# Chapter 13 : Non newtonian fluid flow in circular pipes¶

### Example 13.1 page no : 432¶

In [1]:
#Calculate the pressure gradient
import math

# variables
v=1.                          #ft/s
d=0.5                         #ft

# calculation
A=(math.pi)/4*d**2            #ft**2
Q=v*A                         #ft**3/s
#Let DP denote the pressure gradient
n=0.41                        #dimentionless
K=0.66                        #kg/m/s
#1 m = 3.281 ft
Q1=Q/3.281**3                 #m**3/s
d1=d/3.281                    #m
DP=(Q1*8*(3*n+1)/(n*(math.pi)*d1**3))**n*(4*K/d1)         #Pa/m

# result
print "The pressure gradient is %f Pa/m"%DP

The pressure gradient is 61.241859 Pa/m


### Example 13.3 page no : 437¶

In [2]:
#Calculate the fanning friction factor and reynolds number by power law

# variables
DP=61.3                      #Pa/m (pressure gradient)
D=0.152                      #m
V_avg=0.305                  #m/s
rho=1000.                    #kg/m**3

# calculation
f=DP*D/(4*rho*V_avg**2/2.)    #dimentionless
print "The fanning friction factor is %f"%f
n=0.41                       #dimentionless
K=0.66                       #dimentionless
R_pl=8*rho*V_avg**(2-n)*D**n/(K*(2*(3*n+1)/n)**n)                   #dimentionless

# result
print "The reynolds number is %f"%R_pl
if (R_pl<2000):
print "The flow is Laminar"
else:
print "The flow is turbulent"

The fanning friction factor is 0.050081
The reynolds number is 318.531771
The flow is Laminar


### Example 13.4 page no : 438¶

In [1]:
#Calculate the pressure gradient

# variables
D=0.152                                #m
V_avg=3.04                             #m/s
rho=1000.                              #kg/m**3
n=0.41                                 #dimentionless
K=0.66                                 #dimentionless

# calculation
R_pl=8*rho*V_avg**(2-n)*D**n/(K*(2*(3*n+1)/n)**n)                     #dimentionless
#print "The reynolds number is %f"%R_pl
f=0.004                                #dimentionless (fanning friction factor)
#Let DP denote the pressure gradient
DP=4*f*(rho/D)*(V_avg**2/2)/1000       #KPa/m

# result
print "The pressure gradient is %f KPa/m"%DP

The pressure gradient is 0.486400 KPa/m


### Example 13.5 page no : 440¶

In [4]:
#Calculate the headstrom ,reynold numbers and the fanning friction factor

# variables
tow_yield=3.8                      #Pa
mew=0.00686                        #Pa.s
D=0.0206                           #m
rho=1530.0                         #kg/m**3
V=3.47                             #m/s

# calculation and Result
He=tow_yield*D**2*rho/mew**2       #dimentionless (headstrom number)
print "The headstrom number is %f"%He
R=D*V*rho/mew                      #dimentionless (reynolds number)
print "The reynolds number is %f"%R
dP=11069.                          #Pa/m
f=dP*D/(4*rho*V**2/2)              #dimentionless (fanning friction factor)
print "The fanning friction factor is %f"%f

The headstrom number is 52427.752042
The reynolds number is 15942.778426
The fanning friction factor is 0.006189