By presenting relationships for spatially varied flow with combined increasing and decreasing discharge, and relating those relationships to prior work, a clearer exposition of spatially varied flow concepts is provided. The applicability and usefulness of energy (First Law of Thermodynamics) and momentum (Newton’s Second Law) principles to spatially varied flows are addressed. The history of the debate initiated in the nineteenth century over the role of the First Law of Thermodynamics in general and hydrodynamics specifically is discussed, related to current issues regarding spatially varied flows, and hopefully resolved in the context of such flows and more generally.

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