# Chapter 27 : Filteration¶

## Example 27.2 Page no 413¶

In [1]:
from __future__ import division
print "Example 27.2 page no 413\n\n"
#plate and frame filter press is to be employed to filter a slurry
m_dot_slurry=600*60#mass flow rate ,lb/h
m=0.1#sluury contain 10% by mass solid
m_dot_solids = m*m_dot_slurry#the solid flow rate in the slurry
a=(1/5)#filter colth area required for 1 lb/h of solid
A=m_dot_solids*(a)#filter colth area for 3600 lb/h of solids
print "\n filter colth area A=%0.2f ft**2"%(A)#

Example 27.2 page no 413

filter colth area A=720.00 ft**2


## Example 27.4 Page no 414¶

In [2]:
from __future__ import division
print "Example 27.4 page no. 414\n\n"
m=1947#slope of curve b/w t/V vs V,s/ft**6
K_c=2*m
c=217#intercept on graph
q_r=c#reciprocal of q
print "\n coeff. K_c=%0.2f s/ft**6\n coeff. q_r=%0.2f s/ft**3"%(K_c,q_r)

Example 27.4 page no. 414

coeff. K_c=3894.00 s/ft**6
coeff. q_r=217.00 s/ft**3


## Example 27.5 Page no 415¶

In [3]:
from __future__ import division
print "Example 27.5 page no 415\n\n"
#refer to example 27.4
meu=5.95e-4#viscosity
g_c=32.174#grav. acc
P_drop=20*144#pressure drop
q_o=(1/217)#flow rate
S=0.35#filteration area per unit
K_c=3894#coefficentc
c=4.142#slurry conentration
R_m=S*g_c*P_drop/(q_o*meu)#filteration coeff.
print "R_m=%0.2e ft"%(R_m)#
alpha=K_c*S**2*g_c*P_drop/(c*meu)#filteration coeff.
print "\n alpha=%0.2e ft/lb"%(alpha)#

Example 27.5 page no 415

R_m=1.18e+10 ft

alpha=1.79e+10 ft/lb


## Example 27.7 Page no 418¶

In [4]:
from __future__ import division
print "Example 27.7 page no 418\n\n"
#the following result were obtained during the running of a filteration experiment
alpha=4.57e+11#cake resistance,ft/lb
P_drop=1554#pressure drop ,lbf/ft**2
alpha_o=alpha/(P_drop**0.21)#specific cake resistance
print "\n specific cake resistance alpha_o=%0.2e ft/lb"%(alpha_o)#

Example 27.7 page no 418

specific cake resistance alpha_o=9.77e+10 ft/lb


## Example 27.9 Page no 418¶

In [5]:
from __future__ import division
print "Example 27.9 page no 418\n\n"
#a filter press operates at a constant pressure
P=50#pressure,psig
q=10#flow rate,ft**3/min
#applying eq.27.12
#q = P/(B*V_s + C)
#in this case,V_s=0
C=P/q#constant
#for constant pressure applying equation 27.13
#t = B*V_s**2/(2P) + C*V_s/P
t=60#time ,min
V_s=100#volume,ft**3
B= 2*P*t/(V_s**2) - 2*C/V_s#constant
#during the washing cycle t_w = V_w/q_w
#B and C remain same
V_w=15#volume of water for washing per hr
t_w= V_w*(B*V_s + C)/P#time in washing
print "\n washing time t_w=%0.2f min"%(t_w)#
t_d=30#time for dumping and cleanig
t_c=(t + t_w +t_d)/60#collecting time,in hr
q_c =V_s/t_c#flow rate for 100 ft**3
print "\n flow rate q_c=%0.2f gal/hr "%(q_c)#

Example 27.9 page no 418

washing time t_w=16.50 min

flow rate q_c=56.34 gal/hr