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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 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. This decreased velocity allows more lime (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.
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.
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