What do these damn numbers mean

This week I gave a student seminar at CREATe (Cnetre of Renewable Energy and Aerodynamic Technology). CREATe is a big collection of research groups aimed at working in aerohydrodynamics and has these seminars every friday afternoon where a social (it’s generally coffee and donuts) takes place followed by a studetn giving a talk. My talk? It bombed. I tried to make a lot ofjokes but from some whispered giggles I heard nothing. I got some insights from Agastya, a senior Ph.D. student who said I did well for my first CFD talk but I feel I bombed this whole thing…well you always got something to improve.

But that’s not what I want to talk about today. On Tuesday eveing while going back, I suddenly read Reynolds stress and thought about the reynolds Number. And I realized I could not remember the formula. (I now remember it as a Valentine’s rhyme:

“Roses are red,

Violets are blue

Reynolds Number is,

rho v L over mu!”

)

But coming back, I could remember it because of the rhyme. Gee, that’s a formula I learnt in grade 11, my sophomore year, preparing for competitive examinations for graduate studies and I yet could not remember. No problem, let’s try Froude Number. Doesnt’ ring a bell. Ok third time’s the charm, weber number? No frickin idea. Okay, how about Strouhal Number? No I don’t know and I am a grad student! And it suddenly brought me to the days when I used to write a cheat sheet befroe my undergrad end semester exams and practise them as a final revision. I read them on the walk from my hostel to the campus and I used ot forget the moment I used to reach. I went back more in time because I rememebr this question titled

What is the Reynolds Number? Write its formula.

It was grade 11 physics end term. I knew it because I barely passed the exam. But I still could not remember what was the formula of this damn number!

But I knew at least something about it. Now, if we have a fluid like water flowing over a body and we increase the number, I knew it would transition from laminar to turbulent flow…the flow would not be as silky as it used to be as I increase the number. My research deals witht he reynolds Number of 1.9e5. This means the flow is very turbulent, you can see eddies of the resulting turbulent flows. that’s extremely tuburlnet flow. But I didn’t knew the formula. I found the froude Number on Wikipedia next. The formula is defined as:

Fr = u/sqrt{gL}

Here u is the local flow velocity, g is the external field and L is the characterstic length. To be honest, I saw the formula over 4 times to make sure I wrote it correctly. But what does it say about this damn number? NOTHING! I won’t remember it by next hour. I would have to use take out a Fluid Mechanics book and read this number. But when I see L, I think gee, this L should be low to maintain this number good and its flow field, let’s say in a mass of water should be low too while the velocity should not be too high. there’s a squre whic means the value of this number is not big something, around 2 or 3 will be more than enough. This means this number would help us in marine architecture as you don’t need your length to be too large or velocity to be too large that you face more resistance from th water. This means it helps us to determine the resistance of a ship to its water body. Now, just remembering the formula won’t do anything. IT won’t help you or me imagine it’s importance or anything- it just is a simple formula. Consider another question we could find in any grade 11 physics book:

The density of honey is 1380 kg/m cubed. The velocity is the 5 m/s. The characterstic length is 2 cm and the viscosity is 2000 mPa.s. Find its Reynolds Number

Well, that’s some arithmetic we can do mentally. But it doesn’t make any sense! What makes sense is damn, honey is highly viscous liquid and despite such a velcoity and density you still have a very laminar flow. And you think of the honey’s large viscosity. Your thought train goes either with buying it at Kroger or the Newton’s law of viscosity. Mine went with the latter; and I think man, there would be an enormous amount of force required for a body to flow with a very low velocity in honey as compared to water. And that’s because you stop looking over the damn formula and realize what that number means. So goes the Weber number, strouhal number and what have you

Now there will always be a guy/girl who’s like “Dude, that’s because you know the formula! “- there always is. But they don’t realize the crux of my rambling- I ain’t saying them formulas are not important. I am saying they are not important to learn memorize You have your formula books for that. You need to realize the essence of those numbers, what those numbers actually mean and how their founders found their formulae. The numbers are NOT defined by the math around them but the damn physics!

TL:DR, It would be much better to have a question like “Draw a flow over a body with Reynolds Number of 8000. The number is defined so-and-so” That would test the person’s knowledge of physics. That would help the person build a proper fundamental interest when he/she sees this number somewhere and reckons, “Damn, this number value means something”. and that’s it. I realized from now on, I would always try to understand the essence and flow physics behind them. What they actually mean. And Forget the formulas of these damn numbers!

In case someone wants to memorize the numbers and then use them to define as questions in an examination, try memorizing the logarithm table and asking yourself “What’s log 17.11?”