Laboratory exercises in FYS200 Laboratory exercises in FYS200 THERMO- AND fLuID DyNAMIcS Diana Lucia Quintero Castro, Stian Penev Ramsnes 2021 University of Stavanger Contents Instructions 3...

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Laboratory exercises in FYS200 Laboratory exercises in FYS200 THERMO- AND fLuID DyNAMIcS Diana Lucia Quintero Castro, Stian Penev Ramsnes 2021 University of Stavanger Contents Instructions 3 Programming setup 5 1 Specific heat capacity of air 7 2 Viscosity and pipe flow 10 3 Bernoulli’s equation 13 4 Ideal gas and Boyle’s law 16 University of Stavanger Last updated on 2021-09-21 2 Instructions Procedure The laboratory exercises must be carried out individually. That is, each one of you need to submit a report. The report consists of a Jupyter Notebook. This template will be published on Canvas before the laboratory session. This report has to be uploaded to Canvas. The deadline for submission is no later than one week after the experiments were performed. (We keep a record of when you were in the lab!) Four exercises have to be performed at the physics laboratory with room number D-352. Which exercise to start with is indicated during registration for the lab session. For the following exercises, the groups will circulate to vacant experiments until everyone is finished. Be aware that some waiting may occur due to different numbers of identical setups. You may cooperate whilst analysing the data. Still, the submitted report should be original and clearly stating how the data was processed to obtain the results. Suspicion of plagiarism or cheating will be reported to the TN Faculty for further investigation. It is important to include units for all numbers and figures. Many mistakes arise from omitting powers (e.g. using cm instead of m), and would be easily avoided. Be aware of uncertainties when performing the measurements and analysis, and use interpolation to estimate random uncertainty when using analogue instruments. A tutorial session will be given explaining measurement uncertainties and error propagation. Everyone has to be well prepared for all four laboratory exercises to make sure the laboratory session runs smoothly. General instructions for working in the physics laboratory are written in the following paragraph. It is assumed that everyone showing up to the laboratory session have read, understood and approved of these instructions. The laboratory tasks need to be completed and the report handed in and approved before entering the exam in this subject. The general HSE course has to be done before the laboratory week. It may be found as a general course in Canvas. Access Only students who are registered to the laboratory session have access to the room (D-352). Access is only provided at the scheduled times when the laboratory sessions run. Preparation Each student is to meet precisely, well prepared and in a “suitable condition”. The instruction manual must be read before attending the laboratory session. Short video footage may be found at Mediasite for students to get acquainted with the setups in advance. A QR code for this link: Laboratory report A template may be found on the Canvas course page. All final answers should be presented with a suitable number of significant figures and uncertainty. The necessary software is free and may be installed on a private computer. Computers in the «computer lab» (D-354) have Anaconda installed, a program suite containing Jupyter. A basic guide is provided in the next section. 3 https://mediasite.uis.no/Mediasite/Channel/5bb2c397b5a0415dbcfb9007383c0cd35f https://use.mazemap.com/#v=1&zlevel=3¢er=5.691384,58.938309&zoom=19.8&campusid=33&sharepoitype=poi&sharepoi=135649&utm_medium=longurl https://www.anaconda.com/ https://jupyter.org Equipment The equipment used is often pre-calibrated. Settings and features should not be changed beyond what is described in the instruction manual or directed by supervisors. Errors and defects with the equipment need to be reported immediately to the laboratory technician or the main supervisor. Using equipment to perform other «experiments» than those advised in the instruction manual is not permitted. Do not move any of the equipment. Theft will be reported to the police. Order and tidiness To get the best possible working environment, keeping good order is important. The workplace must be left clean and tidy. Safety The laboratory equipment and exercises to be performed represents a low risk as long as equipment is used as inten- ded. A first aid kit is available in the lab. 4 Programming setup In this course, you will be recording your data in a Jupyter Notebook (.ipynb) to compile your report. Although these are programmed in the Python language, no programming skills are required since a template will be provided in which you only need to substitute consecutive question marks (??) with your own measured values. You must still be able to open such notebooks and perform basic operations. Installation Python and Jupyter must be installed on the computer you are using. There are several options—here are some suggested ways of accomplishing this: a) The quick and easy way: Log in on a PC in the «computer lab» and start Anaconda Navigator. Launch the Jupyter Notebook program. b) The flexible and easy way: Go to the web page of Anaconda and download the free, «Individual Edition» to your computer. Install it and launch the navigator as described in the point above. c) Theprofessional way: Install Visual StudioCode†. Install the «Python» extension by Microsoft in Visual Studio Code. Open the template notebook in Visual Studio Code. Install miscellaneous requirements prompted by Visual Studio Code that seem relevant (such as ipykernel). It may be that you have to install Python beforehand.‡ Finally, we need to install the required components/packages that we will be using. This is done by opening a terminal/command prompt window on your system and enter the following: pip install numpy sympy pandas matplotlib sklearn Getting started Download the notebook template file from Canvas if you have not done so already. If you chose to use Visual Studio Code you can open the template file in that program. Otherwise, open Jupyter via Anaconda. In the Internet browser window that appears, locate the notebook template file and click on it to open it. Note how the document consists of numerous blocks, or cells. You can move up and down with the arrow keys, and , to select different cells, and enter edit mode på clicking (or double-clicking on a cell). The cells come in two types—they either contain code or Markdown. A code cell contains actual Python code, while a Markdown cell contains text in which one can use special syntax to make headlines, bold text, lists and the like. In our template notebook, the first cell contains Markdown. Select that and go into edit mode. Not how the headline is created with a number sign (#) and the bold text with two asterisks (**). If you leave this cell, the content may not go back to the way it was. That is because the cell «waits» to be executed. For code cells, this means actually running the code contained. For Markdown cells, this means rendering the various formatting. To do this, you can use the Run button in the Jupyter browser, but it is recommended to learn the keyboard shortcut: ctrl + . A related shortcut is + , which runs the cell and then selects the cell below. In addition to the two types of cells, there are two modes in the notebooks. We have seen how you can enter edit mode with the return key. The opposite is the command mode. This is when you are moving up and down to the various cells, and not in a particular cell. You automatically enter the command mode when you run a cell, but you may also leave the editing mode with esc (alternatively: ctrl + M ). You may notice that the code cells have an input label on the left-hand side, In [ ]:, with an index that increments each time a cell is executed. †Also available in Homebrew: brew install --cask visual-studio-code. ‡It is advisable to add Python to the environment variable PATH if possible (check «Add Python to PATH» if encountered). 5 https://www.python.org https://jupyter.org/index.html https://www.anaconda.com/products/individual https://code.visualstudio.com https://marketplace.visualstudio.com/items?itemName=ms-python.python https://www.python.org/downloads/ https://en.wikipedia.org/wiki/Markdown https://brew.sh In command mode, you can insert a new cell above with a and a new cell below with b . Cells can be cut, copied and pasted with x , c and v , respectively. To delete the selected cell, double tap on d . To undo this, use z . It is possible to convert a code cell to Markdown with m , and vice-versa with y . Additional keyboard shortcuts may be found here. Short notes on the template content • Scientific notation is essential in this report. In Python numbers are written in scientific notation by appending an «E» at the end of the mantissa, then the power term. Some examples: – 1.2345E2 (and 1.2345 * 1E2) equals 123.45 – 1.2345E-2 equals 0.012 345 – 4.567e3 equals 4567.0 – np.array([1.2, 4.5, -39.8]) * 1E-1 equals a NumPy array with the numbers 0.12, 0.45 and −3.98 Note that a lower-case «e» may be used. In the template notebook, you will also see that a common coefficient may be used to scale an entire array, like the last example above (when using NumPy). • Formatted strings can be used to mix text and numbers, and also control the number of decimals to be printed. Here are som examples where we assume x = 12.345678: – f'Two decimals: {x:.2f}' produces: "Two decimals: 12.35" – f'Three decimals: {x:.3f}' produces: "Two decimals: 12.346" – f'Exponential form: {x:.3e}' produces: "Exponential form: 1.235e+01" In the examples above, the syntax f'' signifies that the «content» is to be a formatted string (these are therefore called «f-strings»). The variables or expressions we want to substitute in, come inside the curly brackets. In our examples we wish to insert the value of x. The colon following x is a delimiter. The .2 and .3 tells the program to use two and three decimals, respectively, and the final f tells it that the form should be a floating-point number, and using e yields exponential notation. Using the notebook to generate a report When you are done making the report, you can export it to a finalised document in the form of a pdf or html file. If you are using the Jupyter Notebook interface in Anaconda, use the file menu: File Download as . 6 https://duckduckgo.com/?q=jupyter+notebook+keyboard+shortcuts&ia=cheatsheet&iax=1 EXERCISE 1 Specific heat capacity of air Purpose In this exercise the specific heat capacity of air at constant pressure will be determined by measuring the speed of sound in the gas. Theory The heat capacity of gases depends on whether it is measured at constant pressure or constant volume. The difficulty when doing measurements with gas, is to control these conditions. In this experiment it is therefore decided that indirect measurements will be most suitable. By finding the speed of sound of a standing wave in a pipe of a certain length, the heat capacity of the gas can be determined. Standing waves are created when two waves
Answered 3 days AfterOct 18, 2021

Answer To: Laboratory exercises in FYS200 Laboratory exercises in FYS200 THERMO- AND fLuID DyNAMIcS Diana Lucia...

Komal answered on Oct 19 2021
125 Votes
1.1 Plot xmax as a function of n. Calculate the wavelength, λ, from the gradient of the line.
Xmax = wavelength/2

Or wavelength = 2 * xmax
So, wavelength = 2* 3.1
wavelength = 6.2
1.2 Determine the speed of sound v with uncertainty. Use equation (1.2).
Frequency = 6.397
v = wavelength * frequency
so, v = 6.2 * 6.397
so, v = 39.66
1.3 Calculate the adiabatic constant κ.
v = under root((k * density)/pressure)
or k = v(square) *(density/pressure)
k = 1866.24 *(1.2/0.76)
so, k = 2929.9
1.4 Determine the specific heat capacity, cp. Use equation (1.4). The expected value is cp = 1.007 kJ/(kg K). How does your value compare to the expected value?
Cp = R * (k / (k-1))
Cp = 287 *(2929.9/2928.9)
Cp = 0.28kJ
The difference in the value given and mine is of 0.7.
1.5 Given that the bulk modulus (Ks = κ P) is approximately 2.2 GPa for water and 140 kPa for air, and that ρwater/ρair ≈ 780, will the speed of sound be smaller or greater in water compared to air?
The speed of sound will be greater in water compared to air.
2.1 Plot ∆V as a function of ∆t and determine V˙ .
V = 0.4/28
V = 0.014
2.2 Calculate a value for...
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