DIMENSIONLESS MODELING OF SUBMERGED FLOW CONDITIONS IN SMALL OVERFLOW DAMS

Abstract

This paper presents a novel theoretical investigation into the hydraulic behavior of small overflow dams operating under submerged flow conditions. Motivated by the lack of analytical tools tailored to this class of hydraulic structures, the study introduces a dimensionless modeling framework capable of predicting the transition between submerged and free-flow regimes. The methodology is rooted in fundamental hydraulic principles, particularly the conservation of energy and continuity, under the assumption that frictional losses are negligible - a valid simplification for small-scale dams.

Key dimensionless parameters are defined, notably the upstream depth ratio z = h/s, the unit discharge intensity parameter , and the downstream depth ratio w= h₁/(s + h), where h is the upstream flow depth above the dam crest, s is the dam’s height, q is the unit discharge, h₁ is the downstream flow depth at the toe of the small dam, and g is the acceleration due to gravity. Using these, the authors derive second-order equations that yield explicit expressions for determining the flow regime, the downstream flow depth, and the submergence ratio β. A critical outcome is the identification of a unique predictive curve that separates submerged from unsubmerged conditions in the (ψ, z) domain. This theoretical boundary enables practitioners to rapidly diagnose the hydraulic status of a small dam using basic input parameters.

The study further demonstrates that the downstream depth ratio w is governed by a second-order equation, the solution of which yields an explicit expression for computing w based on known values of ψ and z.

A relevant relationship is proposed enabling computing the downstream flow depth at the toe of the small depth, using only a minimal set of known dimensionless key parameters, namely, ψ, s, and z.

Further, the paper introduces and analytically formulates the submergence ratio β, which encapsulates the influence of downstream conditions on the overall flow behavior. This parameter, provides engineers with a robust and intuitive framework for the operational assessment of small overflow dams, especially the nature of the flow.

The proposed methodology avoiding empirical calibration, is generalizable across a wide range of dam configurations, and enhances decision-making in both design and field applications. In doing so, this work fills a significant gap in the hydraulic literature and offers a practical yet theoretically rigorous solution to the challenge of assessing submerged flow conditions in small hydraulic structures.

It is noteworthy that the present study, grounded in the authors’ own earlier foundational work, advances a renewed perspective - placing particular emphasis on delivering more nuanced qualitative interpretations of the hydraulic phenomena and the parameters that govern them.