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#1)Wall Friction: We can attribute the increase in error as flow rate increased due to the increase in wall friction on the test vial. We can minimize this by increasing the size of our bench scale experiments.
#2) Sand Properties Parameters: We might have used an incorrect D60 and porosity for the filter bed in our equations. We tested this in our Mathcad code and found that if we increased the porosity from 0.4 to 0.5, the graph looked changed to Figure 3:
Figure 3: Fluidization Velocity Experiment-porosity change
Then we also found that if we instead increased the d60 from 0.55 to 0.9, the graph changed to Figure 4:
This shows that small errors in our d60 or porosity term could easily account for the major errors we have. Therefore, future experiments should carefully measure these properties before conducting experiments.
The above sources of error will be very difficult to control for the actual filtration design. Consequently, we surmise that we need to apply a safety factor of around 10-30% when applying the empirical fluidization velocity equation. The follow up experiments for multi-media experimentation with larger bench scale model will further specify the safety factor required and we expect the larger scale model to reduce the overall error.