This paper is concerned with the design of a practical quadratic weir of a simple geometrical shape, having an inward trapezoidal weir of crest width 2\iw and vertex angle 2θ, over which a rectangular weir is fitted at an optimum depth \ip=0.95\id (\id=overall depth of the inward trapezoidal weir) above the weir crest. It is shown that the flow through this weir is proportional to the square root of head \ih measured from the datum or reference plane situated at 0.5\id above the crest, for all flows in the range of \ip≤\ih≤2.95p within a maximum error deviation of ±2% from the exact theoretical discharge. A numerical optimization procedure is developed to obtain the optimum parameters of the weir yielding a maximum quadratic head-discharge relationship. Experiments with two different weirs show excellent agreement with the theory by giving a constant average coefficient of discharge. The application of the weir in the proportionate method of flow measurement using a bypass in an open channel and as a sensitive flow-measuring device in irrigation canals are highlighted.