Common mechanical operation section 7

1. Common Mechanical Operation
Section 7
Eng. Kareem H. Mokhtar

2. Rules
• Constant pressure filtration
• Plot t/v versus v to get (Kp/2) as a slope and B as the intercept

3. • Constant rate
• Draw delta P against time, at time=zero get delta Pm
• Plot log t versus log delta Pc to get (1-S) as a slope
• Get Kr
• Get alpha

4. Q1
• It is required to evaluate the characteristics of the cake obtained on
filtering a slurry containing 120 kg/m3 water using canvas filter
medium. To this effect, a one plate filter of dimensions 300×300 mm2
was used under a positive pressure of 0.8 atmg. The following data
were obtained for the variation of volume of filtrate with time.
• Estimate the specific cake resistance and the filter medium resistance

5. Q1- Answer
• Const. P
V 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
T/v 840000 1140000 1400000 1590000 1824000 2040000 2245714.29 2445000
y = 5E+08x + 677148
0
500000
1000000
1500000
2000000
2500000
3000000
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

6. • Kp = 109 s/m6 and B = 677148 s/m3
• Alpha = 5.4 x 1012 m/kg
• Rm = 4.87x 1012 m-1

7. Q4
• The following relation has been determined between specific cake
resistance and pressure drop for light P.E.
• A slurry of this material containing 50 kg of cake per cubic meter
filtrate is to be filtered under a constant pressure of 70 psig. Taking
the filter medium resistance as 4x 1010 m-1 , how many square meters
of filter surface are needed to yield 7 m3 of filtrate in one hour
filtration?
• Where, ∆p is in psi and α in ft/lb.

8. Q4 - answer
• 3600/7 = Kp * (7/2) +B
• From relation: alpha= 8.9x 1010 ft/lb = 5.43 x 1010 m/kg
• Kp =
0.001∗5.43∗1010∗50
𝐴2∗4.76∗105
• B =
0.001∗4∗1010
𝐴∗4.76∗105
• A= 6.31 m2

9. Assignment Next time
• 5)The filter in problem (2) is operated at constant rate = 15 lit.m-2
.min-1. from the start of the run until the pressure reaches 70 psig.
Then a constant pressure is applied until 40 lit of filtrate are collected.
Calculate the total time required for filtration