Chapter 7 : A General Strategy for Solving Material Balance Problems

Example 7.1 Page no.169

In [1]:
# Variables
v_ts = 105.0 ;          # velocity of train wrt station-[cm/s]
v_mt = 30.0 ;           # velocity of man wrt train-[cm/s]
v_hm = 2.0 ;            # velocity of hot dough wrt man-[cm/s]
v_am = 1.0 ;            # velocity of ant wrt man- [cm/s]
# By careful reading of problem you can see that ant is moving away from man's mouth at 1 cm/s , so ant's velocity wrt station 
#is say v_as

# Calculation
v_as  =  v_ts + v_mt + v_am;

# Results
print ' The ant is moving towards station at the rate of %.1f cm/s.'%v_as

 The ant is moving towards station at the rate of 136.0 cm/s.

Example 7.4 Page no. 180

In [2]:
# Variables
n_un= 7 ;            # Number of unknowns in the given problem- 3 values of xi and 4 values Fi
n_ie = 5 ;           # Number of independent equations

# Calculations
d_o_f = n_un-n_ie ;  # No. of degree of freedom

# Results
print 'Number of degree of freedom for the given system is  %i .'%d_o_f

Number of degree of freedom for the given system is  2 .

Example 7.5 Page no. 182

In [3]:
# variables
n_un=8 ;          # Number of unknowns in the given problem- 8 values of mole fractions
n_ie =6 ;         # Number of independent equations- six elemental balances 

# Calculation
d_o_f= n_un-n_ie ;# Number of degree of freedom

# Results
print 'Number of degree of freedom for the given system is %i .'%d_o_f
#Note: Experiments show that the change in CH1.8O.5N.16S.0045P.0055 and the change in C(alpha)H(beta)O(gamma) prove to be 
#related by amount of biomass present and the maintenance coefficient(the moles of substrate per mole of biomass per second) 
#so the respective quantities cannot be chosen independently.Consequently with this extra constraint,only one degree of freedom 
#remains to be specified, the basis

Number of degree of freedom for the given system is 2 .
In [ ]: