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ENGRD 241: Engineering Computation Synthesis Mini Project, Spring 2007 Individual Assignment due April 19, 2007 Synthesis Mini Project: Controlling Eutrophication Background & DescriptionShortly after graduating from Cornell University, you decide to take a job with a local engineering firm that mostly does government work in the upstate NY area. Although you are only a Junior Engineer, you feel the jobs you have been working on thus far have not been challenging enough for your inquisitive mind. In particular, you have been hoping you could put to use your numerical computation skills learned in the ENGRD 241 during the Spring semester of 2007. Lucky for you, Ithaca needs your help with such a problem! Recently, the mayor has been concerned with the water quality in a lake located a few miles north of Ithaca. The lake is subject to excess phosphorous inputs from industry and municipal waste plants. Under normal conditions, the algal population is low, but the excess phosphorous is a “fertilizer” for these tiny organisms. Hence the excess phosphorous causes excessive amounts of algal biomass to inhabit the lake during the warm months of the summer. This is an example of “eutrophication”. When they die, high levels of algae can quickly deplete the oxygen from the lake, causing other fish and plant life to die. In addition the high concentration of algae can increase the need for filtration of water extracted from the lake for a drinking water supply. Among other things, the mayor is interested in determining how much the waste load (daily input) needs to be reduced in order to maintain adequate water quality in the lake. Adequate water quality means that the algae level is never greater than 1 x 10-4g/L. The algae growth is affected by how much dissolved phosphorous they can adsorb. When the algae die, they become “particulate phosphorous”. Over time, the particulate phosphorous slowly is transformed in to “dissolved phosphorous”. The living algae require dissolved phosphorous for growth. Figure 1 shows the three major components in the lake—dissolved phosphorous, algae, and particulate phosphorous—and their corresponding rates of growth and decay. You can model this problem as a system of coupled ordinary differential equations, and solve them numerically over a specified time interval. The mayor asks your firm to help the city, and the head engineer puts you in charge of this aspect of the project and expects you to give him a complete, technical report by Thursday, April 19th2007.Page 1
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