CD float height to outflow Fall 08

Experimental Methods

Two CD experimental set ups (the lab prototype and the robust CD) were used in identical experiments to collect data sets relating change in float height to dosing in Fall 2008. First the chemical doser was positioned at 5 cm intervals along the lever arm. The water level in the grit chamber bucket was varied while readings were taken of the changing water height in the collection column (explained below).

The 7 kPa pressure sensor at the base of the bucket was calibrated to read in centimeters of water and it was zeroed for the condition when the float just became buoyant and was no longer resting on the bottom of the bucket. The lever arm was made horizontal at the point by adjusting the length of fishing line tied to its end. This was checked with a level. By zeroing the pressure sensor at a lever arm height of zero all readings from the bucket pressure sensor were then equivalent to change in float height, which was also equal to negative change in the height of the end of the lever arm because of the fishing line connecting the float to the end of the lever arm.

A flow controller (FC) was connected to the chemical dosing tube at the T as is described in the CD experimental set up. The FC was fed from a bucket of water less than 1 m above it at all times, ensuring that there were not significant changes in water level within the FC. The FC was positioned at a level even with the lever arm such that it dosed no water when the lever arm was zeroed. The FC began to dose with a change in driving head of 1mm from that zero.

To measure flowrate from the FC through the CD a 7kPa pressure sensor was used at the bottom of the collection column. Water flowed from the FC through the T into the chemical dosing tube and then into the column. The pressure sensor at the base of the collection column was calibrated to read in centimeters of water, and it was zeroed after the valve at the base of the column had been opened and the water completely drained out. As water was dosed from the FC into the column, the pressure sensor transmitted data to a computer running the program Easy Data, which recorded both water level and time lapse in 1 second steps. Since the column dimensions are known, these variables can then be used to solve for a flowrate.

Concurrent data from the pressure sensor at the base of the bucket can be used to show the exact height of the float relative to the apparatus for each flowrate. Data was collected at several float heights for each distance the chemical dosing tube was attached along the lever arm or 10 cm, 15 cm, 20 cm, and 25 cm.

Experimental Results

All laboratory data was analyzed using the MathCAD program CDFall08LeverT, which can be found attached to the main CD page. Data arrays of column water height were transformed to flowrates at each float height and chem doser position studied. The data can be seen in the figure below. Each set of color coded data represents readings from one specific chem doser position along the lever arm, given in centimeters out from the pivot.

For the Lab Prototype

The data appears linear when the chem doser was placed 15 cm (pink points on graph below), 20 cm (green), or 25 cm (blue) from the pivot point, but it becomes less predictable at only 10 cm (red). The system also loses reliability around 0.08 mL/sec dosing, as can been seen in both the red and blue data sets below. This is a very low flow rate, and it is possible that surface tension and head loss are playing a significant role in the system at this point.

The final concern with this data is that there is not equal distance in the y-axis direction between the four lines. Theoretically we should expect the slope of each line to equal the sum of the slope of the line below it and the slope of the 5 cm line. In other words, moving out each 5 cm interval along the lever arm should result in a line that is rotated by a consistent angle around the origin. Visual inspection of the graph above shows that the data from the doser being located 15 cm from the pivot (shown in blue) appears to be translated downward slightly. The data does not appear to go through the origin, and it does not lie evenly between the 10 cm and 20 cm data lines when rotated around the origin.

Overall the data does follow an expected pattern, with a few unexpected readings. Flow rate increases as float height and distance from the pivot increases, allowing us to consider the CD reliable enough to dose alum to a precise enough degree.

For the Robust System

Data for the robust CD system is much less accurate than for the prototype. Data for the doser at 5 cm from the pivot (in red points), at 20 cm (in pink), and at 25 cm (in teal) appears to be linear, passing through the origin, and approximately evenly spaced. On the other hand the data from 10 cm and 15 cm out (in blue and green respectively) do not fit the expected pattern. The 10 cm data appears to be higher than expected, with a less steep slope. Similarly to the prototype testing, the 15 cm data appears to have too high of a slope and be translated downwards.

Comparing Both Systems

The inconsistencies become apparent when the data sets are laid on top of one another. In the graph below, the triangle points are data collected with the robust set up, while the circular points are from testing the prototype. Theoretically the two data sets should lay on identical trajectories, but only the 15 cm and 25 cm data sets are close. The 15 cm data sets fit the best, but they are also the farthest off of the theoretical trajectory anticipated.

Sources of Error

The largest source of error is that the system may not have had enough time to come to equilibrium each time it was moved. Changing the position of the dosing tube changed the driving head, which takes an unknown amount of time to re-equilibrate. Also each time the bucket water level was changed, it took and unknown amount of time for the float to come completely back to rest. The bucket was small enough that any mixing from adding or removing water would send relatively large ripples throughout. These visibly caused the float to move, which would in turn directly effect the doser for some period of time.

Another major issue with the experimental set up was that the pressure sensors were not reliable. The pressure sensors became unresponsive and had to be re-zeroed at least twice while testing the robust set up. This may indicate that the sensors were not producing accurate data at other points during the experiment without our noticing.