This thesis is devoted to the study and designs of two important proportional weirs having the discharge-head characteristics of Q α H 2/3 In the first design a geometrically simple weir in the form of a rectangular weir over a inverted V-notch (Chimney weir) is presented. This weir gives for all flows above a threshold depth a discharge proportional to H 2/3 within a maximum percentage error of ±1.5, (measured above a reference plane) within certain limits of head. Second design is concerned with the self-basing weir in which a portion of the weir above the crest acts as a base. This design is achieved by using the complementary weir profile of a Quadratic weir above the parabolic base which has the significant property of fast convergence. This weir gives discharge for all flows above the threshold depth, proportional to (head)2/3 measured above a reference plane, with increasing accuracy as head increases. Experiments with these two weirs confirm the theory by giving a constant average Coefficient of Discharge (Cd) of 0.62. The importance of these weirs as a sensitive discharge measuring device in field and laboratory is highlighted.