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# Buckingham Pi Theorem? watch

1. I really don't understand the B.P Theorem.

Could anyone tell me exactly how it works and what it is used for? I tried looking online but I cannot get the concept really.

I don't understand what these dimensionless numbers mean and how to make them.

Any help?
2. (Original post by poorform)
I really don't understand the B.P Theorem.

Could anyone tell me exactly how it works and what it is used for? I tried looking online but I cannot get the concept really.

I don't understand what these dimensionless numbers mean and how to make them.

Any help?
It's used for checking your model is correct, for instance. I call it "juggling the units".

Example: if I were to misremember that the formula for exponential decay of a system was with a rate constant , I could immediately know that my formula is wrong, because isn't allowed to have units in its argument, but has the unit "seconds". On the other hand, has no units ("is dimensionless") because the "seconds" from t have cancelled with the "1/seconds" from k. Therefore this is a formula that has a chance of physically making sense.

Example: the volume of a sphere cannot be , because this has units "square metres" but volumes must be in "cubic metres".

Buckingham- lets you derive meaningful formulae, and I used it extensively in A-level physics to avoid learning anything. Suppose I know (perhaps from a formula booklet) that Newton's gravitational constant is . I can work out the gravitational attraction between two masses as follows: suppose the masses are and , and the distance between them metres.
Our final equation will be of the form . There is a dependence relation among these, and that's what Buck-Pi tells us: does exist. We can work out that relation by just juggling the units: we see that , so to get the units to match up, we're going to want . No other combination of these will work, unless you multiply/divide by or a dimensionless constant like . It turns out that this formula is correct, by the way (normally, you wouldn't know whether there should be a constant at the front, or multiplied by a dimensionless factor of , or something).

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Updated: January 16, 2015
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