Bernoulli Loops in Smoke Rings

Abstract

Bernoulli’s law is applied to the closed streamlines of a smoke ring, and the centrifugal force of the curved flow is balanced by a pressure gradient. Two equations in two unknowns, pressure and velocity, are combined into one equation in one unknown, velocity. Solving the governing equation algebraically produces a radial shear in the velocity such that the speed decreases outward inversely as the radius increases, which is the main result. Measurements are needed to verify the predicted structure of the velocity field.