rhog=5.51; #Density of gas in kg/m**3
rhos=1200; #Density of solid in kg/m**3
dpbar=130; #Average size of particles in micrometer
uo=0.61; #Superficial gas velocity in m/s
g=9.80; #Acceleration due to gravity in m/s**2
#CALCULATION
#Assuming that freeboard in higher than TDH, computation of entrainment rate by Zenz & Weil's method
x=(uo**2)/(g*(dpbar*10**-6)*rhos**2);#Calculation of value of x-axis for Fig.(6), page 175
y=1.2; # Value of y-axis from Fig.(6)
Gsstar=y*rhog*uo; #Computation of rate of entrainment
#OUTPUT
print '\nRate of entrainment=%.2fkg/m**2s'%Gsstar
x=0.2; #Fraction of fines in the bed
Gsstar=4.033320 #Rate of entrainment in kg/m**2s(from Exa.1)
#CALCULATION
Gsstar1=x*Gsstar;#Rate of entrainment by Eqn.(3)
#OUTPUT
print '\nRate of entrainment=%.3fkg/m**2s'%Gsstar1
rhog=5.51; #Density of gas in kg/m**3
rhos=1200; #Density of solid in kg/m**3
uo=0.61; #Superficial gas velocity in m/s
g=9.80; #Acceleration due to gravity in m/s**2
dp=[10,30,50,70,90,110,130]; #Diameter of particle in micrometer
p=[0.,0.0110,0.0179,0.0130,0.0058,0.0020,0.];
pi=3.142857;
dt=6;
#CALCULATION
n=len(dp);
i=0;
x = [0,0,0,0,0,0,0]
while i<n:
x[i]=(uo**2)/(g*(dp[i]*10**-6)*rhos**2);#Computation of value of x-axis for Fig.(6), page 175)
i=i+1;
y=[40,12,6,3.2,2.,1.3,1];#Value of y-axis corresponding to each value of x-axis
y1 = []
for i in range(n):
y1.append(y[i]*p[i]);
i=0;
k=0;
while i<n-2:
y1[i]=(y[i]*p[i]);
k=k+((0.5)*(dp[i+1]-dp[i])*(y1[i+1]+y1[i]));#Integration using Trapezoidal rule
i=i+1;
rhosbar=k*rhog;#Computation of solid loading
te=(pi/4)*(dt**2)*rhosbar*uo;#Computation of total entrainment
#OUTPUT
print '\nSolid loading =%.1fkg/m**3'%rhosbar
print '\nTotal Entrainment =%.0fkg/s'%te
dp=[40,60,80,100,120]; #Diameter of particle in micrometer
uo=0.381; #Superficial gas velocity in m/s
#CALCULATION
Gs=0.9;#Rate of entrainment in kg/m**2 s from Fig.3(a)
pb = [0.45,1.00,1.25,1.00,0.60];#Size distribution for bed particles from Fig.3(b)
pe=[1.20,2.00,1.25,0.45,0.10]; #Size distribution for entrained particles from Fig.3(b)
n=len(dp);
for i in range(n):
pb[i] = pb[i]/100.
pe[i] = pe[i]/100.
i=0;
ki = []
while i<n:
ki.append((Gs*pe[i])/pb[i]);#Calculation of ki* using Eqn.(13)
i=i+1;
#OUTPUT
print '\ndpi(micrometer)',
print '\t100pb(dpi)(micrometer**-1)',
print '\t100pe(dpi)(micrometer**-1)',
print '\tki*(kg/m**2 s)'
j=0;
while j<n:
print '%f'%dp[j],
print '\t%f'%(100*pb[j]),
print '\t\t\t%f'%(100*pe[j]),
print '\t\t\t%f'%ki[j]
j=j+1;
import math
#Variable declaration
rhog=1.217; #Density of gas in kg/m**3
myu=1.8E-5; #Viscosity of gas in kg/m s
umf=0.11; #Velocity at minimum fluidization condition in m/s
rhos=2000.0; #Density of solid in kg/m**3
uo=1.0; #Superficial gas velocity in m/s
g=9.80; #Acceleration due to gravity in m/s**2
dp=[30,40,50,60,80,100,120]; #Diameter of particle in micrometer
uti=[0.066,0.115,0.175,0.240,0.385,0.555,1.0];#Terminal velocity of particles in m/s
#CALCULATION
n=len(dp);
i=0;
Ret = []
kistar1 = []
kistar2 = []
kistar3 = []
kistar4 = []
kistar5 = []
kistar6 = []
x1 = []
x2 = []
while i<n:
#Using Yagi & Aochi's correlation
Ret.append((rhog*(uti[i])*dp[i]*10**-6)/myu)
a =((myu*((uo-uti[i])**2))/(g*(dp[i]*10**-6)**2))*(0.0015*(Ret[i]**0.5)+(0.01*(Ret[i]**1.2)));
kistar1.append(a)
#Using Wen & Hasinger's correlation
a=(((1.52E-5)*((uo-uti[i])**2)*rhog)/(g*dp[i]*10**-6)**0.5)*(Ret[i]**0.725)*((rhos-rhog)/rhog)**1.15;
kistar2.append(a)
#Using Merrick & Highley's correlation
a=uo*rhog*(0.0001+130*math.exp(-10.4*((uti[i]/uo)**0.5)*((umf/(uo-umf))**0.25)));
kistar3.append(a)
#Using Geldart's correlation
a=23.7*uo*rhog*math.exp(-5.4*(uti[i]/uo));
kistar4.append(a)
#Using Zenz & Weil's procedure
a=(uo**2)/(g*(dp[i]*10.0**-6)*rhos**2);#Computation of value of x-axis for Fig.(6), page 175)
x1.append(a)
y1=[12.2,8.6,6.4,4.9,2.75,1.8,1.2];#Value of y-axis corresponding to each value of x-axis
kistar5.append(y1[i]*rhog*uo)
#Using Gugnoni & Zenz's procedure
a=(uo-uti[i])/((g*dp[i]*10**-6)**0.5);#Computation of value of x-axis for Fig.(6), page 175)
x2.append(a)
y=[5.8,5.4,3.2,2.8,1.3,0.6,0];#Value of y-axis corresponding to each value of x-axis
kistar6.append(y[i]*rhog*uo)
i=i+1;
i=0;
print 'dp(micrometer)',
print '\tYagi & Aochi',
print '\tWen & Hashinger',
print '\t\tMerrick & Highley',
print '\tGeldart et al.',
print '\t\tZenz & Well',
print '\t\tGugnoni & Zenz'
while i<n:
print '\n%f'%dp[i],
print '\t%f'%kistar1[i],
print '\t%f'%kistar2[i],
print '\t\t%f'%kistar3[i],
print '\t\t%f'%kistar4[i],
print '\t\t%f'%kistar5[i],
print '\t\t%f'%kistar6[i],
i=i+1;
#Note: There is huge deviation of the calculated answer and the answer given in the textbook for the correlation of Merrick & Highley. There is a contradiction in the correlation used in the problem and the one given in page 179.
#We tried to retrieve the original paper i.e. D.Merrick and J.Highley, AICHE J., 6, 220(1960). But the effort was not fruitful.
import math
#Variable declaration
dpbar=60.0; #Average size of particles in micrometer
rhog=1.3; #Density of gas in kg/m**3
rhos=1500.0; #Density of solid in kg/m**3
umf=0.003; #Velocity at minimum fluidization condition in m/s
uo=0.503; #Superficial gas velocity in m/s
g=9.80; #Acceleration due to gravity in m/s**2
Hf=2.0; #Height at which the cyclone inlet is to be located in m
#CALCULATION
y=(uo**2)/(g*(dpbar*10**-3)*rhos**2);#Calculation of value of y-axis for Fig.(6), page 175
x=1;#Value of x-axis from Fig.(6), page 175
Gsstar=x*rhog*uo;#Computation of rate of entrainment
Gsuo=5.0;#Ejection rate pf particles in kg/m**2 s from Fig.(11), page 188
a=0.72/uo;#From Fig.(12), page 189
Gs=Gsstar+(Gsuo-Gsstar)*math.exp(-a*Hf);
p=((Gs-Gsstar)/Gsstar)*100.0;
#OUTPUT
print '\nRate of entrainment from short bed=%.3fkg/m**2s'%Gs
print '\nThis entrainment is %f percent higher than it would be if the gas exit were at the TDH'%p