The physical laws that govern fluid motions are examined to gain justification for the grouping of physical variables that we call Reynolds number. First, a perfect incompressible viscous fluid is considered, and it is shown that Reynolds number is the only flow parameter of its kind upon which the performance of a turbomachine can depend. The extent to which Reynolds number loses this uniqueness when real fluids are employed in real test situations is then discussed. The necessity of the use of educated engineering judgment, not furnished by dimensional analysis, is pointed out.