Laboratory exercises in FYS200
Laboratory exercises in FYS200
THERMO- AND fLuID DyNAMIcS
Diana Lucia Quintero Castro, Stian Penev Ramsnes
2021
University of Stavange
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 XXXXXXXXXX
Instructions
Procedure
The laboratory exercises must be ca
ied out individually. That is, each one of you need to submit a report. The
eport consists of a Jupyter Notebook. This template will be published on Canvas before the laboratory session. This
eport 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 e
or 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 numbe
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/5
2c397b5a0415dbcfb9007383c0cd35f
https:
use.mazemap.com/#v=1&zlevel=3¢er= XXXXXXXXXX, XXXXXXXXXX&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-cali
ated. Settings and features should not be changed beyond what is described
in the instruction manual or directed by supervisors. E
ors 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
eported 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.
) 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
y Visual Studio Code that seem relevant (such as ipykernel). It may be that you have to install Python
eforehand.‡ Finally, we need to install the required components/packages that we will be using. This is done
y 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
owser 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 a
ow 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
unning the code contained. For Markdown cells, this means rendering the various formatting. To do this, you can
use the Run button in the Jupyter
owser, but it is recommended to learn the keyboard shortcut: ctrl + . A
elated 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 Home
ew:
ew 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:
ew.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 XXXXXXXXXX
– 4.567e3 equals 4567.0
– np.a
ay([1.2, 4.5, -39.8]) * 1E-1 equals a NumPy a
ay 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 a
ay, 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 = XXXXXXXXXX:
– 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
ackets. 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 ai
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