EXPERIMENT 3
In order to overcome the difficulties faced at the end of the second experiment, the team considered a new design, 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 determined according to MathCad calculations, we have two constraints of choosing the tube's length, the terminal velocity of the particle 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 length should be long enough to let the flow in the slanting tube could become fully developed flow; the relevant criteria can be found in our Mathcad file. MathCad file
Calculations were made using the following assumptions for simplification:
- 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 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 the smallest particle a tube can capture is when the terminal velocity equals to capture velocity, and we find the longer tube can capture smaller size particles(The relation are shown in graph below), the tube length at 1.5m has a capture velocity of 10m/day,and the smallest particel it could capture is 0.00135mm. Lime particles will have a larger density than the flocs, which means their settling velocities will be higher than the assumed 10m/day. Also, it is not necesary 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 than 1.5m.
We also caculate the relationship bewteen critical velocity and terminal velocity, and with the particle's size increase, terminal velocity become much bigger than critical velocity, this is due to critical velocity is liner to particle diameter but terminal velocity is diameter's square. But if slanting tube's diameter decrease, there will be certain amount of small particle roll up to the tube, which would not happen in our case.
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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 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 conclussion, 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 successful in maintaining the pH at 12 and if so, for how long.
Figure - 3 : the picture of new apparatus will be taken this week and put up (since we will get the constructed apparatus only by 10/27/09).
For this trial, distilled water will be used instead of tap water. In the picture below (figure 4), 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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