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Abstract
Here the method used by Wood (1968, 1970) is extended to cover the case of the flow of a stably layered fluid from a reservoir through a contraction with a round crested weir at its min imum width. The conditions under which a single layer may be separated form a two layer system by having this lighter layer alone flowing over a weir are first examined. The conditions under which two layers continuously decrease in depth from the reservoir to and downstream of the weir are determined. It is shown that in this case the theory involves computations not only at the section of minimum width but also a section upstream of this point (the virtual point of control). For a weir shape, chosen so as to simplify the algebra, complete solutions are obtained. For the case of the flow of single layer, the depth of flow over the weir depends only on the depth of the upstream layer, and is two thirds of that depth. For the two layer system it is shown that the depth of the layers over the weir depend not only on the depth updtream but also on the width of the crest and indirectly on the geometry of the crest and the contraction. Some simple experiments were carried out to verify the major conclusions of this theory. The method presented should have applications in predicting flow in numerous engineering fields where more than one layer is flowing and where viscous effects are likely to be small.