Input the loading data into excel and Mathematica.
a. Create a plot in both programs.
b. Fit a curve to the data using Excel and Mathematica. Please recall that we created a file called “FittingCurvesClass” that you can use as a guide for the Mathematica work. We will also review the “FindFit” command today in class with Mathematica.
c. Discuss the quality of the fit and the flexibility of the types of functions available in both programs
2. Draw a mass balance for the lake system including the following;
a. First order decay of phosphorus = 0.03/day
b. Settling rate of the phosphorus = 12m/yr
c. Assume the inflow and outflow of the lake are the same and the inflow includes the pollutant loading.
3. Develop the mass balance equation for the lake system, defining clearly all variables in your equation.
4. Your influent load into the lake is variable. Decide how you will handle that in your model.
a. Assume a steady input loading based on the average of all years presented
b. Assume a background concentration of phosphorus based on the maximum value from the loading data and the influent loading coincident with the most current loading data
c. Define an equation to describe the influent loading into the lake using Mathematica and your results from item 1 above.
d. Any other option you decide as long as you explain it clearly.
5. Find the steady state concentration for the system.
a. Clearly show your work in a hand calculation.
b. Define any assumptions you made
6. Solve the equation developed in step 3 above using the decision you made in step 4 to define the phosphorus loading. Use Mathematica and the DSolve and NDSolve protocol defined in class on November 29th and available in the Class 13 link in LIVE to solve the problem.
7. In Mathematica, plot the equation you developed and discuss how the phosphate concentration is predicted to change in the timeframe that occurs after the collected data.
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