Estimating discharge in rivers through the combined use of dimensionless isovels and point velocity measurements

This paper presents a procedure for estimating discharge in a river cross-section based on the combined use of dimensionless isovels and point velocity measurements. Specifically, taking the Biot-Savart law on the magnetic field induced by an electric current in a wire as their basis as already done by other researchers, the authors propose a new formulation of the relationship characterizing the effect of the wetted perimeter on the range of velocities in a cross-section in order to take explicit account of roughness, expressed by means of Manning's coefficient. Once appropriately nondimensionalized, the isoeffect contours can be read as dimensionless isovels. Assuming in situ velocity measurements are available, discharge at a cross-section can be computed using two different methods. The proposed procedure was applied to six case studies characterized by river cross-sections which differed greatly from one another. The results show that the two methods proposed for estimating discharge lead to equivalent outcomes, and in all the cases the procedure as a whole enables a sufficiently accurate estimation of discharge, even when it is based on a limited number of velocity measurements or on the measurement of maximum surface-water velocity alone.