Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations

This study presents a historical review, a meta-analysis, and recommendations for users about weight–length relationships, condition factors and relative weight equations. The historical review traces the developments of the respective concepts. The meta-analysis explores 3929 weight–length relationships of the type W = aLb for 1773 species of fishes. It shows that 82% of the variance in a plot of log a over b can be explained by allometric versus isometric growth patterns and by different body shapes of the respective species. Across species median b = 3.03 is significantly larger than 3.0, thus indicating a tendency towards slightly positive-allometric growth (increase in relative body thickness or plumpness) in most fishes. The expected range of 2.5 < b < 3.5 is confirmed. Mean estimates of b outside this range are often based on only one or two weight–length relationships per species. However, true cases of strong allometric growth do exist and three examples are given. Within species, a plot of log a vs b can be used to detect outliers in weight–length relationships. An equation to calculate mean condition factors from weight–length relationships is given as Kmean = 100aLb−3. Relative weight Wrm = 100W/(amLbm) can be used for comparing the condition of individuals across populations, where am is the geometric mean of a and bm is the mean of b across all available weight–length relationships for a given species. Twelve recommendations for proper use and presentation of weight–length relationships, condition factors and relative weight are given

Delineamento de zonas de manejo para o planejamento de experimentação on-farm na cultura do algodão.

RESUMO: O Brasil é atualmente um dos maiores produtores e exportadores mundiais de algodão. O principal desafio dos produtores é a busca contínua do aumento da produtividade, aliado à qualidade do produto final, com foco no aumento da lucratividade e redução de impactos ao meio ambiente, tornando a produção de algodão no país cada vez mais sustentável. Desse modo, se torna cada vez mais necessária a adoção de técnicas de manejo que envolvam a coleta, análise e intervenção com base em dados, como a agricultura de precisão (AP). A subdivisão das áreas de produção em zonas de manejo (ZM) é uma das formas de se iniciar a adoção da AP em uma área de cultivo agrícola. Este trabalho teve como objetivo principal realizar o delineamento de ZM para uma área de produção de algodão de safra localizada em Sapezal-MT, utilizando técnicas computacionais de agrupamento de dados. A função principal desse delineamento foi auxiliar na estratégia para construção de experimentação on-farm para o estabelecimento de recomendações de adubação de cobertura nas diferentes ZM delimitadas para a área de estudo.Edição Técnica: Leandro Maria Gimenez, Christian Bredemeier. ConBAP 2022

Interaction of Reflected Shock Waves with Solid or Liquid Particulates

When performing shock-tube experiments with a gaseous mixture containing small particles, uncertainties can arise in the knowledge of the test conditions. Of particular importance is the accuracy of the test temperature when conducting chemistry and spectroscopic measurements behind the reflected shock wave. The primary uncertainty in an aerosol-laden flow field arises from the thermal and momentum (i.e., drag) relaxation of the particles, since a finite amount of time is required for the particles to achieve the temperature and speed of the shocked carrier gas. The net result is a transient relaxation zone leading to a final, equilibrium temperature and pressure of the gas/particle mixture that differ from the temperature and pressure if the particles were not present. The duration and magnitude of the effects depend on several factors, including the particle-to-gas mass loading ratio (η), the average particle diameter, the material properties of the condensed phase, and the shock speed. A one-dimensional model of the gas dynamics was compiled from models in the literature and used to estimate how the presence of the particles ultimately affects the uncertainty in reflected-shock test temperature over a range of temperatures from 1500 to 4000 K, η from 0 to 10, particle diameters from 0.1 to 100 μm, and two characteristic powders: silica and titania. When compared to a pure-gas shock wave at the same velocity, the equilibrium temperature in a gas/particle mixture is lower, the static pressure is higher, and the mixture specific heat ratio is lower. For example, a shock speed providing 3000 K, 1.0 atm behind the reflected shock wave in pure argon results in a temperature and pressure of 2735 K and 1.33 atm in a mixture of SiO2 and Ar at η = 0.10. The duration of the particle relaxation time can be several hundred microseconds or longer, depending on the particle size and loading. Even for η as low as 0.001, this relaxation time can be a significant fraction of the total test time since the test time is usually on the order of only a few milliseconds. In general, the relaxation zone introduces uncertainties in the equilibrium temperature as high as 10% for η0.10 and depends strongly on the material composition