EXPERIMENT 3: Addition of sloping glass column above the lime feeder and Tube-length Calculations
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 help the saturated lime-water solution stay inside the apparatus, while allowing the saturated lime water to still having the needed concentration at the 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 decreased velocity angle of inclination and laminar flow regime allows certain more 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 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)
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 similiarly to aluminum hydroxide flocs actually. 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)
2) Density of lime is 2.211 g/m^3: Particles are uniform.
3) Shape Factor of lime particles = 1: The lime particles are perfectly spherical.
4) Settling velocity = 10 m/day: Given a flow rate of 80 mL/min (as determined by experiment 1). This velocity corresponds to the finer lime particles. (What size does this correspond to?)
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 10m/day,and the smallest particle it can capture is 0.00135mm. (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.)
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 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?)
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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 10cm 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 (for what purpose?). 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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