In this report a review is given of boundary layer theory and its application to the analytical derivation of a discharge relationship of broad-crested weirs with a rectangular control section. A general method is proposed to derive the boundary layer displacement thickness on the crest from measured velocity profiles, for which two small-scale laboratory models of different sizes have been used. Special attention is paid to the boundary layer development on flat plates in infinite fluids as compared with the development in accelerating flow over the weir. The discharge coefficients derived from an application of critical depth theory allowing for boundary layer growth on the crest are compared with experimental coefficient data, obtained from the laboratory models. No recommendations for the dimensions of the weir in its use as a field structure for flow measurement are made in this report. It was found that a positive pressure gradient at the upstream end of the weir initially caused the boundary layer to develop faster than in the comparative case of a flat plate in an infinite fluid. The drawdown and consequent negative pressure gradient towards the downstream end of the crest prevent the boundary layer to grow further and even reduce it. (Note: this is an English translation of a Dutch thesis)