# Chapter 19 : Mixing¶

### Example 19.1 page no : 563¶

In [1]:
#Calculate the time required for mixing

# variables
L=10**(-6)                             #m
D=1.2*10**(-9)                         #m**2/s

# calculation
t=2*L**2/D                             #s

# result
print "The time required for mixing is %f seconds"%t

The time required for mixing is 0.001667 seconds


### Example 19.2 page no : 567¶

In [2]:
#Calculate the power required to run an impeller

# variables
D_tank=3.                        #ft
D_impeller=D_tank/3              #ft
N=4.                             #rps
v=1.077*10**(-5)                 #ft**2/s

# calculation
R_impeller=N*D_impeller**2       #dimentionless (reynold's number)
#1 lbf.s**2 = 32.2 lbm.ft
#1 hp.s = 550 lbf.ft
rho_water=62.3                   #lbm/ft**3
P=5*rho_water*N**3*D_impeller**5/32.2/550.0         #hp

# result
print "The power required to run an impeller is %.2f hp"%P

The power required to run an impeller is 1.13 hp


### Example 19.3 page no : 567¶

In [4]:
#Calculate the impeller speed in a model of a large mixer if the power per unit volume remains the same

# variables
#let D1/D2 be denoted by ratio_D
ratio_D=5.                     #dimentionless
N2=240.                        #rpm

# calculation
N1=N2/ratio_D**(2/3.)          #rpm

# result
print "the impeller speed in a model of a large mixer if the power per unit volume remains the same is %d rpm"%N1

the impeller speed in a model of a large mixer if the power per unit volume remains the same is 82 rpm


### Example 19.4 page no : 569¶

In [5]:
#Calculate the time required to blend two miscible, low viscosity liquids

# variables
D_tank=3.                        #ft
D_impeller=D_tank/3              #ft
H_tank=D_tank                    #ft
N=4.0                            #rps

# calculation
t_blend=4.3*(D_tank/H_tank)*(D_tank/D_impeller)**2/N       #s

# result
print "the time required to blend two miscible, low viscosity liquids is %.1f s"%t_blend

the time required to blend two miscible, low viscosity liquids is 9.7 s


### Example 19.5 page no : 570¶

In [1]:
#Calculate how far is the concentration of 0.1% from initial interface and the volume mixed

# variables
c=0.1                         #percent
c_interface=50.               #percent
c_original=0.                 #percent
ratio_c=(c-c_interface)/(c_original-c_interface)              #dimentionless

# calculations
#erf(0.998)=2.15
#time required forfluid to travel 700 miles at 8ft/s is 4.57*10**5 sec
t=4.57*10**5                  #s
D=2*10**(-9)                  #m**2/s
x=2*2.15*(D*t)**0.5           #m
print "x=%.2f m"%x
v0=0.355                      #ft**3 of liquid/ft of pipe
#1 m = 3.281 ft
V_mixed=2*(3.281*x)*v0        #ft**3

# result
print "The mixed volume is %.2f ft**3"%V_mixed

x=0.13 m
The mixed volume is 0.30 ft**3


### Example 19.6 page no : 571¶

In [2]:
#Calculate how far is the concentration of 0.1% from initial interface and the volume mixed

# variables
v=8.                                   #ft/s
f=0.0039                               #dimentionless (fanning friction factor)
D_turbulent=0.665*v*3.57*(f)**0.5      #ft**2/s

# calculation
#time required forfluid to travel 700 miles at 8ft/s is 4.57*10**5 sec
t=4.57*10**5                           #s
x=2*2.15*(D_turbulent*t)**0.5          #ft
print "x=%f m"%x
v0=0.355                               #ft**3 of liquid/ft of pipe
V_mixed=2*x*v0                         #ft**3

# result
print "The mixed volume is %f ft**3"%V_mixed

x=3165.793854 m
The mixed volume is 2247.713636 ft**3


### Example 19.7 page no : 572¶

In [8]:
#Calculate how far downstream does the dye become uniformly distributed throughout the fluid

# variables
f=0.0039             #dimentionless (fanning friction factor)
D=0.665              #ft

# calculation
L=D*0.56/(f)**0.5    #ft

# result
print "L = %.0f ft"%L

L = 6 ft


### Example 19.8 page no : 573¶

In [3]:
#Calculate the width of jet and entrainment ratio
import math

# variables
Vo=40.                      #ft/s
Do=1.                       #ft
x=10.                       #ft
K=6.2                       #dimentionless

# calculation
V_centerline=Vo*K*(Do/x)    #ft/s
alpha=20.                   #degrees
Dx=Do*(1+(x/Do)*math.sin(alpha*math.pi/180.0))        #ft

#Let entrainment ratio be r
r=0.62*(x/Do)**0.5#dimentionless

# result
print "The jet diameter is %.2f ft\n"%Dx
print "The entrainment ratio is %.2f"%r

The jet diameter is 4.42 ft

The entrainment ratio is 1.96


### Example 19.9 page no : 577¶

In [4]:
#Calculate the SO2 concentration at the centerline
import math

# variables
Q=20.                        #gm/s
u=3.                         #m/s
sigma_y=30.0                 #m
sigma_z=20.0                 #m
y=60.                        #m
z=20.                        #m
H=0.                         #m

# calculation
c=Q/(2.0*math.pi*u*sigma_y*sigma_z)*math.exp(-((y**2/2.0/sigma_y**2)+((z-H)**2/2.0/sigma_z**2)))#gm/m**3

# result
print "The SO2 concentration at the centerline is %f gm/m**3"%c

The SO2 concentration at the centerline is 0.000145 gm/m**3