In Praise of Dimensional Analysis

It sounds like you failed at life. Success at life is to observe it, and become deeply cynical. Its hard not to tolerate anything when you are sufficiently cynical. :-)

Steve

I suppose so, but my first thought is to convert to meters/minute**2

-- glen

A large calculation can be made up of many small steps. If one computes intermediate results on a calculator, one can attach the appropriate units onto the intermediate result from the calculator. The numbers go through the calculator, the units go around and are attached appropriately onto the result. Usually the steps will be small enough not to lose track of the units.

(snip)

I used to know of a computer based physics teaching system using PLATO:

physics problems the user was expected to enter an answer with units. As I understand it, each unit was given a numerical value, and the resulting expression was evaluated and expected to be close to the correct answer. As an example, m (for meter) might be 123.45, cm would then be 1.2345, in (inch) 3.13563, etc. Once for a problem expecting velocity units entered erg**0.5 g**-0.5 (I forget the actual exponential operator), and the answer was judged correct.

It is ChE that uses pound for mass, and adds another constant into the equations to make them consistent. I used to work in a lab with ChE people, with many experiments related to absorption or emission spectra. I once did an emission spectrum in BTU/pound mole, a unit that only ChE would use. (A pound mole, similar to the more common gram mole, is the amount of some substance such that its mass in pounds equals its molecular weight in Daltons.)

-- glen

Nah, furlong-seconds per cubic fortnight.

Cheers,

Phil Hobbs

Miles/hour/second is a pretty common unit. Of course, an hour-second equals a square minute. :-)

Jerry

A furlong per fortnight is a velocity. That leaves second per square fortnight (a frequency) if we factor it out. Frequency of what?

Microlightyear per century is another interesting speed.

Jerry

A venerable approach. Galileo used it, in fact. Algebra, at the time, he felt was not yet rigorously founded while ratios had been for quite some time.

Jon

I think you mean that a KW-hour is a unit of energy. It is also (indirectly) a unit of revenue. Hence the usage.

Jerry

Glen,

Your timestamp seems to be a bit into the future.

Jerry

No, you meant that KW-hr/day is a unit of power. My mistake.

...

Jerry

Jonathan Kirwan wrote: (snip)

I had known that Galileo's first experiments with rolling balls were an attempt to slow down the fall of gravity, and allow him to understand the effect. I hadn't known why he decided to do it that way, without the algebra to show what the result would mean.

-- glen

(snip)

One of my least favorite units is the one power companies like to use to describe usage: Kilowatt hours/day. Kilowatt seems like a fine power unit, without an extra factor of 24.

-- glen

But are the units right?

;)

Eric Jacobsen Minister of Algorithms Abineau Communications

Unfortunate for technical people, but good for 'normal' customers.

Everyone knows what a day is, and we all get billed in KW-hours. I doubt that very many people could tell you that a KW-hour/day is a hair under 42 watts, and even fewer could do it in a blink without a calculator.

Galileo probably began considering motion like this at least as early as 1586, I think, having written a dialogue on problems of motion that year. He must have considered inclined plane experiments as early as

1591, since he added them to his De Motu that year. But I seem to recall that his immersion into building them would have been around 1601-1602.

The details about his thinking, as well as copies of some of his folios, can be found in Sillman Drake's "Galileo: Pioneer Scientist." I recommend it.

Jon