Chapter 6 : Introduction to Material Balances

Example 6.1 Page no. 142

In [2]:
from numpy import matrix

# Variables
# Given
P_O = 89 ;      # Premium octane -[octane/gal]
S_O = 93 ;      # Supereme octane - [octane/gal]
R_O = 87 ;      # Regular octane - [octane/gal]
CP = 1.269 ;    # Cost of premium octane -[$/gal]
SP = 1.349 ;    # Cost of supereme octane -[$/gal]
RP = 1.149 ;    # Cost of regular octane -[$/gal]

# Let x and y fraction of regular octane and supreme octane  is blended respectively,therefore: x + y = 1 ...(a)
# and 89 = 87x + 93y ...(b)
# Solve equations (a) and (b) simultaneously
# Calculation
a = matrix([[1,1],[87,93]]) ;          # Matrix of coefficients of unknown
b = matrix([[1.0],[89.0]]) ;           # Matrix of constant
a = a.I
c = a * b
cost =  c[0]*RP + c[1]*SP ;       # Cost after blending - [$/gal]
sv = CP - cost ;                  # Save on blending - [$/gal]

# Result
# Check whether there is loss or save
if (sv<0):
    print 'We will not save money by blending.'
else:
    print 'We will save money by blending, and save is %.3f $/gal.'%sv

We will save money by blending, and save is 0.053 $/gal.

Example 6.2 Page no. 147

In [3]:
# Variables
fd= 1000.0 ;      #feed rate-[L/hr]
cfd= 500.0;       #Weight of cells per litre- [mg/L]
dn= 1.0 ;         #Density of feed-[g/cm**3]
wp= 50.0 ;        # Weight percent of cells in product stream

# Calculation and Result
Pg=(fd*cfd*dn)/(1000*wp*.01) ;      # Mass balance for cells 
print ' Product flow(P) per hour is %.1f g'%Pg
Dg= (fd*dn*1000) - Pg*(wp*.01) ;    # Mass balance for the fluid
print '  Discharge flow per hour is %.3e g'%Dg

 Product flow(P) per hour is 1000.0 g
  Discharge flow per hour is 9.995e+05 g

Example 6.3 Page no. 154

In [4]:
dn =  0.80 ;                        #Density of motor oil-[g/cm**3]

# Calculation and Result
in_ms = (10000*(0.1337)*62.4*dn) ;  #  Initial mass of motor oil in the tank -[lb]
print ' Initial mass of motor oil in the tank is %.1f lb'%in_ms

m_fr = .0015 ;                      #Mass fractional loss
print '  Mass fractional loss is %.4f '%m_fr

Dsg = m_fr*in_ms ;                  # Mass balance for the fluid
print '  Discharge of motor oil on flushing flow for 10000 gal motor oil is %.1f lb'%Dsg

 Initial mass of motor oil in the tank is 66743.0 lb
  Mass fractional loss is 0.0015 
  Discharge of motor oil on flushing flow for 10000 gal motor oil is 100.1 lb
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