How do you non-dimensionalize a general linear equation?

[newstudent]

Hi All,

I have often heard the term 'non-dimensionalising', and am unsure as to what it really means. I gather that it literally means non dimensionalising the units such that it may be applied to a wider range of situations. My question is, if i have a general linear equation and wish to non dimensionalise it, where should be my starting point? I would appreciate if someone could point me in the right direction. Thank you.

=)
cheers,
newstudent

 

[mathPimpDaddy]

Hi All,

I have often heard the term 'non-dimensionalising', and am unsure as to what it really means. I gather that it literally means non dimensionalising the units such that it may be applied to a wider range of situations. My question is, if i have a general linear equation and wish to non dimensionalise it, where should be my starting point? I would appreciate if someone could point me in the right direction. Thank you.

=)
cheers,
newstudent

I'm curious too. Would radians be a undimentionalising unit?

 

[HallsofIvy]

"Radians", not "radiants". Yes, radians are an example of a non-dimensional quantity. Given a circle of any radius, the radian measure of an angle is the length of the arc it cuts from the circle, divided by the radius of the circle. Since those are both lengths, any units of length will cancel out. For example, a 60 degree angle, in a 40 inch in radius circle, would cut an arc length of $(60/360)(2\pi 40)= 41.9$ inches long. The angle, in radians, is 251.3/40= 6.28. It is because the "radian" is really "dimensionless" that we can use it in purely algebraic equations with no mention of angles:
f(x)= cos(x) assumes x is "in radians".

In general, one forms dimensionless expressions by dividing by a fixed quantity having the same units as the original expression.

You might want to look at this:
http://astro.nmsu.edu/~aklypin/PM/pmcode/node2.html

 

[Crosson]

Here is a systematic way to obtain powerful results using non-dimensional variables:

http://en.wikipedia.org/wiki/Buckingham_π_theorem