# Buckingham pi theorem 2

1. Jan 25, 2016

### hotjohn

1. The problem statement, all variables and given/known data
in the third photo attached , why do we need to raise the whole pi _3 to power of -1/2 ?
can we do so ? if we do so , the original pi_3 will be changed , right ?

2. Relevant equations

3. The attempt at a solution

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• ###### 0031.jpg
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2. Jan 25, 2016

### Staff: Mentor

That's impossible to read and maybe a little long. Could you type in a more condensed question in latex?

3. Jan 25, 2016

### haruspex

I can't read the attachments either, much too fuzzy.
But maybe I can answer the question. The basic idea is to find dimensionless terms (the 'pi' terms) formed by raising the parameters to various powers and multiplying them together. There is 1 degree if freedom in each such term. E.g. If you came up with m1l1F-1t-2, you could equally write it as m2l2F-2t-4. That combines the same parameters in the same ratios, so is still dimensionless, and represents the same mixture.
Does that explain it?