Dimensionless numbers are VERY important in the understanding of physical problems and their solution. In particular,
- The value of the dimensionless numbers often determine the behavior of the solution. For example, a flow problem with a low Reynolds Number will be laminar, while a larger value will imply turbulent behavior.
- The number of dimensionless numbers determines the dimensionality of the space of solutions. For example, if a problem has two dimensionless numbers, then by varying both numbers, all the different behaviors in the problem can be accounted for.
- Using the dimensionless numbers, one can gain insight about the behavior of different variables in different problems. This is because variables with different dimensions have to be constructed by "dismantling" the different dimensionless numbers.
Here is a list of different dimensionless numbers: