Dimensionless formulation for human stability in open flows

Abstract

The stability of humans partially immersed in risky open water flows, resulting from urban flooding caused for example by dam breaks, or failures in drainage systems, or natural extreme events, is a topic of increasing interest because it involves the human safety in an environment that is more and more subjected to extreme events of hydraulic nature. The studies in this field of the applied fluid mechanics generally present equations that handle the results through dimensional quantities. These results were generally obtained in specific experiments for the evaluation of the stability of models of the human body. Intending to advance in the direction of a more general formulation, a dimensional analysis for the problem of human stability in open flows is presented here, showing dimensionless groups that represent the mentioned problem. Equations using these nondimensional groups were then developed using statistical analyses and approximations based on principles of physics and on data of the human body. The results obtained with the proposed methodology are of very good quality, presenting high correlation coefficients and good agreement between measured and calculated data.Keywords: Dimensional analysis; Stability of the human body; Dimensionless formulation; Floods. RESUMOA estabilidade de humanos imersos em escoamentos superficiais por exemplo resultantes de inundações urbanas provocadas por ruptura de barragens, falhas em sistemas de drenagem ou eventos extremos é um tema de elevado interesse quando se trata de segurança humana e hidráulica de eventos extremos. Os trabalhos propostos neste campo apresentam seus resultados através de grandezas dimensionais, resultados de origem experimental ou formulações aproximadas para avaliação da estabilidade de modelos para o corpo humano. Aqui é apresentada uma análise dimensional que mostra a obtenção dos grupos adimensionais que representam o referido problema. Formulações em termos desses grupos adimensionais foram então desenvolvidas com análise estatística e aproximações fundamentadas em princípios físicos e dados do corpo humano. Destaca-se a boa qualidade dos resultados obtidos com a metodologia proposta, baseada em adimensionais, com elevados coeficientes de correlação e boa concordância entre dados medidos e calculados.

Analysis of physical mechanisms of human body instability for the definition of hazard zones present in emergency action plans of dams. Case study: Santa Helena Dam, Bahia

“…In accordance with Rotava, Mendiondo and Souza (2013) and Simões, Schulz and Luz (2016), several are the criteria of destabilization of a body and the consideration of physical aspects can be useful to estimate vulnerability levels of a person exposed to danger. In order for this to happen, a methodology can be represented by a mathematical model with values of active forces ( Figure 2) in critical conditions to establish stability.…”

“…Over time, studies became less simplified, complying more criteria on the attempt to approximate to more realistic situations. In Brazil, few are the works that cover the analyses of those mechanisms, it is possible to cite Rotava, Mendiondo and Souza (2013) and Simões, Schulz and Luz (2016), with analyses that approach essentially the behaviour of different variables and parameters on the formulations of physical mechanisms of body instability and hydrodynamic hazard. Jonkman and Penning-Rowsell (2008) affirm that few are the data about the dangerous circumstances that may occur in flood events considering the affected population, mostly those associated to depth and velocities of water that offer risk to life.…”

Stability of Solids in Stepped Flume Nappe Flows: Subsidies for Human Stability in Flows

“…People partially immersed in flows may lose their balance for a number of overlapping reasons: i) reduced friction of the shoe or foot with the floor, ii) transfer of momentum from the flow to the human body, which may cause tipping and dragging and iii) fluctuation due to the distribution of pressure on the body (Archimedes buoyancy). There is also the possibility of collision with floating objects and the instability of the human balance due to the generation and release of vortexes and the forces caused by these detachments (evidenced by Simões et al 2016).…”

“…With the exception of studies by Arrighi (2016), Arrighi et al (2017) and Shu et al (2016), according to the conculted literature, the quantities used to characterize the problem are presented in dimensional form (that is, not normalized in the sense of allowing exploring scale effects). Simões et al (2016) applied the Vaschy-Buckingham theorem in the sense to generalize the formulation of human instability in flows. The authors selected a functional involving the Reynolds number, Froude number, drag coefficients, aspect ratios, relative roughness, slope of background, and three non conventional dimensionless parameters: the first related to the individual's age, the second related to the individual's psychical interaction with the flood and the third related to the individual's mass.…”

“…The authors selected a functional involving the Reynolds number, Froude number, drag coefficients, aspect ratios, relative roughness, slope of background, and three non conventional dimensionless parameters: the first related to the individual's age, the second related to the individual's psychical interaction with the flood and the third related to the individual's mass. Literature data of Abt et al (1989), Karvonen et al (2000) and Xia et al (2014) were used in the study, which involved a sensitivity analysis between the different parameters, enabling Simões et al (2016) to obtain equations that correlate the mentioned dimensionless parameters. Good correlations were presented between those parameters indicated as the most relevant in the sensitivity analysis.…”