The downstream reach of the Sacramento River in California receives the treated effluent from the City of Sacramento at mile point 53, the single significant input in this region.

The longitudinal profiles of flow, cross-sectional area, depth, biochemical oxygen demand and dissolved oxygen are shown below and in the attached spreadsheet for a five-day period in the fall of 1960. Assume the water temperature is 15 oC. There are flow withdrawals as shown. The table of BOD, DO, and interpolated stream data are listed below and are included in the spreadsheet.

1. Use the VBA program that you developed in Assignment 5 that computes the BOD and DO solutions in a series of segments with constant parameters. Document the code. Include the equations being solved in the comments. Include a print out of the code as part of this exam.

2. For each segment of the model compute the reaeration coefficient using the O'Connor Dobbins formula with temperature correction

3. For each segment of the model compute the DO saturation concentration using the equation in Chapra

4. In your spreadsheet, set up plots of BOD5 and DO data (see plots below) that will be used to that compare model output to data

5. Check the code using a constant parameters for every segment model and the analytical solutions for BOD and DO. Use the geometry in segment 1 of the Sacramento River

6. Fit the model to the Sacramento river data as follows: Use the model developed in questions 1-3 and the plots developed in question 4. Use a single kd. Estimate the parameters that produce the best fit of both the BOD and DO data. Use an "eyeball" fit, i.e. play around with the parameters until the fits are "reasonable" for both BOD and DO. After approximately mile point 25, the river becomes more like an estuary and the stream model no longer applies. So ignore the data after milt point 25. Fit the following parameters

a. The initial BOD5 and DO deficit concentrations at mile 60.

b. The Sacramento treatment plant BOD5 loading rate in lbs/day at mile 53

c. The ultimate to 5 day BOD ratio

d. A single deoxygenation coefficient kd(/day)

7. Compare the values that you obtain to values that are reasonable for primary effluent.

8. Use two deoxygenation coefficients: one for the upstream sections 1-4 and another for the downstream sections after the beginning of flow withdrawals. Try various locations for the starting point of the second kdthat achieves a better fit of the BOD and DO data. Estimatea. The initial BOD5 and DO deficit concentrations at mile 60.

b. The Sacramento treatment plant BOD5 loading rate

c. The ultimate to 5 day BOD ratio

d. The two deoxygenation coefficients kd1 and kd2 and the location where kd2 starts

9. Can you justify the need for the two kd's?

10. Graduate Students only

a. Do the same calculations in Problem 6 using the finite difference program that you developed in Assignment 5. Use the varying  parameters rather than the
constants for the piecewise constant solution in Problem 6

b. Compare the two solutions. Analyze the differences and comment on the significance of the differences.