Submerged Discharge Relations of Logarithmic Weirs

Abstract

Theoretical and experimental investigations of the effect of weir submersion on the logarithmic discharge characteristic were performed. The problem was solved theoretically by accepting the simplifying assumption that the coefficient of discharge has a constant value. Strict formulae which determine the relative accuracy, ε, of conformity with the logarithmic characteristic for the weir operating under the submersion condition were derived as a function of the submersion ratio, h/H, and the filling ratio, a/H. The function ε (h/H, a/H) was derived for the logarithmic weir with a rectangular crest at height a. Because of the complicated structure of this function, an approximate formula which simplifies computation was derived. Experimental studies showed that the coefficient of discharge is a function of nappe head. However, the acceptance of a constant value for this coefficient results in a discrepancy between theoretical and experimental discharge values that does not exceed 3.5%.