Dimensionless number and their importances

There are so many dimensionless numbers that we see in the chemical engineering. What is the importance of these dimensionless numbers and how they form? In dimensionless number we group the variable that affects a parameter. For example heat transfer coefficient h depends on viscosity, velocity, density, temperature, specific heat, thermal conductivity, length. How do these factors affect the heat transfer coefficient can be analysed through experiments but the number of experiments will be numerous. For each factor, we have to do a set of experiments and analyse its effect on heat transfer coefficient. We can group them in a dimensionless form which shows the ratio of two terms like forces, resistance etc. The equation can be written as a function of the dimensionless number and the exponent and constant can be taken from experimental results i.e. empirical correlations. Like the example of well known dimensionless number Reynolds number (dvρ/μ) gives the ratio of inertia forces and viscous forces. With the help of Re no we can find the type of flow whether it is laminar or turbulent. This no gives the effect of diameter, velocity, density and viscosity on type of flow. Every dimensionless number may not have its significance. This is a trial and error procedure to get meaningful dimensionless number.