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In order to overcome the difficulties faced at the end of the second experiment, the team considered a new design was considered, which consists of a diagonal column attached at the top of the vertical column. The design would help the saturated lime-water solution stay inside the apparatus, while 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 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 for a more uniform saturated lime mixture.
The dimensions of apparatus are were determined according to MathCad calculations, we have in MathCad. The two constraints of choosing are the tube's length , and the terminal velocity of the particle. This terminal velocity should be larger than both of the capture velocity and the critical velocity in order to settle the big particle and prevent the small particles roll up, we also consider the of settling. The length should be long large enough to let the flow in the slanting tube could to become a fully developed flow; the relevant criteria can be found in our Mathcad file. MathCad file
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- 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, that which have a Dfrac of 2.3.
- Density of lime is 2.211 g/m^3: Particles are uniform.
- Shape Factor of lime particles = 1: The lime particles are perfectly spherical.
- Settling velocity = 10 m/day: Given a flow rate of 80 mL/min (as determined by Trial 1). This velocity corresponds to the finer lime particles that have a diameter of about 1 micrometer.
CALCULATIONS ANALYSIS
Based on our caculation, we assume It was assumed that the smallest particle a the tube can could capture is when has the same terminal velocity equals to as the capture velocity, and we find the longer a longer tube can capture smaller size sized particles (The relation are is shown in figure 1), the . The tube length at 1.5m has a capture velocity of 10m/day,and the smallest particel particle it could can capture is 0.00135mm. 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 necesary 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 lower less than 1.5m.
We also caculate the relationship bewteen The relationship between critical velocity and terminal velocity was also calculated, and with the as the particle's size increaseincreases, terminal velocity become becomes much bigger larger than critical velocity, this is due due to the fact that critical velocity is liner linear with respect to particle diameter but terminal velocity is diameter's square. But if proportional to the square of the diameter. However, if the slanting tube's diameter decreasedecreases, there will be a certain amount of small particle particles that roll up to the tube, which would not happen in our this case.
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Figure 1, the relationship between tube length, capture velocity, and the smallest particle diameter the tube can capture.
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The length needed for the pipe in order to obtain a developed laminar flow 'Le', was also calculated and determined in 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 conclussionconclusion, the length of the tube must be greater than Le.
With the new apparatus, as shown in figure-3 below, the team will carry out a fourth trial , and will make the required arrangements for more experiments, checking to see if the modification 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.
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