Criteria for Similarity in the Transportation of Sediment

Abstract

Any phenomenon of fluid motion may be described mathematically by means of a functional relationship among a group of dimensionless parameters so constituted as to include the one dependent factor to be studied and all the independent quantities which govern its variation. Were the forms of these functional relationships known for all phases of hydraulics, there would be no need whatever of investigating the behavior of projected engineering works by means of laboratory models. However, in most cases these complex functions are at best only qualitatively understood, and one must generally resort to the principle of similitude as a practical substitute for rigorous or even approximate functional analysis. This principle merely embodies the fact that flow in a model will be dynamically similar to that in its prototype if all dimensionless parameters describing the flow in the model are numerically equal to the corresponding parameters for flow in the prototype. There is obviously no necessity of knowing how the several parameters are functionally interrelated, but for complete similarity it is essential that they include every variable which has an influence upon the fluid motion.