how do you check a formula for dimensional consistency?

Question

why does this method of checking not give definite confirmation that an equation is correct?

Answer 1

You should write the physical variables based on basic dimensions. i.e the equation:

V = L / t

V (velocity) is length over time which is the same as dimension of the other side of equation. The dimension of the two sides of any equation are the same. However, every dimension can be achieved in many different ways. i.e:

V = L / t = a*t

when 'a' is the acceleration. you can't recognize between them just based on the dimension.

Answer 2

Write each number as if it were just its dimensions. Treat the dimensions as if they were numbers. If all is equal, then your number answer has a better chance of being correct.

Dimensional analysis can prove an answer wrong, but can only show an answer to be more likely to be correct.

e.g.: F = ma means that the dimensions of force are mass x distance / time squared or (g x cm) /(s^2). If your information were the mass in grams and the acceleration in cm/s, then you look at (g) x (cm / s) . If you treat these as numbers, you would get (g x cm) / (s) which isn't right.

The more complicated the equation, the more likely that dimensional analysis will help.

Answer 3

Since it only checks dimensions, there's no guarantee that you did the actual math correctly. That said, it's an EXCELLENT means of verifying that you got the basic FORM of the calculation correctly.

For example, if you were calculating energy, and you wound up with kg*s^2/m, you know something was wrong, since the unit of energy is kg*m^2/s^2, which comes from 1/2mv^2