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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
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CALCULATIONS ANALYSIS
Based on our caculation, the longer 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 the 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.
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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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