import math
T2 = 488.0
T1 = 298.0
n = 1.3
R =8314.0/44.0
rp = (T2/T1)**(n/(n-1))
b = 0.12 # Bore of compressor
L = 0.15 # Stroke of compressor
V1 = (math.pi/4)*(b)**2*L
P1 = 120e03 # in kPa
W = ((n*P1*V1)/(n-1))*(((rp)**((n-1)/n))-1)
P = (W*1200*0.001)/60
V1_dot = V1*(1200.0/60.0)
m_dot = (P1*V1_dot)/(R*T1)
rp_1 = rp**2
V2 = (1/rp)**(1/n)*V1
d = math.sqrt((V2*4)/(L*math.pi))
print "\n Example 19.1\n"
print "\n Pressure ratio is ",rp
print "\n Indicated power is ",P ," kW"
print "\n Shaft power is ",P/0.8 ," kW"
print "\n Mass flow rate is ",m_dot ," kg/s"
print "\n Pressure ratio when second stage is added is ",rp_1
print "\n Volume derived per cycle is V2 ",V2 ," m**3"
print "\n Second stage bore would be ",d*1000 ," mm"
#The answers vary due to round off error
import math
c = 0.05 # Clearance volume
p1 = 96.0 # Inlet ressure in bar
p2 = 725.0 # Outlet pressure in bar
pa = 101.3 # Atmospheric pressure
Ta = 292.0 # Atmospheric temperature in kelvin
T1 = 305.0 # Inlet temperature in Kelvin
n = 1.3 # polytropic index
print "\n Example 19.2 \n "
n_v = (1+c-c*((p2/p1)**(1/n)))*(p1/pa)*(Ta/T1)
print "\n Volumetric efficiency of system is ",n_v*100 ," percent"
# Answer is not mentioned in book
import math
P1 = 101.3e03
P4 = P1 # in Pa
P2 = 8*P1
P3 = P2
T1 = 288
Vs = 2000
V3 = 100
Vc = V3
V1 = Vs + Vc
n = 1.25
R = 287
V4 = ((P3/P4)**(1/n))*V3
W = ((n*P1*(V1-V4)*1e-06)/(n-1))*(((P2/P1)**((n-1)/n))-1)
P = (W*800*0.001)/60
m = (P1*(V1-V4)*1e-06)/(R*T1)
m_dot = m*800
FAD = (V1-V4)*1e-06*800
Wt = P1*(V1-V4)*1e-06*math.log(P2/P1)
n_isothermal = (Wt*800*0.001)/(P*60)
Pi = P/0.85
n_v =100*(V1-V4)/Vs
print "\n Example 19.3\n"
print "\n Indicated poer is ",P ," kW"
print "\n Volumetric efficiency is ",n_v ," percent"
print "\n Mass flow rate is ",m_dot ," kg/min"
print "\n Free air delivery is ",FAD ," m**3/min"
print "\n Isothermal efficiency is ",100*n_isothermal ," percent"
print "\n Input power is ",Pi ," kW"
#The answers vary due to round off error
import math
# Given that
m = 3.0 # Mass flow rate in kg/min
p1 = 1.0 # Initial pressure in bar
T1 = 300.0 # Initial temperature in K
p3 = 6.0 # Pressure after compression in bar
p5 = 15.0 # Maximum pressure in bar
N = 300.0 # Rpm of compressure
n = 1.3 # Index of compression and expansion
r = 1.5 # Stroke to bore ratio
R = 287.0 # Gas constant of air
t = 15.0 # Temperature in degree centigrade
print "\n Example 19.4\n"
T = t+273
Wc = (n/(n-1))*(m/60)*(R*(1e-3)*T1)*(((p3/p1)**((n-1)/n))-1)
r1 = (p5/p1)**(1.0/n)# Where r1 = V1/Vc
r2 = r1-1 # Where r2 = Vs/Vc
r3 = (p3/p1)**(1.0/n)
n_vol = (r1-r3)*(T/T1)/r2
V = m*R*T/(2*(1e5)*N)
Vs = V/n_vol
d = (Vs*4/(math.pi*r))**(1.0/3.0)
l = r*d
print "\n Power input is ",Wc ," kW, \n Volumetric efficiency is ",n_vol*100 ," percent, \n Bore of the cylinder is ",d ," m, \n Stroke of the cylinder is ",l ," m"
#The answers vary due to round off error
import math
# Given that
d = 15.0 # Diameter in cm
l = 18.0 # Stroke in cm
C = 0.04 # Ratio of clearance volume and sweft volume
p1 = 1.0 # Pressure in bar
t1 = 25.0 # Temperature in degree centigrade
p2 = 8.0# Pressure in bar
N = 1200.0 # Rpm of compressure
W = 18.0 # Actual power input in kW
m = 4.0 # Mass flow rate in kg/min
R = 0.287
print "\n Example 19.5\n"
T1 = t1+273
v = R*T1/(p1*100)
V = m*v
Vs = (math.pi/4)*((d*(1e-2))**2)*(l*1e-2)*N
n_vol = V/Vs
n = (math.log(p2/p1))/(math.log((1+C-n_vol)/C))
# The value of n given in the example is wrong
n = 1.573
T2 = T1*(p2/p1)**((n-1)/n)
Wc = (n/(n-1))*(m*R/60)*(T2-T1)
n_mech = Wc/W
W_isothermal = m*R*T1*math.log(p2/p1)/60
n_iso = W_isothermal/W
print "\n Power required to drive the unit is ",Wc ," kW,\n Isothermal efficiency is ",n_iso*100 ," percent,\n Mechanical efficiency is ",n_mech*100 ," percent"
#The answers vary due to round off error
import math
# Given that
d = 40.0 # Diameter in cm
l = 50.0 # Stroke in cm
D = 5.0 # Piston rod diameter in cm
C = 0.04 # Ratio of clearance volume and sweft volume
p1 = 1.0 # Pressure in bar
t1 = 15.0 # Temperature in degree centigrade
p2 = 7.5# Pressure in bar
N = 300.0 # Rpm of compressure
n_vol = 0.8 # Volumetric efficiency
n_mech = 0.95 # Mechanical efficiency
n_iso = .7 # Isothermal efficiency
R = 0.287
print "\n Example 19.6\n"
Vs = (math.pi/4)*((d*(1e-2))**2)*(l*(1e-2))
Vs_ = (math.pi/4)*(((d*(1e-2))**2)-(D*(1e-2))**2)*(l*1e-2)
Vs_min = (Vs+Vs_)*2*N
V1 = Vs_min*n_vol
W_iso = p1*V1*(math.log(p2/p1))
Win = W_iso/n_iso
Wc = Win/n_mech
print "\n Power required to drive the compressure is ",Wc ," kW"
#The answers vary due to round off error
import math
# Given that
p1 = 1.0 # Pressure in bar
t1 = 27.0 # Temperature in degree centigrade
n = 1.3 # Index of the compression process
p3 = 9.0# Pressure in bar
R = 0.287
print "\n Example 19.7\n"
T1 = t1+273
p2 = math.sqrt(p1*p3)
Wc = ((2*n*R*T1)/(n-1))*(((p2/p1)**((n-1)/n))-1)
T2 = T1*((p2/p1)**((n-1)/n))
H = 1.005*(T2-T1)
print "\n Minimum work done is ",Wc ," kJ/kg,\n Heat rejected to intercooler is ",H ," kJ/kg"
#The answers vary due to round off error
import math
# Given that
V = 4.0 # Volume flow rate in m**3/min
p1 = 1.013 # Pressure in bar
t1 = 15.0 # Temperature in degree centigrade
N = 250.0 # Speed in RPM
p4 = 80.0# Delivery pressure in bar
v = 3.0 #Speed of piston in m/sec
n_mech = .75 # Mechanical efficiency
n_vol = .8 # Volumetric efficiency
n = 1.25 # Polytropic index
print "\n Example 19.8\n"
T1 = t1+273
p2 = math.sqrt(p1*p4)
W = (2*n/(n-1))*(p1*100/n_mech)*(V/60)*((p2/p1)**((n-1)/n) - 1)
L = v*60/(N*2)
Vs = V/N
D_LP = math.sqrt(Vs*V/(math.pi*L*n_vol))
D_HP = D_LP*math.sqrt(p1/p2)
print "\n Minimum power required by the compressure is ",W ," kW,\n Bore of the compressure in low pressure side is ",D_LP*100 ," cm,\n Bore of the compressure in high pressure side is ",D_HP*100 ," cm,\n Stroke of the compressure is ",L*100 ," cm"
#The answers vary due to round off error
import math
# Given that
p1 = 1.0 # Pressure in bar
T1 = 300.0 # Temperature in K
p4 = 9.0# Compressed pressure in bar
n = 1.3 # Polytropic index
R = 0.287 # Gas constant in kJ/kgK
cp = 1.042 # Heat capapcity in kJ/kgK
print "\n Example 19.9\n"
p2 = math.sqrt(p1*p4)
T2 =T1*((p2/p1)**((n-1)/n))
Wc = (2*n/(n-1))*R*1*(T2-T1)
Wc_ = Wc/2
Q = 1*cp*(T2-T1)
Q_ = cp*(T1-T2)+Wc_
H = Q+2*Q_
print "\n Compressor work = ",Wc_ ," kJ/kg,\n Total heat transfer to the surrounding = ",H ," kJ/kg"
#The answers given in the book contain calculation error
import math
# Given that
N = 300.0 # Speed in RPM
# Intake condition of compressor
p1 = 0.98 # Pressure in bar
T1 = 305.0 # Temperature in K
p6 = 20.0# Delivery pressure in bar
p3 = 5.0 # Intermediate pressure in bar
C = .04 # Ratio of clearance volume to the stroke volume
v = 3.0 # Volume flow rate of compressure in m**3/min
p = 1.0 # pressure in bar
t = 25.0 # Temperautre in degree centigrade
n = 1.3 # Polytropic index
R = 0.287 # Gas constant in kJ/kgK
print "\n Example 19.10\n"
T = t+273
r0 = 1+C # Where r0 = v1/vs
r1 = C*(p3/p1)**(1/n)# Where r1 = v4/vs
r2=r0-r1#Where r2 is the ratio of volume of air taken at 0.98 bar,305 k and vs
r3 = r2*(T/T1)*p1/p # Where r3 is the ratio of volume of air taken at free air conditions and vs
n_vol = r3
m = p*(1e5)*(v/60)/(R*1000*T)
T2 = T1*((p3/p1)**((n-1)/n))
# For perfect intercooling
T5 = T1
p5 = p3
T6 = T5*((p6/p5)**((n-1)/n))
Wc = (n/(n-1))*m*R*((T2-T1)+(T6-T5))
m_a_s = m*60/N
v_fa_s = m_a_s *(R*1000)*T/(p*1e5)
d = ((v_fa_s/n_vol)*(4/math.pi))**(1.0/3.0)
l = d # As given in the question
P_iso = m*R*T1*(math.log(p6/p1))
n_iso = P_iso/Wc
print "\n Diameter of cylinder = ",Wc,d*100 ," cm, \n Storke of the cylinder = ",l*100 ," cm,\n Isothermal efficiency = ",n_iso*100 ," percent"
#The answers given in the book contain calculation error
import math
# Given that
p1 = 1 # Intake pressure of compressor in bar
T1 = 298 # Intake temperature in K
p_d = 36 # Delivery pressure in bar
T2 = 390 # Maximum temperature in any stage in K
n = 1.3 # Polytropic index
R = 0.287
print "\n Example 19.11\n"
r = (T2/T1)**(n/(n-1))
N = math. ceil(r)
p2 = (p_d/p1)**(1/N)
p3 = (p_d/p1)**(2/N)
p4 = (p_d/p1)**(3/N)
Wc = (N*n*R*T1/(n-1))*((p_d/p1)**((n-1)/(N*n))-1)
Wc_ = (n/(n-1))*(1*R*T1)*((p_d/p1)**((n-1)/n)- 1)
T = T1*((p2/p1)**((n-1)/n))
print "\n No of stages for min power input = ",N ,",\n Power required = ",Wc ," kW/kg air,\n The power required for a single stage compressor = ",Wc_ ," kW,\n Maximum temperature in any stage = ",T ," K"
#The answers given in the book contain round off error
import math
# Given that
p1 = 700.0 # Intake pressure of compressor in kPa
t1 = 38.0 # Intake temperature in degree centigrade
c = 0.4 # Ratio of cutoff volume to stroke volume
p3 = 112.0 # Back pressure in kPa
r = 0.85 # Ratio of area of actual indicator diagram to the outlined in the question
n = 1.3 # Polytropic index
R = 0.287
m = 1.25 # Air mass in kg
print "\n Example 19.12\n"
T1 = t1+273
T2 = T1/((1/c)**(n-1))
p2 = p1*(c**n)
V2 = m*R*T2/p2
v2 = V2/m
A = R*T1 + R*(T1-T2)/(n-1) - p3*v2
Io = A*r*m
print "\n Indicated output = ",Io ," kJ"
# The answer given in the book vary due to round off error
import math
# Given that
d = 450.0 # Bore of low pressure cylinder in mm
l = 300.0 # Stroke in mm
c = 0.05 # Ratio of clearance volume to sweft volume
p1 = 1.0 # Intake pressure in bar
t1 = 18.0 # Intake temperature in degree centigrade
p4 = 15.0 # Delivery pressure in bar
n = 1.3 # Compression and expansion index
R = 0.29 # Gas constant in kJ/kgK
print "\n Example 19.13\n"
T1 = t1+273
r = (p4/p1)**(1.0/3.0)
p2 = p1*r
p3 = p2*r
Vs = (math.pi/4)*((d*1e-3)**2)*(l*1e-3)
V11 = c*Vs
V1 = Vs +V11
V12 = V11*((r)**(1.0/n))
Vs_e = V1 - V12
T3 = T1
T5 = T3
T6 = T1*(r**((n-1)/n))
t6 = T6-273
V6_7 = (p1/p4)*(T6/T1)*(V1 - V12)
W = (3*n*R*T1/(n-1))*((p2/p1)**((n-1)/n)-1)
print "\n The intermediate pressure are - \n p2 = ",p2 ," bar,\n p3 = ",p3 ," bar,\n The effective sweft volume = ",Vs ," m**3,\n Temperature of air delivered per stroke at 15 bar = ",t6 ," degree centigrade,\n The work done per kg of air = ",W ," kJ"
# The answers given in the book vary due to round off error
import math
# Given that
p1 = 1.013 # Inlet pressure in bar
r = 1.5 # Pressure ratio
Vs = 0.03 # Induce volume of air in m**3/rev
gama = 1.4
print "\n Example 19.14\n"
p2 = p1*r
W = (p2-p1)*Vs*100
pi = (p1+p2)/2
A_A = (gama/(gama-1))*(p1*Vs)*((pi/p1)**((gama-1)/gama)-1)*100
Vb = Vs *((p1/pi)**(1/gama))
A_B = (p2-pi)*Vb*100
Wr = A_A + A_B
print "\n Work input = ",W ," kJ/rev,\n Work input for a vane-type compressor = ",Wr ," kJ/rev"
# The answers given in the book vary due to round off error
import math
# Given that
m = 1.0 # Mass flow rate in kg/s
r = 2.0 # Prssure ratio of blower
t1 = 70.0 # Inlet temperature in degree centigrade
p1 = 1.0 # Inlet pressure in bar
R = 0.29 # Gas constant in kJ/kgK
x = 0.7 # Reduction in pressure ratio and intake volume
gama = 1.4
print "\n Example 19.15\n"
T1 = t1+273
V = m*R*T1/(p1*100)
P = V*(p1*r-p1)*100
p2 = p1*((1/x)**(gama))
V2 = x*V
P_ = (gama/(gama-1))*(p1*100*V)*((p2/p1)**((gama-1)/gama)-1) + V2*(p1*r-p2)*100
print "\n Power required to drive the blower = ",P ," kW,\n Power required = ",P_ ," kW"
# The answers given in the book vary due to round off error
import math
# Given that
r1 = 2.5 # Pressure ratio of compressor for first stage
r2 = 2.1 # Pressure ratio of compressor for second stage
m = 5.0 # Mass flow rate of air in kg/s
t1 = 10.0 # Inlet temperature in degree centigrade
p1 = 1.013 # Inlet pressure in bar
td = 50.0 # Temperature drop in intercooler in degree centigreade
n_iso = .85 # Isentropic efficiency
cp = 1.005 # Heat capacity of air in kJ/kgK
x = 0.7 # Reduction in pressure ratio and intake volume
gama = 1.4 # Ratio of heat capacities for air
print "\n Example 19.16\n"
T1 = t1+273
T2s = T1*((r1)**((gama-1)/gama))
T2 = T1 + (T2s-T1)/n_iso
T3 = T2 - td
T4s = T3*((r2)**((gama-1)/gama))
T4 = T3 + (T4s-T3)/n_iso
P = m*cp*((T2-T1)+(T4-T3))
print "\n Actual temperature at the end of first stage = ",T2 ," K,\n Actual temperature at the end of second stage = ",T4 ," K,\n The total compressor power = ",P ," kW"
# The answers given in the book vary due to round off error
import math
# Given that
r = 2.5 # Static pressure ratio of supercharger
p1 = 0.6 # Static inlet pressure in bar
t1 = 5 # Static inlet temperature in degree centigrade
A_r = 13.0 # Air-fuel ratio
m = 0.04 # The rate of fuel consumed by the engine in kg/s
gama= 1.39 # For air-fuel mixture
cp = 1.005 # Heat capacity for air-fuel mixture in kJ/kgk
n_iso = .84 # Isentropic efficiency of compressor
v = 120.0 # Exit velocity from the compressor in m/s
print "\n Example 19.17\n"
T1 = t1+273
T2s = T1*((r)**((gama-1)/gama))
T2 = T1 +(T2s-T1)/n_iso
m_g = m*(A_r+1)
P = m_g*cp*(T2-T1)
T02 = T2 + (v**2)/(2*cp*1000)
t02 = T02-273
p02 = p1*r*((T02/T2)**(gama/(gama-1)))*100
print "\n Power required to drive the compressor = ",P ," kW,\n Stagnatio temperature = ",t02 ," degree centigrade,\n Stagnation pressure = ",p02 ," kPa"
# The answers given in the book vary due to round off error
import math
# Given that
N = 10000 # Speed in RPM
V = 1.2 # Volume flow rate of free air in m**3/s
p1 = 1.0 # Inlet pressure in bar
t1 = 27.0 # Inlet temperature in degree centigrade
r = 5.0 # Pressure ratio
vf = 60.0 # Velocity flow rate in m/s
sigma = 0.9 # Slip factor
n_iso = 0.85 # Isentropic efficiency
gama = 1.4
R = 0.287
cp = 1.005
print "\n Example 19.18\n"
T1 = t1+273
T2s = T1*((r)**((gama-1)/gama))
T2 = T1 +(T2s-T1)/n_iso
m = p1*100*V/(R*288)
Wc = m*cp*(T2-T1)
Vb2 = (Wc*1000/(m*sigma))**(1.0/2.0)
D = Vb2*60/(math.pi*N)
Vb1 = Vb2/2
beta1 = math.atan(vf/Vb1)
alpha = math.atan(vf/(sigma*Vb2))
print "\n The temperature of air at outlet = ",T2-273 ," degree centigrade,\n Power input = ",Wc ," kW,\n Diameter of impeller = ",D ," m, \n Blade inlet angle = ",beta1 ," degree,\n Diffuser inlet angle = ",alpha ," degree "
# The answers given in the book vary due to round off error
import math
# Given that
N = 264 # Speed in RPS
sigma = 0.91 # Slip factor
d = 0.482 # Impeller diameter in m
D = 0.306 # Impeller eye diameter
D_ = 0.153 # Impeller root eye diameter in m
vf = 138 # Uniform axial inlet velocity in m/s
V = 1.2 # Volume flow rate of free air in m**3/s
m = 9.1 # Air mass flow rate in kg/s
T1 = 294 # Inlet air stagnation temperature in K
n_iso = 0.8 # Total head isentropic efficiency
n_mech = 0.98 # Mechanical efficiency
gama = 1.4 # Ratio of heat capacities
cp = 1.006 # Heat capacity in kJ/kgK
print "\n Example 19.19\n"
Wc = m*sigma*(2*math.pi*d*N/2)/1000
P_e = Wc/n_mech
delta_T = Wc/(m*cp)
delta_T_ideal = delta_T*n_iso
T2_i = delta_T_ideal + T1
r = (T2_i/T1)**(gama/(gama-1)) # Where r = p02/p01
Vb = 2*math.pi*N*D/2
V_er = (2*math.pi*N*D_/2)
beta1 = math.atan(vf/Vb)
beta2 = math.atan(vf/V_er)
beta1_ = (beta1 - math.floor(beta1))*60
beta2_ = (beta2 - math.floor(beta2))*60
print "\n Total head pressure ratio = ",r ,", \n The required power at input shaft = ",P_e ," kW,\n Inlet angle at the root = ",math.floor(beta1) ," degree and ",beta1_ ," minute,\n Inlet angle at the tip = ",math.floor(beta2) ," degree and ",beta2_ ," minute"
# The answers given in the book for total head pressure ratio and required power at input shaft contain calculation error
import math
# Given that
N = 16000.0 # Speed in RPM
t1 = 17.0 # Intake temperture of gas in degree centigrade
rp = 4.0 # Pressure ratio
sigma = 0.85# Slip factor
n_iso = 0.82 # Isentropic efficiency
alpha_wirl = 20.0 # Pre-wirl angle in degree
d1 = 200.0 # Mean diameter of impeller eye in mm
V1 = 120.0 #Absolute air velocity in m/s
gama = 1.4 # Ratio of heat capacities
cp = 1.005 # Heat capacity in kJ/kgK
print "\n Example 19.20\n"
T1 = t1 + 273
T2s = T1*((rp)**((gama-1)/gama))
delta_Ts = T2s-1
delta_T = delta_Ts/n_iso
Wc = 1 *cp*delta_T
Vb1 = (math.pi*d1*(1e-3)*N)/60
Vw1 = V1*math.sin(alpha_wirl)
Vb2 = 459.78 # By solving quadratic equation 172.81e3=0.85*Vb2**2-167.55*41.05
d2 = Vb2*60/(math.pi*N)
print "\n Impeller tip diameter = ",d2*1000 ," mm"
# The answer given in the book varies due to round off error
import math
# Given that
m = 2.5 # Mass flow rate in kg/s
p1 = 1.0 # Inlet pressure in bar
T1 = 300.0 # Inlet temperature in bar
n_s = 0.88 # Stage efficiency
Wc = 600.0 # Power input in kW
delta_t = 21.0 # Temperature rise in first stage in degree centigrade
gama = 1.4 # Ratio of heat capacities
cp = 1.005 # Heat capacity in kJ/kgK
print "\n Example 19.21\n"
x = n_s*gama/(gama-1)# Where x = (n/(n-1))
T = Wc/(m*cp)+T1
p = p1*((T/T1)**(x))
T2 = T1 + n_s*delta_t
r = ((T2/T1)**(gama/(gama-1)))# Where r = p2/p1
N = math.log(p/p1)/math.log(r)
N_ = math. ceil(N)
Ts = T1*(p/p1)**((gama-1)/gama)
n_inter = (Ts-T1)/(T-T1)
print "\n The delivery pressure = ",p ," bar,\n The no of stages = ",N_ ,",\n The internal efficiency = ",n_inter ," "
import math
# Given that
D = 0.5 # Mean diameter of impeller in m
N = 15000.0 # Speed in RPM
Vf = 230.0 # Velocity of flow in m/s
p1 = 1.0 # Inlet pressure in bar
T1 = 300.0 # Inlet temperature in K
Vw1 = 80.0 # Velocity of whirl at inlet in m/s
n_s = 0.88 # Stage efficiency
rp = 1.5 # Pressure ratio
gama = 1.4
cp = 1.0005
print "\n Example 19.22\n"
Vb = (math.pi*D*N/60)
Ts = T1*((rp)**((gama-1)/gama))
T = T1 + (Ts-T1)/n_s
Wc = cp*(T-T1)
Vw2 = Vw1 + (Wc*1000)/(Vb)
beta1 = math.atan(Vf/(Vb-Vw1))
beta2 = math.atan(Vf/(Vb-Vw2))
theta = beta2-beta1
R = 1-((Vw1+Vw2)/(2*Vb))
print "\n Fluid deflection angle = ",theta ," degree,\n Power input = ",Wc ," kJ/kg,\n The degree of reaction = ",R*100 ," percent"
# The answers given in the book vary because of round off error
import math
# Given that
v = 5.0 #olume flow rate in m**3/s
d = 1.0 #ean impeller diameter in m
D = 0.6 # Hub diameter in m
N = 600.0 #otational speed in RPM
h = 35.0 #heoratical head in mm
rho = 1.2 # Density of air in kg/m**3
rho_w = 1000.0 #ensity of water in kg/m**3
print "\n Example 19.23\n"
Vf = v*4/(math.pi*(d**2 - D**2))
Vb = (math.pi*d*N/60)
Vb_ = (math.pi*D*N/60)
H = h/rho
Vw2 = H*9.81/(Vb)
Vw2_ = H*9.81/(Vb_)
beta_tip = (Vf/(Vb_-Vw2))
beta_hub = (Vf/(Vb_-Vw2_))
print "\n Blade angle at the tip = ",beta_tip ," degree,\n Blade angle at the hub = ",beta_hub ," degree"
# The answers given in the book vary because of round off error
import math
# Given that
N0 = 9000.0 # Rotational speed in RPM
Q = 6.0 # Volume flow rate in m**3/s
p1 = 1.0 # Initial pressure in bar
t1 = 25.0 # Initial temperature in degree centigrade
p2 = 2.2 # Compressed pressure in bar
n = 1.33 # Compression index
Vf = 75.0 # Velocity of flow in m/s
beta1 = 30.0 # Blade angle at inlet in degree
beta2 = 55.0 # Blade angle at outlet in degree
d = 0.75 # Diameter of impeller in m
cp = 1.005
print "\n Example 19.24\n"
T1 = t1+273
T2 = T1*(p2/p1)**((n-1)/n)
Wc = cp*(T2-T1)
x = Wc # Where x = Vw2*Vb2
y = Vf/math.tan(beta2)# Where y = Vb2-Vw2(Equation 1)
z = (y**2 +4*x*1000)**(0.5) # Where z = Vw2+Vb2(Equation 2)
# By solving Equation 1 and Equation 2
Vb2 = (y+z)/2
Vw2 = ((z-y)/2)
N = Vb2*60/(math.pi*d)
Vb1 = Vf/math.tan(beta1)
D1 = Vb1*60/(math.pi*N)
b1 = Q/(math.pi*D1*Vf)
Q_ = Q* (1/p2)*(T2/T1)
b2 = Q_/(math.pi*d*Vf)
print "\n Speed of impeller = ",N ," RPM,\n Impeller width at inlet = ",b1*100 ," cm,\n Impeller width at outlet = ",b2*100 ," cm,"
# The answers given in the book vary because of round off error