weight = [0,60,150,270,330,360.0]; # Weight in grams for the oversized particles
psize = [50,75,100,125,150,175]; #PSD in micrometers
#CALCULATION
l = len(psize); # To obtain the size of input array
# Computation of sauter mean diameter for the given PSD
i = 0;
dpi = [0,0,0,0,0,0]
weightf = [0,0,0,0,0,0]
dp = [0,0,0,0,0,0]
while i<l-1:
dpi[i]=(psize[i]+ psize[i+1])/2.0;
weightf[i]=(weight[i+1]-weight[i])/weight[5];
dp[i]=weightf[i]/float(dpi[i]);
i=i+1;
dpbar=1/sum(dp); #Calculation of average particle daimeter Eq.(15)
#OUTPUT
print '\n The Sauter mean diameter of the material with the given particle size distribution = %.0f micrometer'%dpbar
#Estimation of Minimum fluidizing velocity
#INPUT
ephsilon=0.55; #Void fraction of bed
rhog=0.0012; #Density of gas in g/cc
myu=.00018; #Viscosity of gas in g/cm s
dpbar=0.016; #Mean diameter of solids in centimeter
phis=0.67; #Sphericity of solids
rhos=2.6; #Density of solids in g/cc
g=980; #Acceleration due to gravity in square cm/s**2
#CALCULATION
#Computation of umf using the simplified equation for small particles
umf=((dpbar**2)*(rhos-rhog)*g*(ephsilon**3)*(phis**2))/(150*myu*(1-ephsilon));#Simplified equation to calculate minimum fluidizing velocity
#for small particles Eq.(21)
Re=(dpbar*umf*rhog)/myu;#To calculate Reynolds number for particle
#Computation of umf if neither void fraction of bed nor sphericity is known
c1=28.7
c2=0.0494; #Value of constants from Table 4, page 70
umf1=(myu/(dpbar*rhog))*(((c1**2)+((c2*(dpbar**3)*rhog*(rhos-rhog)*g)/(myu**2)))**0.5-c1); #Equation to calculate minimum fluidizing velocity
#for coarse particles Eq.(25)
err=((umf-umf1)/umf)*100; #Calculation of error from experimental value
#OUTPUT
if Re<20:
print 'The particle Reynolds no = %f'%Re
print 'The simplified equation used for calculating minimum fluidizing velocity is valid.'
print 'The minimum fluidizing velocity by simplified equation for small particles = %.2fcm/s'%umf
print 'The minimum fluidizing velocity by equation for coarse partilces = %.2fcm/s'%umf1
print 'This value is %d percent below the experimentally reported value.'%err
rhog=1.2e-3; #Density of air in g/cc
myu=1.8e-4 #Viscosity of air in g/cm s
dpbar=0.016 #Mean diameter of solids in centimeter
phis=0.67; #Sphericity of solids
rhos=2.6; #Density of solids in g/cc
g=980 #Acceleration due to gravity in square cm/s**2
#CALCULATION
dpstar=dpbar*((rhog*(rhos-rhog)*g)/myu**2)**(1/3.0); #Calculation of dimensionless particle size Eq.(31)
utstar=((18/(dpstar**2))+(2.335-(1.744*phis))/(dpstar**0.5))**-1; #Calculation of dimensionless gas velocity Eq.(33)
ut=utstar*((myu*(rhos-rhog)*g)/rhog**2)**(1/3.0); #Calculation of terminal velocity of falling particles Eq.(32)
#OUTPUT
print 'The dimensionless particle size = %.2f'%dpstar
print 'The dimensionless gas velocity = %.3f'%utstar
print 'The terminal velocity of falling particles = %d cm/s'%ut
rhos=1.5; #Density of Solid in g/cc
uo1=40; uo2=80; #Superficial gas velocity in cm/s
dp1=0.006; dp2=0.045; #Particle size in centimeter
rhog1=1.5E-3; rhog2=1E-3; #Density of gas in g/cc
myu1=2E-4; myu2=2.5E-4; #Viscosity of air in g/cm s
g=980; #Acceleration due to gravity in square cm/s**2
#CALCULATION
#for smaller particles
dpstar1=dp1*((rhog1*(rhos-rhog1)*g)/myu1**2)**(1/3.0); #Calculation of dimensionless particle diamter Eq.(31)
uostar1=uo1*((rhog1**2)/((myu1)*(rhos-rhog1)*g))**(1/3.0);
uostar2=uo2*((rhog1**2)/((myu1)*(rhos-rhog1)*g))**(1/3.0); #Calculation of dimensionless superficial gas velocity Eq.(32)
#for larger particles
dpstar2=dp2*((rhog2*(rhos-rhog2)*g)/myu2**2)**(1/3.0); #Calculation of dimensionless particle diamter Eq.(31)
uostar3=uo1*((rhog2**2)/((myu2)*(rhos-rhog2)*g))**(1/3.0);
uostar4=uo2*((rhog2**2)/((myu2)*(rhos-rhog2)*g))**(1/3.0); #Calculation of dimensionless superficial gas velocity Eq.(32)
#OUTPUT
print 'For particle of size %.3f centimeter'%dp1
print 'The dimensionless particle diameter = %.2f'%dpstar1
print 'The dimensionless superficial gas velocity = %.4fcm/s(for superficial gas velocity of %dcm/s)'%(uostar1,uo1)
print 'The dimensionless superficial gas velocity = %.3fcm/s(for superficial gas velocity of %dcm/s)'%(uostar2,uo2)
print 'From Fig.16(page 89)comparing u*=%.4f vs dp*=%.2f'%(uostar1,dpstar1)
print 'For Superficial gas velocity =%d Mode of Fluidization:Onset of turbulent fluidization in an ordinary bubbling bed'%(uo1)
print 'From Fig.16(page 89)comparing u* =%.3f vs dp* =%f'%(uostar2,dpstar1)
print 'For Superficial gas velocity =%f Mode of Fluidization:Fast fluidization(requires a circulating solid system)'%(uo2)
print 'For particle of size %f centimeter'%(dp2)
print 'The dimensionless particle diameter = %f'%(dpstar2)
print 'The dimensionless superficial gas velocity = %fcm/s(for superficial gas velocity of %fcm/s)'%(uostar3,uo1)
print 'The dimensionless superficial gas velocity = %fcm/s(for superficial gas velocity of %fcm/s)'%(uostar4,uo2)
print 'From Fig.16(page 89)comparing u*=%f vs dp*=%f'%(uostar3,dpstar2)
print 'For Superficial gas velocity =%f Mode of Fluidization:Bublling Fluidization'%(uo1)
print 'From Fig.16(page 89)comparing u* =%f vs dp* =%f'%(uostar4,dpstar2)
print 'For Superficial gas velocity =%f Mode of Fluidization:Bubbling Fluidization'%(uo2)