The lesson on Monday, 26^{th} Oct was split into 2 sessions, where the first 2 hours were on water treatment and the next 2 hours were on mathematics, focusing mainly on the topic of probability.
Water Treatment
Treatment frees the water of harmful bacteria and suspended particulate matters including those in the micron range, making it clear, sparkling, odourless, colourless and safe for consumption. This can be perceived as a “cleaning” method of sorts. Altogether, there are 4 stages in water treatment: coagulation, flocculation, sedimentation and filtration.
In this session, we carried out the first 2 stages of water treatment – coagulation and flocculation
Materials
1.5 litres of contaminated water, gloves, potassium aluminium sulfate, KAl(SO4)2 (alum).
Apparatus
3 plastic cups, spatula, turbidity meter [1], pH meter, conductivity meter [2] , dissolved oxygen meter, and a pipette
1 = The measure of how cloudy the fluid is, measured in Nephelometric Turbidity Units (NTU). The cloudier the fluid, the higher the turbidity, hence the higher NTU value.
2 = The measure of the ability of a fluid to pass an electric current, measured in Siemens per meter (S/m). It works upon the presence of electrons. The more electrons in a solution, the higher the conductivity.
Procedure
- Pour 500ml of contaminated water into 3 plastic cups and label them as cup A, B and C respectively.
- Measure the turbidity value, pH value, conductivity level and dissolved oxygen percentage of the water samples using the meters the various groups had calibrated. Record the data in the table.
- Measure and squeeze 5ml of alum into cup B and 10ml of alum into cup C by using the pipette.
- Stir the mixtures in each of the 3 cups continuously with the spatula for 5 minutes.
Figure 1: Stirring the cup of mixture with spatula
- Observe the differences in each cup every 5 minutes for 20 minutes.
- Measure the turbidity value, pH value, conductivity level and dissolved oxygen percentage of each of the samples using the various meters. Record the data in the table.
Figure 2: Observing the dirt particles in the cup
Clip of the dirt particles settling at the bottom over 5 minutes of time
Observations
- Tiny particles were slowly starting to form into a bigger clumps
- Mixtures with alum are getting clearer and clearer
- Particles began settling at the bottom of the cups
Explanation
Most dirt particles are negatively charged. Thus, the particles would repel one another. Also, the particles are very small and due to the resolution of forces, despite there being a gravitational force present, they did not settle at the bottom of the cups.
- Through the dissociation of alum, particles of a positive charge are produced and this causes it to be attracted to the dirt particles. Now that the charges are balanced out, they tend to clump together to form flocs [3].
- The large clumps tend to settle down at the bottom of the water due to gravitational force.
3 = A loosely clumped mass of fine particles.
Data
A | B | C | |
Turbidity (NTU) | 161 | 58.2 | 43.4 |
pH | 7.64 | 4.822 | 3.445 |
Conductivity (µS/cm) | 202.2 | 1174 | 2002 |
Inferences
The pH of the solution increases when more alum is added between 5ml to 10ml of 50g/L solution. When more alum is added, more aluminium sulfate ions collide with the particles in the solution to produce more H+ ions in the solution which are responsible for creating a more acidic solution.
This raises the pH as the concentration of OH- ions increases,
The net effect is that the amount of H+ ions produced is greater than the amount of OH- ions produced, resulting in an overall lowering of pH as it becomes more acidic.
Mathematics
For the next 2 hours, we learnt about probability and its applications. We were asked to watch a couple of videos before the lesson so that we would have a rough idea on what was involved in z-tests and t-tests.
We were then given a few questions to solve in the classroom and that required the knowledge derived from the videos.
The first few questions dealt with things we have learnt before in Engineering Mathematics, about normal probability distributions, coupled with the z-tests we learnt from the videos. However, Dr Xinli taught us about something new – t-tests, a subset of hypothesis testing. T-tests are in essence tests used to determine if two samples of data are different, as extrapolating from the data at face value is not sufficient to conclude whether or not two samples of data are the same or different.
Dr Xinli did not teach us exactly how to perform a t-test, but pointed us on the right track to find out more about how to perform t-tests. She also provided the following links to learn more about t-tests:
- Hypothesis Testing: http://stattrek.com/hypothesis-test/hypothesis-testing.aspx
- Hypothesis Testing for a mean: http://stattrek.com/hypothesis-test/mean.aspx?Tutorial=AP
- Hypothesis Testing for a different in means: http://stattrek.com/hypothesis-test/difference-in-means.aspx?Tutorial=AP
- Khan Academy videos on Hypothesis Testing and p-values: https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/hypothesis-testing-and-p-values
The aforementioned links came in very useful when we were given an assignment to apply the two-sample t-test to determine if two samples of data gave the same trend or not.
Conclusion
It was rather confusing when we first started carrying out the experiment. We were uncertain on the procedural steps initially, however, lecturers and friends were there to assist us. They reminded us and took a glance at our progress from time to time, making sure we were on the right track and not missing anything out. For that, we are grateful.
Kudos to Hwee Peng for compiling the data, Ajay for keeping us on track and Ryan for helping us taking the photos. Good job guys! 🙂
When it was time for Mathematics, gosh, I have to admit that I was very lost. I did not know what it was about and how to start. Thankfully, Ajay understood it and was very calm in explaining it to us and clearing our doubts very patiently. Slowly but surely, we managed to solve all of the questions.
I am truly thankful to be in a group with such helpful friends and I hope to learn more from them!
Thomas Wong