Mass Accretion During the Motion of Raindrops

Exploration of dynamics of raindrops is one of the simple yet most complicated mechanical problems. Mass accretion from moist air during the motion of raindrop through resistive medium holds an arbitrary power law equation. Its integral part is the change of shape, terminal motions and terminal solutions, etc. Classical Newtonian formalism is used to formulate a mathematical model of generalized first order differential equation. We have discussed about the terminal velocity of raindrop and its variation with the extensive use of python program and library. It is found that terminal velocity 𝐯𝐓𝐜𝛂𝛃 is achieved within 20 seconds where 𝛂=, 𝛃=(𝟎,𝟏) and 𝐧=𝟎,𝟏,𝟐,𝟑,𝟒,…. Its variations due to mass accretion roughly follows the earlier predicted range 𝐠/𝟕 to 𝐠/𝟑.

A Comprehensive Study of Mass Accretion and Atmospheric Effect of Raindrop

The mass accretion of a raindrop in different layers of the atmosphere is not dealt with so far. A comprehensive brief study of the motion of raindrops through the atmosphere (i) without mass accretion, (ii) with mass accretion and (iii) finally pressure variation in the atmosphere with altitude using Bernoulli’s equation is illustrated. Acquirement of mass from moist air is mass accretion and mass accretion during the motion of raindrop through resistive medium holds an arbitrary power-law equation. Bernoulli’s equation when applied to it, the generalized first-order differential equation is reduced to a polynomial equation. Results show a single intersecting point of approximate terminal velocity 1 m/s and mass 10-06 mg as illustrated. Terminal velocity is achieved within 25 sec. There is the approximate exponential growth of terminal velocity. An increase in momentum is due to mass accretion during motion. Various conditions of no mass accretion and mass accretion show the same result while for atmospheric effect using Bernoulli’s equation the first-order differential equation reduces to a polynomial equation.

Mechanisms of Pond Expansion in a Rapidly Submerging Marsh

The development and expansion of ponds within otherwise vegetated coastal marshes is a primary driver of marsh loss throughout the world. Previous studies propose that large ponds expand through a wind wave-driven positive feedback, where pond edge erosion rates increase with pond size, whereas biochemical processes control the formation and expansion of smaller ponds. However, it remains unclear which mechanisms dominate at a given scale, and thus how, and how fast, ponds increase their size. Here, we use historical photographs and field measurements in a rapidly submerging microtidal marsh to quantify pond development and identify the processes involved. We find that as small ponds emerge on the marsh platform, they quickly coalesce and merge, increasing the number of larger ponds. Pond expansion rates are maximized for intermediate size ponds and decrease for larger ponds, where the contribution of wave-driven erosion is negligible. Vegetation biomass, soil shear strength, and porewater biogeochemical indices of marsh health are higher in marshes adjacent to stable ponds than in those adjacent to unstable ponds, suggesting that pond growth rates are negatively related to the health of the surrounding marsh. We find that the model of Vinent et al. (2021) correctly predicts measured pond growth rates and size distribution, which suggest the different mechanisms driving pond growth are a result of marsh drowning due to sea level rise (SLR) and can be estimated by simplified physical models. Finally, we show that all relevant processes increasing pond size can be summarized by an empirical power-law equation for pond growth which predicts the temporal change of the maximum pond size as a lower bound for the total pond area in the system. This gives a timescale for the growth of ponds by merging and thus the critical time window for interventions to prevent the irreversible pond expansion associated with large scale pond merging.

Viscous coupled fluids in terms of a log-corrected equation-of-state

In this paper, we consider a class of cosmological fluids that possess properties analogous to those of crystalline solids undergoing isotropic deformations. Our research is based on a modified log-corrected power-law equation of state in the presence of a bulk viscosity. This formalism represents a class of the so-called logotropic fluids, and allows explaining an accelerating late-time universe. In order to obtain a more detailed picture of its evolution, we add in our model a coupling of the log-corrected power-law fluid to dark matter, and study various interacting forms between them. We solve the system of equations for a modified log-power-law fluid coupled to dark matter, and obtain expressions for the log-corrected power-law energy density, and the energy density for dark matter. A comparative analysis is made with the model of a nonviscous log-corrected power-law fluid without interaction with dark matter.

The Challenge of Elastomer Seals for Blowout Preventer BOP and Wellhead/Christmas Trees under High Temperature

It is critically important for elastomer sealing components in blowout preventers (BOP) and wellheads to meet the pressure and temperature rating requirements under the newly released American Petroleum Institute (API) standards, API 16A (fourth edition) and API 6A (twenty-first edition) respectively. Extrusion resistance under high pressure and high temperature is one of the most critical challenge for the elastomer sealing components to meet the above API standards. This challenge is related to the basic properties of elastomer materials and mechanical design of the sealing components. This paper outlines how a simple and low-cost approach was developed to evaluate extrusion resistance of elastomer sealing components, and the correlation between critical tear pressure and extrusion gap of the two elastomers seals was evaluated using a power law equation. This correlation revealed that the above challenges of elastomer sealing components for BOPs and wellheads/Christmas trees is related to the weak strength of elastomers under high temperature and large clearances (extrusion gap) in current designs. New materials and/or new mechanical design to overcome such a challenge were also provided and discussed in this paper. The paper will help practicing engineers understand the challenge of material selection, mechanical design, and API testing as well as better understand the capability and limitation of sealing components for blowout preventors and wellhead applications under high pressure and/or high temperature (HPHT).

Simplified Interception/Evaporation Model

It is known that at the event scale, evaporation losses of rainfall intercepted by canopy are a few millimeters, which is often not much in comparison to other stocks in the water balance. Nevertheless, at yearly scale, the number of times that the canopy is filled by rainfall and then depleted can be so large that the interception flux may become an important fraction of rainfall. Many accurate interception models and models that describe evaporation by wet canopy have been proposed. However, they often require parameters that are difficult to obtain, especially for large-scale applications. In this paper, a simplified interception/evaporation model is proposed, which considers a modified Merrian model to compute interception during wet spells, and a simple power-law equation to model evaporation by wet canopy during dry spells. Thus, the model can be applied for continuous simulation, according to the sub hourly rainfall data that is appropriate to study both processes. It is shown that the Merrian model can be derived according to a simple linear storage model, also accounting for the antecedent intercepted stored volume, which is useful to consider for the suggested simplified approach. For faba bean cover crop, an application of the suggested procedure, providing reasonable results, is performed and discussed.

Yield stress of concentrated wheat straw suspensions

The yield stress of concentrated wheat straw suspensions was measured by a vane with a Bohlin rheometer. Wheat straw fibers were made by grinding (wet and dry) wheat straw and separated into four sizes by sieving (8, 12, 20, and 40 mesh). The yield stress was found to increase with concentration as well as with the size of the wheat straw fibers. The yield stress data fitted to power law equation proposed by Kerekes et al. (1985) for pulp fibers. It was found that only 40 mesh size wheat straw fibers agreed with the relation. Effect of stress ramp rate was studied on 5% (20 mesh) w/v, wheat straw suspension. It was observed that stress ramp rate had an effect on measured yield stress value. No yield stress was observed in the suspension of 5% (40 mesh) w/v, due to sedimentation of wheat straw fibers. For effective utilization and mixing of enzymes with wheat straw fibers during hydrolysis, knowledge of yield stress of suspension was important.

Yield stress of concentrated wheat straw suspensions

The yield stress of concentrated wheat straw suspensions was measured by a vane with a Bohlin rheometer. Wheat straw fibers were made by grinding (wet and dry) wheat straw and separated into four sizes by sieving (8, 12, 20, and 40 mesh). The yield stress was found to increase with concentration as well as with the size of the wheat straw fibers. The yield stress data fitted to power law equation proposed by Kerekes et al. (1985) for pulp fibers. It was found that only 40 mesh size wheat straw fibers agreed with the relation. Effect of stress ramp rate was studied on 5% (20 mesh) w/v, wheat straw suspension. It was observed that stress ramp rate had an effect on measured yield stress value. No yield stress was observed in the suspension of 5% (40 mesh) w/v, due to sedimentation of wheat straw fibers. For effective utilization and mixing of enzymes with wheat straw fibers during hydrolysis, knowledge of yield stress of suspension was important.

Investigation of the Dynamic Breakdown of a Dielectric Elastomer Actuator Under Cyclic Voltage Excitation

The dielectric elastomer (DE) is a new kind of functional polymer that can be used as a smart actuator due to the large deformation induced by voltage excitation. Dielectric elastomer actuators (DEAs) are usually excited by dynamic voltages to generate alternating motions. DEAs are prone to premature breakdown failure during the dynamic excitation, while the research on the breakdown of DEAs under cyclic voltage excitation is still not fully revealed. In this paper, the dynamic breakdown behaviors of DEAs made from VHB4910 film were experimentally investigated. The factors affecting the breakdown behavior of DEAs under dynamic voltages were determined, and the relevant changing laws were summarized accordingly. The experimental results show that under dynamic voltage excitation, the critical breakdown voltage of DEAs were augmented slowly with voltage frequency and showed a substantial dispersion. In addition, the maximum cycle numbers before breakdown were significantly affected by voltage parameters (such as frequency, amplitude, waveform). Finally, the underlying mechanisms of breakdown under cyclic voltages were discussed qualitatively, a power-law equation was proposed to characterize the maximum cycle number for the dynamic breakdown of DEAs, and related parameters were fitted. This study provides a new path to predict the service life of DEAs under dynamic voltage.

Rheological modeling of pasta dough flow processes in channels of convergent-divergent inserts of molding matrix

One of efficient directions for pasta press designs modernization is installation of special conical-and-cylindrical inserts in the matrix wells in front of the dies having, like Venturi tubes, narrowing zones (convergent), expansion (divergent) and a cylindrical path located between them. However, rheological aspects of such method of forming tool modernizing in relation to pasta presses have not been studied, recommendations for structural elements calculation and design have not been developed. All this is a significant obstacle for using the method in engineering and industrial practice. The research purpose is to develop rheological models the pasta dough flow in the conical-cylindrical channels of convergent-divergent inserts and to evaluate with their help the impact of structural dimensions and rheological properties on resistance to pasta dough flow. Pasta dough was considered as a rheological complex nonlinearly viscous plastic material. In technical calculations contribution of shear strength was neglected and a rheological analysis was performed using the Oswald-de-Vila power law equation. Analytical dependences obtained make it possible to calculate the pressure drops in the convergent-divergent insert and its elements. Numerical modeling was performed and calculated data were obtained regarding the impact of dimensions of structural elements of the insert and rheological parameters of pasta dough on its resistance to viscous flow. The results obtained can form the basis of engineering and technological calculations in design of convergent-divergent inserts for laboratory and industrial matrices of pasta presses.