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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 belowfigure 1), 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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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 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.
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