Development of a Mathematical Model Essay Example | Topics and Well Written Essays - 1000 words

Development of a Mathematical Model - Essay Example Major immediate concerns are the possibility of underground movement of the gasoline, pollution of ground water and sewage systems and contamination of housing by toxic and flammable fumes. The effects of this spillage is mainly on water pollution and air pollution, the sewage pollution is not likely to have any effect on the people, the pollution of underground water as a result of this spillage and air pollution due to the effects of flammable flames are likely to affect the people and therefore we will develop a mathematical model as follows that explains this effects. Petroleum products are hydrocarbons and have the chemical formula CnH2n+2; Trimethylpentane is used as gasoline and has the chemical formula C8H18, in this scenario therefore the contact of petroleum with oxygen takes the following reaction: This reaction with oxygen produces carbon dioxide, water and heat; however the incomplete combustion of gasoline is harmful in that it causes the formation of carbon monoxide, and nitric oxide as shown below in the chemical reaction: Therefore this will result to the formation of gases that once they are inhaled endanger health, carbon monoxide reacts with red blood cells which carry oxygen from the lungs to the other pats of the body to form an irreversible compound therefore a person who inhales this gas could die due to insufficient oxygen in the body. Petroleum is insoluble in water and therefore does not react with water, it is less dense than water and therefore will float in water, therefore to its causes to underground water will only affect the availability of clean underground water. We will not consider the effect on land because there are no major direct effects as a result of the spillage, we shall not also consider the effect of the spillage on sewage lines because the contents are not of use to human beings. Our major concern therefore is the production of carbon monoxide and nitric oxide, we can form the following mathematical model that analysis the effect of one litre of fuel: One mole of gas occupies 26.5 litres volume at standard temperature and pressure, therefore one mole of C8H18 will produce 2 moles of carbon monoxide and two moles of nitric oxide, therefore if 1,000 litres of petroleum was spilt then this will produce 37.74 litres of carbon monoxide and 37.74 moles of nitric oxide.3 The model can therefore be specified as follows E= 2 litres carbon monoxide + two litres nitric oxide, and this is per litre of petroleum spilt, Where E is the total effect. Scenario two (b) There has been a spillage of gasoline from a road tanker in a town (population, 5500). Most of the gasoline