# Chapter 13 : The Dispersion ,Wodel¶

## Example 13.1 page no : 305¶

In [1]:
import math

# Variables
T = [0,5,10,15,20,25,30,35];       # time
Cpulse = [0,3,5,5,4,2,1,0];        # gm/liter
sum1 = 0;
sum2 = 0
sum3 = 0;

# Calculations
for i in range(8):
sum1 = sum1+Cpulse[i];
sum2 = sum2+Cpulse[i]*T[i];
sum3 = sum3+Cpulse[i]*T[i]*T[i];

t = sum2/sum1;
sigma_sqr = (sum3/sum1)-((sum2/sum1))**2;
sigmatheta_sqr = sigma_sqr/t**2;
m = 0.1

while m <= 0.2:
sigmat_sqr = 2*m-2*(m**2)*(1-math.exp(-(1./m)));
if sigmat_sqr >=  sigmatheta_sqr:
break;
m += 0.001

# Results
print " The vessel print ersion number is %.3f"%(m)

# answer may vary because of rounding error.

 The vessel print ersion number is 0.100


### Example 13.2 pageno : 306¶

In [3]:
# Variables
l = 1219.;             # long diameter
u = 0.0067;            #Velocity(mm/s)

#Using the probability graph
t1 = 178550.
#84th percentile point fall at
t2 = 187750.;

# Calculations
sigma = (t2-t1)/2;
t = l/u;
sigma_theta = sigma/t;
#Vessel print ersion number
d = sigma_theta**2/2;

# Results
print " The vessel print ersion number is %.5f"%(d)

 The vessel print ersion number is 0.00032


## Example 13.3 page no : 308¶

In [5]:
# Variables
v = 0.4;                # bed voidage
u = 1.2;                # velocity of fluid
l = 90.                 #length(cm)
sigma1_sqr = 39.        # output signals
sigma2_sqr = 64.        # output signals

# Calculations
dsigma_sqr = sigma2_sqr-sigma1_sqr;
t = l*v/u;
sigmatheta_sqr = dsigma_sqr/t**2;
d = sigmatheta_sqr/2;

# Results
print " The vessel print ersion number is %.4f"%(d)

 The vessel print ersion number is 0.0139

In [ ]: