Flow measurement using circular sharp-crested weirs

Circular sharp-crested weirs are used as a flow-measuring device in open channels, reservoirs or tanks. The theoretical discharge equation of a circular thin weir ends up the complete elliptic integrals of the first and second kinds that are not very suitable for practical purposes due to their complexity. No simple and accurate equation is available in the technical literature up until now for the theoretical discharge of this weir. In current research, a simple and accurate theoretical discharge equation has been presented. The maximum percentage error of this equation compared to accurate numerical integration results is less than 0.08%. Also using experimental data, a suitable discharge coefficient equation is presented thus actual discharge can be computed via proposed equations. Moreover, an equation has been derived for the determination of the time required to empty a reservoir or tank by a circular sharp-crested weir.