Alternative Design of Square-Rooting Measuring Device in Open Channel

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 w and vertex angle 2θ, over which a rectangular weir is fitted at an optimum depth p = 0.95 d ( d = 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 h measured from the datum or reference plane situated at 0.5 d above the crest, for all flows in the range of p ≤h≤ 2.95 p 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.