水质污染处理数学模型

摘 要

随着市场经济和现代工业的飞速发展，人类面临了直接危害人类生存的新问题――环境污染。为了治理污染，提出治理污染的新方案，必须建立合理的数学模型来解决现实问题。

这是1个关于湖泊、河流水质污染处理的数学模型，通过模型的建立与问题解决，能够较准确地分析并解决实际生活中的水质污染问题。如何合理地解决湖泊、河流污染问题是1个非常切合实际的问题，本问题是目前1个热门的研究课题。把此模型看成是1个单流入、单流出的系统，流入、流出的水流速度相同。利用质量守恒定律可列出关于浓度变化的微分方程，通过求解此微分方程可得到模型所要求的某1时刻污染物的浓度。本模型较好地解决了湖水污染处理问题，具有1定的经济效用和价值，能比较恰当地解决实际问题。

通过对问题的分析，得出湖水污染浓度的变化的结果。在模型建设中采用了比较理想的求解方法，在实际中还是比较有指导意义的。

关键词 微分方程；质量守恒定律；污染浓度

Abstract

Along with the market economy and the present industry rapid development, the new question of the humanity facing - environmental pollution has directly harmed the human survival. In order to control the pollution and propose a new plan, we have to establish the reasonable model to solve the realistic problem.

This is a mathematical model about processing water pollution of the lake and the rivers. Through the establishment of the mathematical model and the solution of the question, we can accurately analyze and solve the question of water pollution in practical life. This question is an extremely realistic question, how to reasonably solve the question of contamination about the lake and the rivers is a lively researched topic today. We regard as this model as the system with a sole entrance and a sole exportation. And the velocity of the inflow and the outflow are same. Using the law of conservation about the changing density we can list a differential equation, through solving this differential equation we can obtain a certain time pollutant density which the model requests . This model has solved the problem well, and it has certain economic utility and value. The model can quite appropriately solve the actual problem.

Through the analysis of the question, we can obtain the result of changing concentration of the contaminant. We have used the quite ideal solution method in the construction of model, and the model has a certain guiding sense in practice.

Key words Differential equation; Law of conservation of mass; Concentration of contaminant