lab

How do we explain this phenomenon based on what we already know? Do you have a hypothesis of what is occurring? Now that you have explained the purpose of the lab, it is time to introduce the objective of the lab. What are we trying to find out and why?

In other words, this is where you introduce the scientific question at hand. You have introduced lots of knowledge and information and this is the section where you propose what you are trying to demonstrate or explore. Often times we will pose this question in the lab manual.

Experimental Procedure (10%)

Develop testable predictions for the hypotheses that reduce error and bias. This section should be informative but brief. It is important for you to briefly describe the hardware which you utilized but it is not necessary to list every detail as your lab reports are already brief as it is and we provided you with significant hardware. This section is best served by a diagram of the setup and a description of the procedure used to ensure that your data is correct and repeatable.

Results (15%)

What did we find with the experiment? Hopefully this section is self explanatory. This should be populated with plots, charts, graphs with appropriate axes, labels, legends and explanations. Tables can be appropriate as well, but note that the data should be presented in the most succinct way as possible. We would like to see error bars where applicable, your reader should be aware of the uncertainty in any measurement you take. Additionally, if you can include a plot of what the expected answer is or what a theoretical/ numerical comparison would be, it would be highly advisable to include that as well. An ideal plot would have the results which you have collected with the appropriate error bars attached plotted around the expected analytic, theoretical, or numerical results.

Discussion (35%)

How does what we found compare with what we expected/hypothesized?
This is by far the most important section. This section should cover the bulk of the analysis and data processing. Now that you have presented the data, it is time to make sense of it. Below are a few important sections which you should be sure to include, but are by no means limited to.

Error analysis

The discussion is the perfect place to include a rigorous error analysis. This includes both quantitative and qualitative error. Be sure to list the largest and dominant sources of error using the equations covered in the lab lecture to quantify their effects. These values can then be included in your error bars in the Results section. We are primarily interested in finding out the sensitivity of our experiments to certain parameters. In an abstract sense, we can think of our measurement as an approximation of the actual value we hope to measure. In the following is a short derivation of the uncertainty or error analysis. We start with a Taylor expansion of a single measurement and assume it is centered about the mean value (note that ... means there are other, higher order terms we have neglected).

We then note that the sample variance (i.e. what we want) can be re-written with our definition of the Taylor expansion, above:

Then noting that the the variance of our variables is simply

We then sub in to our sample variance to get the following equation for the standard deviation of the sample

What are the units of the above equation? Is this the value you need to calculate error bars?

But what if our sample depends on multiple variables? The classic example of this is measuring resistance using Ohm's law where R = V/I so that R = g(V,I). Here we must expand on the example above by using a Taylor series for multiple variables:

We need an equation for the variance of a function of two variables, which is simply

And now we make a substitution

Then finally we simplify by neglecting higher order terms and substituting in the equation for the variance of variables (as before) to get:

This is a general form of the uncertainty estimate for a sample with two-variable dependence. Note that we have had to neglect terms of higher order, including co-variances among the variables. This means that all variables are independent and is an implicit assumption in this method. You can add additional terms to the above equation if additional variables are involved.

So what is the goal with all of this error analysis? We would like to find if our experiments match the theoretical predictions or expected values. If they do, then you are in good shape. If they do not, then you are most likely not measuring what you think you are measuring or your models are incorrect. This is why error analysis is so important. If the error bars between your model and your experiment do not overlap, one of them is wrong.

Expected Results

Now that you have constructed logical error bounds for your data, you need to know whether your accuracy is sufficient to encapsulate the behavior which you expect. Often times there is an answer which you expect to get. You should make sure to include these values and explain where they come from. Often times the data you expect to get comes from other experiments or physical models, perhaps even numerical simulations. It is important to compare in a quantitative and qualitative manner your results to the expected results. Do they follow the same trends? How far off are they from each other? Does your data capture the same physics?

Relation to scientific concepts

Now that you have constructed the error estimates for the data and you have compared the experimental results to the expected results, you should make sure to tie everything back to the scientific concepts at hand. Do the results make sense? Are your results consistent with the physics you expect? What physical mechanisms are acting to make the results adhere or diverge from your hypotheses? Your TAs and Lamyaa are a great resource for this section. This is truly where you can demonstrate mastery of the subject matter. Here you have to apply the physics and mathematics given in the introduction to explain and make sense of the data which you have collected.

Conclusions (15%)

What did we find and does it confirm/refute our hypotheses?
The conclusion is always a bit tricky to nail down. In its essence it is a summary of the lab, but in a very different way than the abstract. While the abstract is a birds eye view of the lab in order to give all of the major details from start to finish, the conclusion is where you get to focus on the messages that you want the reader to take away. Everyone has a different style for the conclusions, but commonly it is the best place to reiterate the main points you are trying to convey.

This is your last chance to discuss the major findings of the lab and reflect on what you have learned and what you see as logical next steps. Additionally, it is a good place to pontificate ideas for how to improve the experiment. In short, having just made lots of arguments and analysis in the discussion, the conclusion is the final place to persuade the reader of your arguments and analysis.

General Suggestions

Significant Figures

In general it is important to know and acknowledge sig-figs. While we will not take off points for misuse or abuse of sig-figs, it will make your TA cry.

Plots

When possible, plot comparable data on the same plot. Additionally, in fluids, it is usually prudent to non-dimensionalize the data in an intelligent manner. Use your Buckingham Pi skills so that you can relate as much of your data to the fewest relevant parameters. A perfect example of this is from Lab 2 where you compare the friction factor to the Reynolds number. Another, perhaps less obvious example, is from Lab 3. Here it would be prudent to plot the boundary layer as a comparison between the velocity normalized by freestream velocity and the vertical distance by the boundary layer thickness (or perhaps the similarity variables).