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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. (Can you show us the equation for capture velocity and critical velocity or perhaps make a link to the plate settler spacing page?) 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+ for a more uniform saturated lime mixture.
The dimensions of apparatus were determined in MathCad. (The software package isn't important. The assumptions and equations used are important) The two constraints are the tube's length and the terminal velocity of the particle. This terminal velocity should be larger than �both- the capture velocity and the critical velocity of settling. 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
(Document your mathcad file in the wiki. And use the standard wiki link method for an attachment rather than using the https method.)
For example use
MathCad file
Calculations were made using the following assumptions for simplification:
1) When elementary lime particles coagulate, the density of the larger mass stays the same as that of the original particles. This is unlike what happens in flocs, which have a Dfrac of 2.3. (I'm unsure of what you are saying. In the reprecipitation of lime, I'm not sure the fractal dimension stays 3. I would suspect it would behave similarly to aluminum hydroxide flocs. Our assumption is that the solid floc particles are dissolving but not reprecipitating and the original lime is solid with a fractal dimension around 3)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 : Particles are uniformand this remains constant throughout the process.
3) Shape Factor of lime particles = 1 : The i.e. the lime particles are perfectly spherical.
4) Settling velocity = 10 m/day : Given a i.e. 0.012cm/s. A flow rate of 80 mL/min (as determined by experiment 1). This velocity corresponds to the finer lime particles. (How does flow rate connect with settling velocity. Perhaps you are referring to the vertical velocity in the reactor. But the flow rate is a useless parameter. It only has meaning if I know what the cross sectional area of the reactor is. What size does this correspond to?)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 0.00135mm. (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 neccesary 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.
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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 (for what purpose?)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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