In a number of early works involving a simple mathematical, analytical treatment of swirl atomizers, the diameter of the air core within the outlet was determined by the assumption that the air core will adjust itself or optimum flow. This is a minimum entropy condition and is termed the "principle of maximum flow." This is by analogy to the principle of maximum flow as applied to weirs (or "spillways"), where the height and velocity of the water passing over the weir adjusts itself for optimum flow. In these early works the principle of maximum flow was referred to, or mentioned, but not presented, or proven, for the swirl atomizer. Because present-day researchers often refer to these early works, this article sets out to clarify the simplified flow physics made in these inviscid analyses and demonstrate that the principle of maximum flow can indeed be applied to swirl atomizers, in principle, under their inherent limiting, simplifying assumptions. This explanation assists in comparing the early inviscid analyses, one with another, to conclude that they are intrinsically similar.