Mass principle

Deterministic air quaUty models describe in a fundamental manner the individual processes that affect the evolution of pollutant concentrations. These models are based on solving the atmospheric diffusion —reaction equation, which is in essence the conservation-of-mass principle for each pollutant species... 

Euleria.n Models. Of the Eulerian models, the box model is the easiest to conceptualize. The atmosphere over the modeling region is envisioned as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and atmospheric mixing. 

In this chapter we will apply the conservation of mass principle to a number of different kinds of systems. While the systems are different, by the process of analysis they will each be reduced to their most common features and we will find that they are more the same than they are different. When we have completed this chapter, you will understand the concept of a control volume and the conservation of mass, and you will be able to write and solve total material balances for single-component systems. 

Geochemical mass balance studies (also known as input-output budgets) invoke a simple conservation-of-mass principle. If the flux of any element leaving a watershed (e.g., via streams), and the flux of that element into the watershed (e.g., via atmospheric precipitation) are known, the difference between the two can be calculated, and this difference must be due to the sum of all reactions and transformations involving that element which took place within the watershed. Pioneering mass balance studies on weathering profiles and/or small watersheds include those of Garrels and Mackenzie (,51, 52) and Cleaves and Bricker and their... 

The mass flow rate through be is obtained, in turn, by using the conservation of mass principle to give, since the flow is steady ... 

The conservation of mass principle is simply a statement that mass cannot be created or dc.stroyed during a process and all the mass must be accounted for during an analysis. In steady flow, (he amount of mass within the control volume remains constant, and tlius the conservation of mass can be expressed as... 

The value of the average velocity at some streamwise cross-section is determined from the requirement lliat the cottsei-valion of mass principle be satisfied (Fig. 8-2). Tliat is. 

The concentration of species A at any point does not change with lime since operation is steady, and there is no production or destruction of species A since no chemical reactions are occurring in the medium. Then the conservation of mass principle for species A can be expressed as the mass flow rate of species A through the wall at any cross section is the same. That is... 

We adopt common conventions concerning chemical reactions. Each chemical reaction has an arrow indicating (he direction of the chemical transformation and clearly defines the reactants and products of the reaction. Species to the left of the arrow are called reactants, and those on the right are called products. Reversible reactions are treated as two distinct reactions, one forward and one backward. The arrow also serves as an equality sign for the total mass represented by tbe chemical formula. Thus, each chemical reaction should be balanced an unbalanced chemical reaction violates the conservation of mass principle. 

In this chapter, we discussed the application of the conservation of mass principle to derive design equations for chemical reactors. The following topics were covered ... 

The conservation of mass principle is applied to the nutrients being considered in the same way as it has been previously applied to the phytoplankton and zooplankton biomass within a volume segment. The number of mass conservation equations required is equal to the number of nutrients that are explicitly included in the growth rate formulation for the phytoplankton. For the sake of simplicity, the formulation for only one nutrient is discussed below. 

By the 1700s, the study of chemistry began moving from alchemy to the science we know today. It was during this time that the famous French chemist Antoine Lavoisier (1743-1794) determined that, the mass of the reactants equals the mass of the products in a chemical reaction. This is known as the conservation of mass principle. 

The conservation of mass principle, when presented in terms of hydrocarbon volumes, may be written as... 

The Conservation of Mass Principle and the Concept of a Control Volume... 

Conservation of Mass across Phases. The next step is to apply the conservation of mass principle to this problem. We need to write a material balance on salt for both phases. Any mass that leaves one phase must end up in the other phase. Then we can say the following regarding the rate of salt mass accumulation in the two phases ... 

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