Experimental study on the validity of flow region division

Abstract

Einstein first proposed that a river flow can be divided into three parts, corresponding to the banks and its bed, respectively, but he did not explain why the flow is dividable and how to divide the flow, in other words the flow division is only a mathematical treatment to simplify his analysis. Since Einstein's proposition there have been many researches and debates on this topic, many division lines have been proposed, but there is no specially designed experimental research to verify the physical existence of division lines, and these division lines have not been tested against the experimental data. For this purpose, an experiment in a rectangular open channel was conducted to measure whether zero-shear stress exists in an open channel except its existence on the free surface. The measured results reveal that zero-shear stress indeed exists below the free surface, and some proposed equations of division line agree well with the profile of the measured zero-shear line, thus it is clarified that Einstein's hypothesis is not only useful to simplify the mathematical treatment, but also it has the physical basis, i.e., zero-shear division line. As far as the authors know, in the literature, this is the first experimental proof that the division lines indeed exist in channel flows.