ABSTRACT
A simple pendulum is a heavy material particle suspended by a weightless and inextensible string, which is fixed at its other end. The authors limit the set of possible motions by the condition that the pendulum motions are two-dimensional. The great importance of similarity and dimensional theory methods was revealed explicitly for the first time in hydraulics, specifically, studying fluid motion in pipes. Dimensional theory, together with the more precise and general formulation to the problem, made it possible to coordinate and combine many empirical laws, established for motion of different fluids at different temperatures in pipes of different diameters and with different speeds. Laminar regime is observed in the motion of fluids of very high viscosity with low velocities in pipes of small diameters (for example, in capillary tubes). In 1915, Rayleigh applied dimensional theory to the Boussinesq problem of body heat transfer in a fluid flowing around the body.
