# Fluid Mechanics dimensional analysis repeating parameters

1. Jun 4, 2017

### aldo sebastian

This is more of a concept question; if I choose different repeating parameters to someone else, say my lecturer, and got different pi groups to him/her, however my groups are still dimensionless (i.e. the units for each pi group cancel to 1), is my answer still correct?

2. Jun 4, 2017

### zwierz

This is more of a concept answer. Dimensional analysis looks as an elaborated science but actually it is just a trivial section of the vector algebra. Consider for example classical mechanics. All quantities have dimensions of the type $L^{x}M^{y}T^{z}$. You can multiply quantities with dimensions $L^{x}M^{y}T^{z}$ and $L^{x'}M^{y'}T^{z'}$ to obtain a quantity with dimension $L^{x+x'}M^{y+y'}T^{z+z'}$. You also can take a power $\gamma$ of quantity with dimension $L^{x}M^{y}T^{z}$ to obtain $L^{\gamma x}M^{\gamma y}T^{\gamma z}$
So we have a liner isomorphism $L^{x}M^{y}T^{z}\leftrightarrow (x,y,z)\in\mathbb{Q}^3$. All other problems of the Dimensional analysis are easy reformulated and solved in terms of geometry of the vector space $\mathbb{Q}^3$

3. Jun 4, 2017

### Staff: Mentor

Let's see the details.