EXPERIMENT 3: Addition of sloping glass column above the lime feeder and Tube-length Calculations
Introduction
In order to overcome the difficulties faced at the end of the second experiment, a new design was considered, which consists of a diagonal column attached at the top of the vertical column. The design would retain small lime particles while allowing the saturated lime water to exit. Since the velocity in the slanted tube is affected by the angle, its vertical component is lower than the upflow velocity of the primary column. The equation relating the capture velocity to the geometry of lime feeder is:
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The angle of inclination and laminar flow regime allows certain sized lime particles to settle back into the column and thus prevent unnecessary lime loss. Thus the primary column would be used as a storage vessel for the suspended lime bed while the slanted tube above it would allow more lime particles to settle back to the column below, making the process more economical.
The two constraints are the tube's length and the terminal velocity of the particle. This terminal velocity should be larger than the capture velocity. The length should be large enough to let the flow in the slanting tube to become a fully developed flow; the relevant criteria can be found in the MathCad file
Calculations were made using the following assumptions for simplification:
1)It was assumed that the original lime is solid powder with a fractal dimension of lime particles to be around 3. These solid lime particles keep dissolving as we keep pushing in a raw water supply so as to make an effluent solution of saturated lime with a pH of 12.
Hence, giving a fractal dimension of 3 essentially implies that when lime particles stick together or dissolve to attain a smaller size, their density is not affected.
2) Density of lime is 2.211 g/m^3 and this remains constant throughout the process.
3) Shape Factor of lime particles = 1 i.e. the lime particles are perfectly spherical.
4) Settling velocity = 10 m/day i.e. 0.012cm/s. A flow rate of 80 mL/min (as determined by experiment 1)and a tube of inner diameter 2.4cm corresponds to an upflow velocity of 0.295cm/s.
CALCULATIONS ANALYSIS
It was assumed that the smallest particle the tube could capture has the same terminal velocity as the capture velocity, and a longer tube can capture smaller sized particles (The relation is shown in figure 1). The tube length at 1.5m has a capture velocity of 0.12 mm/s, and the smallest particle it can capture is 1.35μm. (Use μm This is reasonable, can you show how you obtained 1.5 m in the wiki? Can you show alternative lengths and what you would predict? See the plate settler spacing team model and Monroe's CEE 4540 for more information on tube settlers.) (Monroe is doubtful that you can capture such small particles at 0.12 mm/s)
Lime particles will have a larger density than the flocs, which means that their settling velocities will be higher than the assumed 10m/day. Also, it is not necessary that ALL lime particles settle down - some amount (not determined yet) will have to fall out of the lime feeder to solve the acidity problem. Consequently, the length of the tube needed will be less than 1.5m.
The relationship between critical velocity and terminal velocity was also calculated, as the particle's size increases, terminal velocity becomes much larger than critical velocity, due to the fact that critical velocity is linear with respect to particle diameter but terminal velocity is proportional to the square of the diameter. However, if the slanting tube's diameter decreases, there will be a certain amount of small particles that roll up the tube, which would not happen in this case. (I did not see how your graph incorporated the critical velocity concept. Did I miss something?)
(You use the terms "terminal", "critical", and "capture". I used to use the term "critical" before beginning to use the more descriptive word "capture". I consider the word "critical" to be obsolete in this context because it isn't clear what it describes. "Capture" is a property of the tube settler geometry and fluid velocity. "terminal" is a property of the particle and the fluid.)
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Figure 1, the relationship between tube length, capture velocity, and the smallest particle diameter the tube can capture.
The length needed for the pipe in order to obtain a developed laminar flow 'Le', was also calculated and determined to be 10 cm with the given (above) conditions. This is required to verify whether or not there is a parabolic profile at the end of the pipe. In conclusion, the length of the tube must be greater than Le. (How was this obtained?)
With the new apparatus, as shown in figure-3 below, a fourth trial will be carried out and evaluated. The modifications will be tested to see whether or not it will be successful in maintaining the pH at 12 and if so, for how long.
For this trial, distilled water will be used instead of tap water. It has been observed that after a few hours into any experimental run using lime, the lime instead of remaining in suspension as soluble particles, forms a single mass and becomes insoluble. It is hypothesized (by the previous research team) that this happens because some or all of the lime gets converted into calcium carbonate(which is insoluble)if tap water is used since the water received at Cornell is alkaline in nature. This should not be a problem in Honduras because the raw water to be treated will not be as alkaline. However, under laboratory conditions, in order to get a true estimate of the lime feeder's efficiency (in dissolving lime for a longer period and thereby lasting for a longer time) distilled water having a lower pH than tap water will prove to be more accurate. In the pictures below, the ANC Control team can be seen carrying the distilled water tank on to the platform where the experiment is to be set up.
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With the design described on Experiment 3, three trials were done:
Trial 1: Using tap water