# Choosing of repeating variables in Buckingham's Pi theorem

What are the criteria for choosing repeating variables in Buckingham's Pi theorem in dimensional analysis? In many problems, it's solved by taking D,V,H (Diameter, Velocity, Height) as repeating variables. Why do they take the above variables as repeating variables, when the problem also contains the following variables g,u (acceleration due to gravity, viscosity)?

• You can chose which variables to use. Often the 'choice' is made in such a way that the resulting dimensionless groups have a physical meaning that interests you in your application, for instance the Reynolds number etc. Mar 24 '16 at 12:06

For example, let's assume that we suspect that a fluid we're studying behaves as a function of several variables including a characteristic length, velocity, viscosity, density, surface tension, etc., and we want to see what dimensionless numbers we can make out of them. A possible choice of repeating variables would be length ($l$), velocity ($v$), and density ($\rho$) (in MKS units they would be $m$, $\frac{m}{s}$, $\frac{kg}{m^3}$), because they cannot be combined in any way to make a dimensionless group. Now add surface tension ($\sigma$, units of $\frac{kg}{s^2}$) and combine all four variables to make a dimensionless group like this:
$$\frac{\rho l v^2}{\sigma}$$
$$\frac{\rho l v}{\mu}$$