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Chapter 12 :  Pneumatic Conveying

example 12.1 page no : 240¶

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import math
from numpy import *

# Initialization of Variable
rho = 1.22
pi = 3.1428
rhos = 518.
rhoav = 321.
mu = 1.73/10**5
g = 9.81
d = 0.65/1000
d2 = 25.5/100           #dia of duct
ms = 22.7/60            #mass flow rate

#calculation
e = (rhos-rhoav)/(rhos-rho)
#coeff of quadratic eqn in U
#a*x**2+b*x+c = 0
c = -(1-e)*(rhos-rho)*g
b = 150.*(1-e)**2*mu/d**2/e**3
a = 1.75*(1.-e)*rho/d/e**3
y = poly1d([a,b,c],False)
U = roots(y)
Us = ms*4/pi/d2**2/rhos         #superficial speed
Ua = e/e*(U/e+Us/(1-e))
print "the actual linear flow rate through duct in (m/s): %.4f"%Ua
the actual linear flow rate through duct in (m/s): 0.2059

example 12.2 page no : 243¶

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import math

# Initialization of Variable
rho = 1.22          #density of air
pi = 3.1428
rhos = 910.         #density of polyethene
d = 3.4/1000.       #dia of particles
mu = 1.73/10**5.
g = 9.81
dt = 3.54/100.      #dia of duct

#calculation
a = 2.*d**3*rho*g*(rhos-rho)/3/mu**2
print "R/rho/U**2*(Re**2) = %.4f"%a

#using Chart
Re = 2.*10**3
U = mu*Re/d/rho
b = U/(g*dt)**.5
if b>0.35:
print "choking can occur of this pipe system"
else:
print "choking can not occur of this pipe system"

#part 2
Uc = 15.            #actual gas velocity
e = ((Uc-U)**2/2./g/dt/100.+1)**(1./-4.7)
Usc = (Uc-U)*(1-e)      #superficial speed of solid
Cmax = Usc*rhos*pi*dt**2./4
print "the maximum carrying capacity of polythene particles in (kg/s) %.4f"%Cmax
R/rho/U**2*(Re**2) = 952227.8618
choking can occur of this pipe system
the maximum carrying capacity of polythene particles in (kg/s) 0.5949

example 12.3 page no : 245¶

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import math

# Initialization of Variable
rho = 1.22              #density of air
pi = 3.1428
rhos = 1400.            #density of coal
mu = 1.73/10**5.
g = 9.81
U = 25.
Ut = 2.80
l = 50.
ms = 1.2                #mass flow rate
mg = ms/10.             #mass flow of gas

#calculation
Qs = ms/rhos            #flow of solid
Qg = mg/rho             #flow of gas
us = U-Ut               #actual linear velocity
A = Qg/U
Us = Qs/A               #solid velocity
e = (us-Us)/us
d = math.sqrt(4*A/pi)
def fround(x,n):
# fround(x,n)
# Round the floating point numbers x to n decimal places
# x may be a vector or matrix# n is the integer number of places to round to
y = round(x*10**n)/10.**n
return y

d = fround(d,4)
Re = d*rho*U/mu

#using moody's chart
phi = 2.1/1000          #friction factor
P1 = 2*phi*U**2*l*rho/d*2
f = 0.05/us
P2 = 2*l*f*(0.0098)*rhos*us**2/d
P2 = fround(P2/1000,1)*1000
delP = rho*e*U**2+rhos*(0.0098)*us**2+P1+P2
#print (delP,"the pressure difference in kN/m**2 ")
print 'The Pressure value in kN/m**2 is %.1f'%(delP/1000)
The Pressure value in kN/m**2 is 33.5

example 12.4 page no : 250¶

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import math

# Initialization of Variable
rho = 1.22          #density of air
pi = 3.1428
rhos = 1090.        #density of steel
mu = 1.73/10.**5
g = 9.81
d = 14.5/100.
Qg = 0.4
Qs = 5000./3600./1090.
Ut = 6.5
ar = 0.046/1000     #absolute roughness
l = 18.5            #length

#calculation
def fround(x,n):
# fround(x,n)
# Round the floating point numbers x to n decimal places
# x may be a vector or matrix# n is the integer number of places to round to
y = round(x*10**n)/10**n
return y

Us = Qs/pi/d**2*4       #solid velocity
U = Qg/pi/d**2*4
us = U-Ut               #actual linear velocity
e = 1-Us/us
e = fround(e,4)
Re = rho*U*d/mu
rr = ar/d               #relative roughness

#using moody's diagram
phi = 2.08/1000
P1 = 2*phi*U**2*l*rho/d*2
f = 0.05/us
P2 = 2*l*f*(1-e)*rhos*us**2/d
P2 = fround(P2/1000,2)*1000
delP = rhos*(1-e)*us**2+rhos*(1-e)*g*l+P1+P2
#print (delP,"the pressure difference in kN/m**2 ")
print 'The Pressure value in kN/m**2 is %.2f'%(delP/1000)
The Pressure value in kN/m**2 is 4.21

example 12.5 pageno :254¶

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import math

# Initialization of Variable
l = 25.
pi = 3.1428
rhos = 2690.        #density of ore
emin = 0.6
emax = 0.8
g = 9.81

#calculation
Pmax = rhos*(1-emin)*g*l
print "The maximum pressure drop in (N/m**2):",Pmax
Pmin = rhos*(1-emax)*g*l
print "The minimum pressure drop in (N/m**2):",Pmin
The maximum pressure drop in (N/m**2): 263889.0
The minimum pressure drop in (N/m**2): 131944.5
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