Industrial mathematics (see attachment)

Project4_FA17DataFitting-WaterUsage.docx

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AMTH 518 Project 5

Data Fitting/Model Refinement

This project is a group effort (teams of three or less). Your team will submit a single report of professional quality, and including appropriate supporting graphs and tables from Excel.

The state water commission is requiring data a certain university housing on the rate of water use, in gallons per hour, and the total amount of water used each day. The available equipment can measure only the level of water in the campus tank, within 0.5% accuracy, every hour. More importantly, whenever the level in the tank drops below some minimum level L, a pump fills the tank up to the maximum level, H, but there is no measurement of the pump flow at these times either. This pumping activity occurs once or twice per day, for a couple of hours each time. So, while the pump is working, no information is available on the level in the tank or the amount of water used. The table below contains the time, in seconds, since the first measurement, and the level of water in the tank in hundredths of a foot. For example, after 3316 seconds, the depth of the water in the tank reached 31.10 feet. The tank is a vertical circular cylinder with a height of 40 feet and a diameter of 57 feet. Usually, the pump starts filling the tank when the level drops to about 27.00 feet and the pump stops when the level rises back to about 35.50 feet.

REQUIREMENTS:

1. Determine an appropriate mathematical model for the state water commission to use in estimating water use (gallons per hour).

a. Using at least two of the methods discussed in class, estimate the flow out of the tank, f(t), at all times (even times when the pump is not working).

b. Consider the strengths and weaknesses of your models. Choose one of these models to use, and explain why it is the better of the two models for estimating water flow.

c. Use your model to estimate the total amount of water used in one day (24 hours).

2. Write a professional-quality report to the commission which details your results. Include a discussion of the two models you considered for use and why the model your team selected is the better choice. Be sure to include a discussion of any assumptions made in the model or the analysis, and a discussion of the strengths and weaknesses of the candidate models.

Time (sec)	Level (.01 ft)	Time (sec)	Level (.01 ft)
0	3175	46636	3350
3316	3110	49953	3260
6635	3054	53936	3167
10619	2994	57254	3087
13937	2947	60574	3012
17921	2892	64554	2927
21240	2850	68535	2842
25223	2795	71854	2757
28543	2752	75021	2697
32884	2697	79254	pump on
35932	pump on	82649	pump on
39332	pump on	85968	3475
39435	3550	89953	3397
43318	3445	93270	3340