They said that lift might be hard to understand, but drag is in fact harder.
There are two kinds of drag, form drag and skin drag.
Skin drag is the resistance between a moving surface and a viscous fluid. The fluid tends to stick onto the surface, thus causing skin drag. That thin layer of fluid that is directly affected by the presence of a surface is the boundary layer.
Reynold's number is a parameter that measures how much of the flow is controlled by viscousity and how much is affected by speed of the flow. At high values (Speed is more dominant), the boundary layers break away from the surface because they can't change direction along the surface fast enough, and the flow tends to become turbulent. This turbulence (or the wake) appearing behind the moving object causes form drag.
Aerofoil
This link might be useful in understanding turbulent wake flow.
At different Reynold's numbers, different flow patterns occur.
Can't find pictures of flows with increasing reynolds numbers. Instead, here is a link about drag.
I can't say anymore myself because I am not familiar with this topic.
One day a HYDROGEN airship selling HELIUM balloons landed in front of a LITHIUM battery shop to buy some precious BERYL crystals.
The shopkeeper told the pilot "we sell batteries here, not crystals you moron!" which was only expected considering the pilot was a bear, making him a BORON. Borons, just like any other living organism consists mostly of carbon with excess nitrogen in them making them really muscular but at the same time exceptionally dumb.
Taking in a deep breath of OXYGEN, the Boron realised that his mouth really stank, so he took out his FLUORIDE toothpaste and started brushing his teeth. This made him grab a lot of attention from other customers like a NEON sign in the middle of a rural village where SODIUM chloride (Salt) was very expensive. What makes this village worse was that it did not contain any traces of chlorophyll (MAGENSIUM) which makes it unsustainable.
The Bear thought of this immediately and boarded a ALUMINIUM hull aeroplane to render assistance to the villagers. Landing was rough, as the ground was covered in SILICON filled sand and soil. The bear cried "No wonder there aren't any plants, this soil is PHOSPHOROUS deficient!
Just then, a snake bit him. The bear threw SULFUR on it and it got angry. The snake chased him and the bear ran and jumped into a CHLORINATED swimming pool. An ARGON filled light bulb sprang up in his mind. He had an idea on how to re-establish this community.
First, he gave POTASSIUM rich fruits and vegetables to the weak and frail villagers to eat. Then, he fed them CALCIUM laden milk to build up their bones. Next, the bear donated high end sports equipment made of SCANDIUM alloys to build up their strength. Then the villagers got strong and started getting greedy. They demanded the bear to give them TITANIUM and VANADIUM alloy fighter jets coated CHROME green. But their metal industry was developed yet, so the bear started ordering MANGANESE to process IRON and steel.
The bear wasn't pleased at the villagers' ungrateful nature, so he secretly installed an electromagnet made of COBALT on his aeroplane and turned it on, sucking all their metal away from the village. The villagers were very sad, and tried to appease the bear by giving him their NICKEL coins.
However, the bear was not easily swayed. Eventually, the villagers were left with no choice but to cut the COPPER wires of the aeroplane electronic system to stop the bear from taking their metal away. The instant they were cut, brass (copper + ZINC) instruments started sounding all around them. The bear ran in and shouted "How dare you people destroy my GALLIUM and GERMANIUM circuit boards?!"
The villagers ran towards the bear and tried to force ARSENIC down his throat in an attempt to silence him. The bear broke free and forced their faces down onto the photocopier that uses SELENIUM to photocopy their faces, used his old-fashioned camera with silver BROMIDE photography film to capture their images. However, the villagers turned on a flashlight filled with KRYPTON gas, directing it towards the camera and ruining the photographic film.
Lesson 4 was an severely crashed course on fluid flow analysis. So crashed, we practically couldn't apply what we learnt. Fluid mechanics really scared the crap out of me this time.
When I am sick, I always have this dream. I wouldn't say dream exactly, but this mental state, where I am half awake, but I perceive the world so complicated that it tortures my mind. Literally, I feel tortured whenever I have this 'dream'. It's like my brain isn't big enough to comprehend whatever I am thinking of, and it is undergoing system errors.
Imagine it this way. Look at your surroundings, resting on the bed, subconsciously aware of them. Everything looks normal. Then, everything suddenly zooms in, your line of sight remains the same, but suddenly, you start seeing things at the molecular level. And you start trying to make sense of each individual molecule working as a part of your surroundings. Thus, your brain now is filled with information the amount of molecules in your room. You are trying to imagine them as lego bricks, and someone at the back of your mind asks you to re-build your surroundings by stacking these molecules, like lego bricks.
Then, you feel so tortured that you fall asleep completely, but you are not let off. Now you float in space, and I cannot recall the details. As you know this happens when I'm sick and I'm sleeping, so I never manage to remember how exactly to describe this horrible feeling. Anyhow, it is a mental torture.
Trying to make sense of fluid mechanics compared to undergoing this sort of mental state is actually nothing. However, it would be good enough to describe fluid mechanics as its counterpart during my consciousness.
I am currently having enough problems in comprehension in very basic E&M, such as Gauss' Law. How I imagine fluid mechanics would work(I might be wrong) is a blend of vector calculus and chaos theory. After all, the vortices I see in pictures of fluid flow really remind me of strange attractors.
DISCLAIMER: Whatever you are going to see from here to there is most probably wrong
Here Then one day this lecturer comes along, starts off by introducing the Taylor series, and starts deriving the expressions for divergence, vorticity and deformation by assuming there is already a function for the system of fluid flow. I can accept that, but how do you even model a function for the fluids in the first place?
Another thing that comes to my mind is that fluid behaves really weirdly and it seems that no two times will I exactly see my bowl of soup behaving the same way. This led me to think that fluid (especially at high speeds) can exhibit chaotic nature, and now even my only pillar for security, the function which we assumed we already know, becomes hazy.
And if you haven't noticed, we (or at least I) have no idea what is going on in vector analysis, as you can see on the chart. It is just mind boggling to imagine infinitely many vectors associated to every point in a field.
I have no idea whether what I said was correct, but to sum it all up, I 'learnt' fluid flow analysis in two pages of notes. In other words, I learnt practically nothing.
This are the 4 main nothings that we learnt in the lecture.
Divergence: The supposedly rate of area change Vorticity: How fast it spins Deformation: Squash squash squash
THERE
Although my understanding did not increase much, the lecturer then started talking about real life applications, and it FEELED like that I started to understand certain phenomena such as cyclones better on an extremely shallow level after an hour of exposure to fluid dynamic jargon and pictures.
I know I haven't.My feeling then was that this was a topic that I will never understand and learn in my life because it was too bizarre for the mind to contemplate. But again, this was the feeling I had when I was in primary school after being told that with something called Integration, you can find the PRECISE area of a mathematical shape without any error.
Here are some interesting videos my lecturer showed us. Don't ask me how they work.
Start off with this tank. It is really simple, just a tank with a hole at the side. But with just a hole, air will bubblie in, so let's make the wall penetrate downwards a bit more so that the air will have a harder time bubbling in.
WARNING: Provided the height of water is low enough such that the pressure at the depth of the whole is less than atmospheric pressure. the water will (hopefully) not flow out. However, if the column of water is too high, atmospheric pressure will not be able to support the weight.
Atmospheric pressure is 760 mmHg. Since mercury is 13.5 times denser than water, 1 atmosphere will hold up 10260 mm = 10 metres of water. As long as you conform to that height limit, the tank is safe. Next you add your fish and plants and stuff inside the tank. Now visitors to your interactive tank will be able to feed your fish and touch your fish.
Warning: Ventilating your tank with an oxygen pump is NOT a good idea. The oxygen will soon displace the water and your fish will be soon swimming in air. Instead, be sure to get someone to design an extremely complicated system for channeling the water out of your tank and aerating it in a chamber independent of the tank, then pumping it back in.
Warning: Do not place exotic fishes in your tank. People might steal them.
And you're done! Probably the worst thing that can happen now would be this.So just make sure that you keep a lookout every now and then.
SECTION 2 - THE BALOONEY EQUATION (sorry I found the common mispronunciation so funny that I just had to put it down)
In a closed system, energy has to be conserved. This basically means that the gravitational potential energy, kinetic energy and pressure exerted perpendicular to the direction of liquid flow is more or less the same. In other words: Pressure + Density*gravitational acceleration*height+0/5*density *velocity^2 is a constant throughout the system.
Whatever that means, just now that the faster something flows the less pressure it exerts and the lower its height the faster it flows. Makes sense doesn't it? Things go faster as it go downhill. Just as usual, the lecture was boring.
The demonstrations were just a tad more interesting.
Erm... I guess many of us had seen this many times. Air flows around the ball, causing a region of low pressure around it. When it goes out of balance, the surrounding stationary air with higher pressure pushes it back in.
Atomizer. Water gets sucked up and a cocktail of body fluids and water is sprayed out.
Some burrow design by prairie dogs. Different shape of entrances to allow different flow speeds at different entraces, resulting in a pressure difference that allows ventilation.
I went to watch the Talent Search Finals on Monday.
The first girl dancing in the individual category had rather slim chances of winning anything. She did some Chinese dance, with those disgusting poses I always see in Chinese dance. (NOTE: I am referring to the performance, not the person) I think the form and all is okay, but this is a talent search, and I do not see any talent in doing such normal stuff.
Second performance was by Fred the pro guitarist. Not really up to professional standard, and some plucked notes did not sound, but compared to anyone else I know playing the guitar, he surpass all of them. First time I saw someone strum and pluck at the same time, live.
Next was a piano performance composed by Bartok. However, to me it sounded awful and boring, even if there were no technical flaws. I prefer instrumental music with more prominent melodic lines, but stuff like Bartok just sounds like a well-tuned elephant rumbling across the keyboard.
Fourth was a singing performance. In tune, but I don't like the way her timbre changing at different pitch ranges. Very boring voice too.
Fifth, a girl called yawen sang and played on the guitar. I'm tired of saying this, almost all singing performances are out of tune. But for this one, it seems like its imperfection was contributing to its style, which i liked. It was as if it was meant to be sang out of tune, like half singing, half talking...
Sixth, lzw singing a chinese song. It would have been rather acceptable, despite a few out tune notes, until...
Well until he started playing the electric organ which was in a totally different key from the music and that was when it started sounding horrible.
Last performance was Nic ho. Piano. Rachaminoff. What do they make together? Plain noise. I guess I am not really appreciative of late romantic piano music. Like I said, it was difficult, but boring. What is the point of playing something that is hard to play, and not enjoyable to hear?
So I choose Ya wen and Fred.
Then came the group category.
Dice, the korean band had drums at all, unfortunately it did not sound too good.
The two a capella groups' vocals was nice, and had a lot of potential in winning, but they needed quite a bit more practice. The different voices don't come in together and don't phrase properly. The 407 lady gaga medley was better the year 6 group though.
604's performance, sorry but no hope to them. The girl's (who looked like a boy) voice is good, but the rest of the class made the whole performance look really random.
And there is Anzhi's and Xuehe's 'more than words'. For a person with a china accent, I am actually surprised and impressed with xuehe's singing. Would have voted for that, but I didn't, because there is a dance group too, CBC. It was really entertaining. Real talent by the girly looking guy in the spotlight, unlike the individual chinese dance performance; he was dancing the best among all the other girls. The feminine actions were really entertaining and humourous.
Then again its only one vote per category. Considering that there were different genres of performances, and each genre had its best performance, I was struggling between Yawen's guitar playing and singing and Fred's guitar solo, and between 'more than words' and CBC. Results
Individual:
1st: Fred (Woohoo!) 2nd: Nicholas Ho (Please don't choose rachaminoff anymore!) 3rd: Jesicca Loo
Group:
1st: CBC (Awesome) 2nd: Kenneth and I (Lady gaga medley a capella singing. Not bad actually) 3rd: Dice (Come on, they can do better...)
I was actually hoping 'more than words' got third place instead.
Finale was "Hallelujah" sung by Mai Trang. Come on, if she participated she would have owned them all. In terms of technical skills, hers was the only perfect one. A real pleasure to hear her sing. Not like others where I keep on thinking "Please hit this note right, please hit this note right. OH NO! *shivers*"
More than words, by westlife:
Hallelujah, by Leonard Cohen. One of the most beautiful songs I have heard.
Singaporean drivers are really 'kiasu', or being scared of second place. From parking lot snatching, reckless overtaking, speeding, many would do anything just to put themselves at an advantage. And my father had these experiences first-hand quite recently.
Like the chinese saying goes, know your enemy well and you will triumph. Mind control isn't really a far fetched concept from sci-fi thrillers, it exists in everyday life, with many 'reactive' personalities falling victim under the control of more 'proactive' beings.
I think J.K. Rowling has put it pretty well in Harry Potter and the Goblet of Fire, that mind-control (Imperius Curse) only works to the self-unaware victims with weak willpower. The first thing to avoid mind control would be to be aware of your actions, and knowing that they come as a result of your will, not of others, which is what I'm going to illustrate below.
Mind control on the road.
1) Drive on the first lane 2) Wait for a seemingly innocent driver on the first lane 3) Signal to go into the first lane
The result would be drivers anxiously speeding forward just to not get overtaken. Before long, a line of cars in front would be tail-gating and you'll have the whole empty stretch of road behind you, perfectly safe for changing lanes. A rather comical sight.
Patient and more self-aware drivers do not suffer this kind of 'mind control' however. It's like the rest of the drivers have this mentality of not letting others overtake them pre-programmed into their minds.
Last Tuesday was a lecture about hydrostatic pressure.
It was really boring. For around 45 minutes the professor tried to explain why pressure throughout a liquid of same depth is constant. I wanted to sleep, but it would seem rude
However, the applications and demonstrations of hydrostatic pressure were rather interesting, yet simple.
1) Land surveying
With a main water tank and pole filled with water connected to the tank with a hose, altitude at which the pole is can be read via markings of the pole. Of course we have to make the water in the tank a lot compared to that in the connecting tube and the pole, so that the change in datum (water level in the tank) is negligible.
2) Hydraulic jack
I always thought that hydraulic jacks were gigantic pieces of equipment controlled by machines, because the great difference between the force humans apply and the weight of the truck is so large, in order to gain sufficient mechanical advantage, one will have to go to the top of the empire state building, hold onto a handle of the same height, and jump off the building in order to lift anything. Turns out that I had the wrong idea. People wouldn't be that stupid. Instead they suck hydraulic liquid from another chamber when needed, so we can push the pump back and forth, drawing liquid and pushing it, instead getting a darwin award.
3) Siphon. Water sucker. Found out about the siphoning effect years ago, but never really thought about how it worked.
4) Magdeburg Water bridge.
As one walk across a conventional bridge, center of mass shifts from one pillar to another. However, in a water bridge, pressure throughout the fluid remains the same, so assuming that there is little turbulence, the force is always evenly spread out across all pillars.
A water bridge in Germany, 918 metres long, the longest aqueduct in whole of Europe. It has been planned for 80 years, but put off after the splitting of East and West Germany. Now, it is used to connect Berlin's inland harbour and ports along the Rhine.
5) Lastly, we were given the task of coming up with a design for a fish tank which allows people to put their hand through a hole at the side to touch the fish. I heard of something like that in Underwater World in Sentosa sometime ago. However I found nothing when I searched the internet. Even went to Yahoo answers, but people gave me useless answers like reach your hand from the top, or have a pump that continuously pumps water back in as it spills out.
Here are some more ideas.
1) Vortex. Vortex tank creates a vortex in front of the opening like a washing machine, so the water does not spill out. Reaching your hand inside might disturb it though, so this 'reach in tank' is a see no touch
2) Plastic gloves. Transparent gloves makes it look as if your hand is reaching in. Gloves are coloured in picture for easier viewing. You can't feed to fish in here, because fish food does not pass through plastic.
The Youth Olympic Games in Singapore are just round the corner. There are a variety of attitudes towards this event. Some are really enthusiastic about the event, as it bonds youths from all over the world and gives Singapore a chance to flair its abilities, while others just think its just a waste of money.
For me, I am sitting on the fence, but there is one newly brewed policy I can't swallow. I might not be a driver, but I am a commuter.
Giving way to YOG vehicles you see on the road, as that helps them get to their venues on time and depict Singapore as a gracious country. And if you are caught not being 'gracious', you can get fined. The next thing you'll know is getting thrown into jail because you didn't greet a YOG star.
Like some netizens have said, road users have contributed to road taxes so I believe all have an equal right of way. Giving way to emergency vehicles are justifiable, because we are talking about the fragile border between life and death here. Giving way to buses, I suppose its rather acceptable, considering that they are constantly filtering in and out of bus stops, and if we do not give way during a peak hour, they will never get out of the bus stop, so let's be a little empathetic.
But how are YOG vehicles any different from other road users? They are practically like taxis, zooming from place to place directly, carrying HUMAN participants who are considered VIPs just because they are good at a sport. Why should anyone give way to them. I mean if I were I driver, I wouldn't overtake them and start cruising at 20mph, but I wouldn't see any reason to give way to them either. Are they explosive or what?
If they are worried of not being able to reach their destination on time, I would quote some suggestions, that they leave early, or take public transport. Considering that they aren't any auxillary police flanking the YOG buses (No I wouldn't want that), I don't think taking the public transport is much more dangerous.
If all these can't be done, then instead of taking it out on road users, we should stop inviting these major(fine, not so major), international events into Singapore. Just admit it, a country with little land space can't get any bigger than what it already is without making more sacrifices. I think wanting to increase the population to 6 million is not a really good idea, because Singapore is already crowded enough.
No matter how good our government is, ultimately we will still be weighed down by physical limitations.
So please remember not to get involved in any accident for the next few months, or you might be fined because the bus driver took a picture of you in the ambulance which did not give way to him, because you got injured at the wrong place and wrong time.
Like at any other start of a new semester, I make a resolution to work really hard at school and keep on top of every task. And like any other semester, I fail to keep it for one moment, get discouraged and from there I spiral hyperbolically into my own self. Then as the holiday approaches work intensity starts to diminish, and a good chance arrives for me to start fresh. And the process repeats itself sinusoidally.
But one thing isn't a problem, or perhaps it is so minute a problem that it IS a problem. I am definitely interested in mathematics, just maybe not so much in number theory. In my opinion, among all the other branches of mathematics, number theory is at my standard, the most useless piece of mathematics, because I can't do it, and I don't see how I can apply it to solve problems. That is why I get so depressed after participating in Mathematical Olympiads. I hope that soon I will be able to break out of this paradigm, and the only way to do it is to learn number theory.
This semester we are starting on calculus. So I finished all the notes and tutorial that the teacher had given out by the third day of lesson. Finishing notes beforehand is not much use, but I just like it. Makes me feel like I have triumphed over my notes. So now in calculus class I don't have much to do other than read my calculus textbook, or talk to other people who have defeated their notes as well. But the urge to finish doing more calculus is still there, and I believe the same thing will happen the moment the next set of notes come.
Unfortunately, this isn't really my attitude towards other subjects.
Something new we started on was Polar co-ordinates, Parametric equations and vector functions. 2 hours of lessons a week for any other subject like biology might seem to much. But for this I find it too little. And I'm glad that the teacher is going faster than other mathematics teachers I have seen.
Polar co-ordinates is something very new to many of us, and thus the shapes of the curves are not easy to visualize. Thus I feel that there is a real need to really spend some quality time thinking about how different curves are formed, in order to get used to it, rather than use the calculator to graph it and get the easy way out. We won't learn much that way.
Timetable this semester is good. Afternoon releases on Tuesday, Wednesday, Thursday and Monday, if no CCA. I thought it was wonderful, before I counted in all the extra stuff I had to do. Waiting for 3 hours on Tuesday for Aerodynamics. Going to DSO on Wednesday, and probably German on Thursday. I wanted to shift German to Monday, then I realised that there would most probably be string ensemble practice on Mondays. I would have had chem olympiad training on thursday, if not for the fact that I am going to have German, the course outline was filled with nausea-inducing topics such as physical chemistry, and some of my friends are not attending it. :(
Nevertheless, this timetable is much more relaxing.
School food finally has its last straw of disgustingness. Now that the timetable isn't so cramped, I will try to eat out on days such as Tuesday, Wednesday and Thursday or I could pack my own lunches, which is surely more healthy than the crap the food stalls are serving. I now hereby boycott all the stalls except for the snacks stall, the Cafe, and the friendly looking vending machines.
String ensemble is going for SYF next year, so yesterday we had an audition. I have been practicing quite a lot, and after waiting for 2 hours++, I got auditioned. I believed I should have played pretty well, if not for the fact that I tend to tremble during solo auditions. So my legs were trembling, and it wasn't that noticeable when I played Brandenburg, but when it came to Vocalise, the trembling of my legs propogated up my body and onto the violin, making the long sustained notes tremble...That was pretty discouraging, because I played pretty badly. I just hope that I will get to play 1st violin, because 2nd violin parts are sleep-inducing.
This year, I hope that orchestra will start playing some real music. There has been gradual improvement, and I don't mind the music being simple, as long as I don't see the words oboe, flute and Stephen Bulla on the violin scores.
Aerofoil
