The end depth ratio and principal component analysis

This paper considers whether the application of principal component analysis to a free overfall in an open channel can yield any further insights into the variables which govern the relationship between the depth of flow at the start of the free overfall and the critical depth. It is shown that for a channel of rectangular cross-section, the width, the end depth, the square root of bed slope and the square root of the critical slope can be considered to be the primary variables of interest. While a possible relationship between these variables is suggested, it is noted that the precise form of the relationship is beyond the abilities of principal component analysis.