Dimensional analysis physical similitude

In his famous and extremely short essay entitled The principle of similitude Lord Rayleigh [4] discussed 15 different physical problems which can be condensed to laws by using dimensional analysis without performing any experiments. The last of these examples concerned the Boussinesq problem of the steady-state heat transfer from a fixed body to a ideal liquid flowing with the velocity of v. 

Next, we proceed to the dimensional analysis of the same problem by the method of physical similitude. Since the force F on the sphere exerted by the moving fluid is balanced by the inertial and viscous forces,... 

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