h2. Data Analysis

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h3. {toggle-cloak:id=Methods} Methods

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h4. Data source

Data from [previous experiments| Overall Tube Floc Research and Past Report] were collected using Process Controller and saved in Excel files. The data of interest (i.e. effluent turbidity) was stored in a file corresponding to the date of experiment run and the status file indicated the state of treatment process (i.e. flocculation state, settling state, etc). Data was extracted using [Meta Data|Meta Data] and analyzed in the steps provided below.

h4. Model fitting
In the settling state (state 4 or 5, depending on the experimental and software setup), the analysis of settling dataset starts from its maximum turbidity reading. This will eliminate the data fluctuation due to a sudden stop of flow.  Data is normalized to the maximum reading of dataset and converted to a positive hyperbolic curve for data interpretation. The dataset will now read as the cumulative amount of settling in the tube. A hyperbolic curve can be linearized using double reciprocal method (or Lineweaver-Burke plot), where the Y-axis is the reciprocal of the cumulative amount of settling and X-axis is the terminal velocity. The length of tube shone by the light is assumed to be 5 cm. 

h4. Equations

Assuming the dataset follows a hyperbolic curve function, therefore it can be represented as:


where 
Y is 1 - NTU/NTU ~max~
t is the time [T]
K will determine how fast the flocs are settling.


h4. Mathcad files

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h3. {toggle-cloak:id=Results and Discussions} Results and Discussions

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# By extracting the data using Meta Data files, we were able to pick sets of settling data of interest and plot and analyze them individually or collectively to see any [trends|First Look into the Data].
# Data fluctuation shows that ...


h4. Model fitting

We're proposing polynomial fit as an option to evaluate the data and [error analysis algorithm|Error Analysis] is utilized to see which equations fit each datasets the best.

[Another datasets example|Another example...] is also analyzed to determine which polynomial fit suits the best. From sum squared error analysis, the third and fourth degree of polynomial were found to be the best.[Another raw sedimentation data|Raw Data of Settling Column] was looked at different angle to get a better sense of parameters that actually effect the curve.

Data is [normalized|Data Normalization] and _Lineweaver-Burke_ data analysis was applied.

We were interested to find out how much the [data fluctuates|Data Fluctuation] during settling in a given experiment if repeated several times and how this might impact our results.

Data is [linearized|Data Linearization] using _double reciprocal_ analysis and the equations can be viewed [here|TubeFloc - Equations].

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h2. {toggle-cloak:id=Progress} Progress

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