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# HW 4 - ((1 Harrison prob 4.1(conventional batch filtration...

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CHEN 4820 Fall 2010 Homework 4 (filtration principles) (1) Harrison prob 4.1. (conventional batch filtration ) Note: interpret “relative significance of the medium resistance” to mean how resistance from the filter medium alone compares to the resistance from the filter cake. Ans: see Harrison key. (2) Interpreting filtration profiles: The graph below gives data from a dead-end filtration process in which a cake of solids forms above the filter as filtration continues. Two conditions were tested, one at 100 KPa filtration pressure and the second at 400 KPa. State next to each line whether the specific cake resistance is increasing, decreasing, or constant for that run, along with a very brief explanation for your answer. State whether the resistance of the filter medium alone is approx. the same for the two runs or whether it is far apart (> 2X apart) for the two runs. Give a very brief explanation for your answer. The straight line for the low pressure run reveals its specific cake resistance is constant during the filtration. See Harrison eqn 4.2.5. The bend in the high pressure line toward increasing slope later in the run indicates its SCR is rising as filtration continues. At this high pressure, the cake must be starting to compress. (If the bend continues, the low pressure filtration could end up filtering more volume in less time.). Harrison eqn 4.2.5 indicates that the y-intercept of the graph is proportional to R m /DP, where Rm is the resistance from the filter medium alone. Judging frm the graph, the y- intercept for the low pressure run is approx. 4X the value of the intercept for the hi pressure run, so both runs give about the same value for R m , which is reassuring. (3) Harrison prob 4.2. (batch filtration with change in pressure ) Note: as part of your analysis, do a linear least squares fit of a straight line to a plot of tA/V (y‐axis) vs V/A (x‐axis). The fit line does not have to go

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through the origin. Re part (d), an “effective” change is anything that shortens filtration time; it does not have to be cheap to do. Ans: see Harrison key. For part (d) warming the product, which reduces filtrate viscosity and speeds filtration, is an acceptable answer in addition to just buying more filter area. (4) Harrison prob 4.3. (filter with uniform cyclindrical pores ) Also, calculate the porosity of the cylindrical pore filter, where porosity is defined to be the total pore entrance area divided by the total filter area. Note: a filter with straight cylindrical pores is “feasible” if all the pores can fit on the surface with room to spare, i.e. there is enough distance between adjacent pores to have some polycarbonate structure between pores. Ans:
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HW 4 - ((1 Harrison prob 4.1(conventional batch filtration...

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