3. A conventional "dead end" filter is used to test the filtration of a suspension of yeast cells at the labscale. The filter has a diameter of 7 cm, the solution has a viscosity of 2 centipoise and a vacuum pumpwas used to create a pressure drop of 0.5 atm across the filter. After systematically measuring thevolume filtered as a function of time, a plot of t/(V/A) vs. (V/A) was constructed and the data fit to astraight line. The fit gave a value of 4 s/cm² for the slope and a value of 6.5 s/cm for the y-intercept.After filtering 1 L of solution, you remove the filter cake from the filter and measure a dry mass of 15 g.You would like to use this information to design an industrial scale filter setup with a filter area of 100m?. However, you will need to use a thicker filter, with an Rm twice that of the lab scale filter. Calculatethe pressure drop in cgs units (centimeter-gram-second) needed to filter 8,000 L of this solution in 8 hthrough the proposed industrial scale filter set up.

Answered: 3. A conventional "dead end" filter is…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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3. A conventional "dead end" filter is used to test the filtration of a suspension of yeast cells at the lab
scale. The filter has a diameter of 7 cm, the solution has a viscosity of 2 centipoise and a vacuum pump
was used to create a pressure drop of 0.5 atm across the filter. After systematically measuring the
volume filtered as a function of time, a plot of t/(V/A) vs. (V/A) was constructed and the data fit to a
straight line. The fit gave a value of 4 s/cm² for the slope and a value of 6.5 s/cm for the y-intercept.
After filtering 1 L of solution, you remove the filter cake from the filter and measure a dry mass of 15 g.
You would like to use this information to design an industrial scale filter setup with a filter area of 100
m?. However, you will need to use a thicker filter, with an Rm twice that of the lab scale filter. Calculate
the pressure drop in cgs units (centimeter-gram-second) needed to filter 8,000 L of this solution in 8 h
through the proposed industrial scale filter set up.

Expert Solution

Step 1

Write the expression for constant pressure filter process as follows:

$\begin{array}{rcl} \frac{t}{V} & = & \frac{μ c α}{2 A^{2} ∆ P} V + \frac{μ R_{m}}{A ∆ P} \\ \frac{t A}{V} & = & \frac{μ c α}{2 A ∆ P} V + \frac{μ R_{m}}{∆ P} \\ \frac{t}{V / A} & = & \frac{μ c α}{2 ∆ P} (\frac{V}{A}) + \frac{μ R_{m}}{∆ P} . . . . . . (1) \end{array}$

Given the graph between $\frac{t}{V / A}$ vs $\frac{V}{A}$ represents a straight line with slope $4 s / {cm}^{2}$ and y-intercept $6.5 s / cm$ .

Slope, $\frac{μ c α}{2 ∆ P} = 4 s / {cm}^{2}$ .......(2)

y-intercept, $\frac{μ R_{m}}{∆ P} = 6.5 s / cm$ .......(3)

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