Saturday, September 28, 2013

Unit Operations

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The one lasting regret of my life is that I had to learn with great difficulty and unlearn and relearn what were called Units & Dimensions.

It all started when I was 5 and Father tried teaching me how to tell time on our grandfather-clock...the Galileo's original pendulum...hanging on our wall. It was a mystery to me since I learned counting up to 100 and I was told that the greatest invention of mankind and Indiankind is the invention of the zero and the decimal system. There was no reason why the day should be split into a dozen hours and so also the night. Why not 10? Or 100?

And that every hour is divided into all of 60 minutes and every minute into 60 seconds. I asked Father why and he kept quiet...maybe he banged me: "Don't ask...just listen!"

I came to know later on that the entire mischief stemmed from the Egyptians (or Greeks?) who fancied that it would be nice if the heavens could be split up into 12 zodiacal signs. If you had ever looked at these so-called signs like the Leo or the Virgo, not to speak of the huge Scorpio, you will see it is utter nonsense...they are all of different sizes and some of them don't resemble anything at all except for fevered imaginations...like say Cancer (I hope I don't get it soon). There could as well have been 50 zodiacal signs named 1, 2, 3...50. And the day could have been divided into a neat 100 hours and so on...no more dozens.

Talking of dozens there is this squeamish baker's dozen (13). When I went to Vizagh, I was duped by the fruit-sellers and flower-sellers into believing that 100 is a hundred. I came to know from cognoscenti later on that, in the Poorna Market, 100 means 115 and 120 if you can drive a hard bargain. 

And then came this mile. We had to mug up that a mile has 8 (?) furlongs and a furlong had 220 (!) yards, a yard has 3 (?) feet and each foot has 12 (again) inches. And I had to mug up things called acres, links and hectares for square things. 

I am told that the Americans in their pigheadeness still stick to miles. Otherwise they were so nice to divide their dollar into 100 cents. Unlike the Brits who stuck to pounds (sterling, not to be confused with avoirdupois) and all those shillings and pence which we had to mug up...also guinea (pig?), crown, farthing and what not. And ours was no better...we had a rupee that was divided into 16 (?) annas. Each anna had four chinna dabbulu. Each chinna dabbu had 3 (?) dammidis. There was a pedda dabbu which was neither here nor there...it had all of 4 dammidis.

I don't know how I survived manipulating all these queer figures...totally unnecessary. 

I then went to the University to do physics (unfortunately) and had to master what were called 1. the fps system, 2. the cgs system, 3. the MKS system and 4. the SI system. In addition, there were the engineering units like the BTU, pounds and poundals and slugs (serves them right). 

And in my third year we had the horrible subject called Electricity and Magnetism. Fortunately by then we could forget the fps business but had to learn two types of cgs (the esu and emu) and the conversion between them...involving only powers of 3 and 10...someone thought that the speed of light was 3 x (10 ^10) somethings.  

Incidentally, I just now typed (by mistake) in Google:

"Speed of light in seconds per cm"

And got this leading boxed-in figure:


the speed of light =
3.33564095 × 10-11 seconds per centimeter


Just another instance of the IBM 1620 Law:

"Input bullshit...output bullshit"

Just when I was about to rejoice, they threw in the Gaussian, the Lorentzian and the Heaviside units (rationalized as well as non-rationalized).

And our books (British pigheadedness this time) had the first chapter on what was called the Units & Dimensions. All in all the British (unlike the Americans like Sears and Feynman) tried their best to make physics as repulsive as possible.

Fortunately by the time I went to IIT KGP to teach physics to unwilling students, things fell into place and we had but to mug up only the SI units, still a pain in the neck since they tried to name the units (as far as they could) in terms of the great physicists like Newton and Faraday...also less know chaps like Tesla and Weber...there must have been terrific fights. I would like to see a unit named 'Feynman' who single-handedly tried to make physics attractive to students. I propose to name the speed of light after Feynman and the gravitational constant after Einstein.

But I had to teach half a semester course on Dimensional Analysis to Engineering students. And I came to love the subject. I found good books by Bridgman and others. And it was a revelation. It had the Buckingham Pi Theorem. Earlier I thought it was a boring subject dealing with 3 dimensions...mass, length, time.

For the first time I learned the importance of dimensionless products like the Reynold's Number. And the subject was of great practical interest in modeling (ahem!). Let us say a civil engineer has to design a bridge over the Hooghly river. He can't do it on the real river...it would collapse and he has to do it all over again. So, he would make a miniature model of the damn thing in say araldite. To reduce the real bridge to the lab model, he has to know by how many factors each parameter like the height, the width, the number and size of the piers etc had to be reduced. And what properties like the density and the elasticity of araldite differ from the ultimate steel bridge. It is not easy. There are too many parameters and only 3 dimensions. So he has to use his horse sense to reduce them into dimensionless products. And test the thing using a tough subject called Photoelastcity that requires a knowledge of polarization of light.

And I learned a lot and it was fun to teach.

And then I made friends with a Chemical Engineer who was all the time talking of Unit Operations. I asked him what they were. And he reeled out:

1. Mass Transfer

2. Heat Transfer

3. Momentum Transfer.

I then told him that I read all of them in my Second Year B Sc (Hons) in the Kinetic Theory. They were called Diffusion, Conduction, and Viscosity and were dismissed in 6 pages.

He then took me to the Central Library and showed me three full racks of books on these three subjects in the Ch E Section!

Somehow it stuck. 

Nowadays every morning I recall the 3 Unit Operations I have to perform grudgingly. They are called:

1. Shit

2. Shave

3. Shampoo.


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