ANC CONTROL
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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$$
{{V_
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} \over {V_c }} = 1 +
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\cos \alpha \sin \alpha
$$
The equation of terminal velocity to the particle diameter is:
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$$
V_t = {{gd_0^2 } \over {18\Phi \nu _
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}}{{\rho _
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- \rho _
} \over {\rho _
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}}\left( {{d \over
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}} \right)^{D_
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- 1}
$$
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. (Perhaps put the design for your tube settler on another page. I would include all relevant equations and summaries in a MathCAD page. I would include the length, angle of inclination, diameter, and predicted capture velocity as well as the critical velocity of floc particles and document these values in the wiki.)
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
Figure 1: Sloping Column Lime feeder
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 continued to dissolve as keep pushing in a raw water was continuously added so as to make an resulting in an effluent solution of saturated lime with a pH of 12.4. (The pH is important to report to the first decimal point)
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. (Your statement is incorrect. If the lime particles stuck together, the fractal dimension would decrease)
2) Density of lime is 2.211 g/m^3 and this remains constant throughout the process (if the fractal dimension remains constant).
3) Shape Factor of lime particles = 1 i.e. the lime particles are perfectly spherical.
4) Settling velocity = 10 m/day i.e. 0.12 mm/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 2.95mm/s
CALCULATIONS ANALYSIS
Under the assumption that the flow rate of the lime feeder keeps at 80mL/min and 2.4cm as diameter of the tube(so the upflow velocity is 2.95mm/s), we can measure the relationship between the tube length and the capture velocity(Capture velocity is a function of the geometry of the tube), we also suppose that the smallest particle the tube can capture has the same terminal velocity as the capture velocity, so we have the relationship between the particle size and it's required capture velocity. Figure 2 shows the change of capture velocity and the particle size it can capture as the function of the slantign tube length.
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Figure 2: the relationship between tube length, capture velocity, and the smallest particle diameter the tube can capture.
We use a 1.3m vertical tube connect with 1.5m slanting tube in our experiment. Under our assumption of flow rate, a length of 1.5m has a capture velocity of 0.12 mm/s, and the smallest particle it can capture is 1.35μm. We could cut the slanting tube for saving space but the capture velocity the tube could provide and the smallest particle size it could capture would both decrease, this relationship could also be found on figure 2.
The lime particles used in our experiment have a nonuniform particle density, it cause some particles with less density fall out at the beginning of our experiment, and the ones which have a larger density than the flocs could be kept in suspension. (Do larger particles necessarily have a larger density?) Many of the larger particles have settling velocities higher than the assumed 10m/day(0.12 mm/s), the particle size could be captured with this velocity is 1.35μm as discussed above. (Remind us here how large a particle has to be.) so we think a 1.5m long slanting tube could help to make a good suspension after the initial period which some of the smallest particals washed out with the effluent water. (Read this sentence again. Please proofread your work. Are you talking about length here?)
To measure if the particle has the rollup risk, the relationship between critical velocity and terminal velocity was also calculated. We assume the particle diameter is small compared to the diameter of the tube, and the flow is fully developed, so we can obtain the linearized equation for critical velocity(floc roll up velocity):
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$$
u\left( {d_
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} \right) \approx {{6d_
} \over S}{{V_
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} \over {\sin \alpha }}
$$
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, the critical velocity will increase, theres is more risk the floc would roll up, but with our appartus, the 2.4cm inner diameter could prove the roll up would not happen(see figure 3). (Why? Refer to the figure and explain why? Also, you introduce the concept of critical velocity without any background and very little explanation about what it is.)
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Figure 3: Critical velocity vs Capture velocity
With the new apparatus, as shown in figure-4 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. (Distilled water has no alkalinity, and its pH will be that of a solution saturated with respect to atmospheric carbon dioxide.) 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.
Figure 4: Apparatus for experiment 3
With the design described on Experiment 3, three trials were done:
Trial 1: Using tap water