# Rules of choosing repeating variable in Buckingham pi theorem

## Homework Statement

i was told by my lecturer that when we choose the repeating variables in pi buckingham theorem , we can choose based on 3 property , which is geometry property which consists of (length , width and area) , then followed by flow property ( velocity , acceleartion, discharge) and lastly fluid property which consists of ( mass density , viscosity and surface tension) ,
but , i couldn't find the prove on the internet and book , i'm wondering is it correct ? can someone clarify?

## The Attempt at a Solution

I could only found this when choosing the variable in Pi Buckingham theorem....
• The dependent variable should not be picked as a repeating variable. Otherwise, it will appear in more than one Pi, which will lead to an implicit expression in Step 6 below.
• The repeating variables must not be able to form a Pi group all by themselves. Otherwise, the procedure in Step 5 will be fruitless.
• Each of the primary dimensions in the problem must be represented. For example, if mass, length, and time appear in the original n variables, these three primary dimensions must also each appear at least once in the repeating variables.
• Variables which are already dimensionless (such as angles) should not be picked. Such variables are already dimensionless Pi groups, and cannot contribute to formulating the remaining Pi groups.
• Two variables with the same dimensions or with dimensions differing by only an exponent should never be picked. For example, if some area and some length are among the list of variables, the length should be chosen as a repeating variable. It would be incorrect to also select the area as a repeating variable, since its dimensions are simply the square of the length, and can contribute nothing additional to the formulation of the Pi groups.
• Variables with very basic dimensions and/or variables that are "common" should be picked as repeating variables. This is perhaps the most difficult aspect of dimensional analysis, especially for the beginning student. After much practice, it becomes more or less obvious which variables to pick. For example, if there is a length, that length should be picked as a repeating variable since it is very basic and desirable in the Pi groups. Likewise, some velocity, mass, time, or density are also good choices. In most fluid flow problems, other flow properties like viscosity or surface tension should not be chosen if there are also more "basic" variables to choose from, such as a length, velocity, time, mass, or density. Why? Because it is usually not desirable to have viscosity or surface tension appear in each of the Pi groups.

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i have not heard this theorem before. This is weird

Tom.G

• welovephysics
the links still doesnt prove we can choose the variables based on 3 property , which is geometry property which consists of (length , width and area) , then followed by flow property ( velocity , acceleartion, discharge) and lastly fluid property which consists of ( mass density , viscosity and surface tension) ,.....
can you find me the prove on this ?

bump

I also want to know, can anyone reply???