Newton's study of fluid mechanics

Abstract

Newton's effort on fluid mechanics was focused almost entirely on the forces of resistance that bodies encounter when moving in fluid mediums. His principal task in Book 2 of the Principia was to infer laws of resistance forces from phenomena of motion in the same way that he had inferred the law of universal gravity from phenomena of planetary motion in the rest of the work. The main problem Newton saw with resistance forces is that they arise from three separate mechanisms—the inertia of the fluid, the internal friction of the fluid, and surface friction. He reasoned that the first of these would vary as the density of the medium and the square of the velocity, and he expected the second to vary linearly with the velocity and the third to be independent of the velocity. This led him to assume that the total resistance force would vary as a 0+ a 1 v+ a 2 v 2, so that the problem became one of identifying what parameters govern each of the coefficients and how they vary with these parameters. For the first edition of the Principia Newton turned to pendulum-decay experiments to characterize a 0, a 1 and a 2. The data he obtained, however, were too inconsistent to yield any results beyond the conclusion that the inertial term is dominant, at least for the pendulum bobs and velocities in the experiments. In the second edition, Newton relied on a hypothetical model of the inertial action of fluids to deduce a priori values for a 2 for spheres. He hoped that the differences between the total resistance forces in experiments and his theoretical values of the inertial component would provide a basis for characterizing the other components. To this end, he conducted a number of vertical fall experiments in both water and air. The total resistance forces Newton obtained from these experiments were impressively accurate. More important, the experimentally determined forces convinced him that his theoretical value for a 2 was sufficiently accurate to enable the other components to be investigated in more carefully conducted vertical fall experiments in the future. He was wrong about this; his approach was doomed to fail from the outset for reasons he could not have foreseen. Its failure nevertheless sheds light not only on Newton's way of carrying out science, but also on the difference between pure science, as Newton conceived it, and engineering science.