{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3 - Centrifugal Compressors & Fans"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.1 Page 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"#input data\n",
"m=10#The mass flow rate of air into compressor in kg/s\n",
"P1=1#The ambient air pressure in compressor in bar\n",
"T1=293#The ambient air temperature in compressor in K\n",
"N=20000#The running speed of the compressor in rpm\n",
"nc=0.8#The isentropic efficiency of the compressor\n",
"P02=4.5#The total exit pressure from the compressor in bar\n",
"C1=150#The air entry velocity into the impeller eye in m/s\n",
"Cx1=0#The pre whirl speed in m/s\n",
"WS=0.95#The ratio of whirl speed to tip speed\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K \n",
"R=287#The universal gas constant in J/kg.K\n",
"Dh=0.15#The eye internal diamater in m\n",
"r=1.4#Ratio of specific heats of air \n",
"d=1.189#The density of the air in kg/m**3\n",
"\n",
"#calculations\n",
"T01=T1+((C1**2)/(2*Cp))#The stagnation temperature at inlet in K\n",
"P01=P1*(T01/T1)**(r/(r-1))#The stagnation pressure at inlet in bar\n",
"T02s=(T01)*(P02/P01)**((r-1)/r)#The temperature after isentropic compression from P01 to P02 in K\n",
"T=(T02s-T01)/nc#The actual rise in total temperature in K\n",
"W=Cp*(10**-3)*(T)#The work done per unit mass in kJ/kg\n",
"U2=((W*(10**3))/(WS))**(1/2)#The impeller tip speed in m/s\n",
"Dt=(U2*60)/(3.1415*N)#The impeller tip diameter in m\n",
"P=m*W#Power required to drive the compressor in kW\n",
"d1=((P1*10**5)/(R*T1))#The density of the air entry in kg/m**3\n",
"De=(((4*m)/(d*C1*3.14))+(Dh**2))**(1/2)#The eye external diameter in m\n",
"\n",
"#output\n",
"print '(a)The actual rise in total temperature of the compressor is %3.1f K\\n(b)\\n (1)The impeller tip speed is %3.2f m/s\\n (2)The impeller tip diameter is %3.2f m\\n(c)The power required to drive the compressor is %3.1f kW\\n(d)The eye external diameter is %0.1f cm'%(T,U2,Dt,P,De*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The actual rise in total temperature of the compressor is 182.6 K\n",
"(b)\n",
" (1)The impeller tip speed is 439.55 m/s\n",
" (2)The impeller tip diameter is 0.42 m\n",
"(c)The power required to drive the compressor is 1835.4 kW\n",
"(d)The eye external diameter is 30.6 cm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.2 Page 95"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import degrees, atan\n",
"#input data\n",
"Q1=20#Discharge of air to the centrifugal compressor in m**3/s\n",
"V1=Q1#Volume of rate is equal to the discharge in m**3/s\n",
"P1=1#Initial pressure of the air to the centrifugal compressor in bar\n",
"T1=288#Initial temperature of the air to the centrifugal compressor in K\n",
"P=1.5#The pressure ratio of compression in centrifugal compressor\n",
"C1=60#The velocity of flow of air at inlet in m/s\n",
"Cr2=C1#The radial velocity of flow of air at outlet in m/s\n",
"Dh=0.6#The inlet impeller diameter in m\n",
"Dt=1.2#The outlet impeller diameter in m\n",
"N=5000#The speed of rotation of centrifugal compressor in rpm\n",
"n=1.5#polytropic index constant in the given law PV**n\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K \n",
"\n",
"#calculations\n",
"U1=(3.14*Dh*N)/60#Peripheral velocity of impeller at inlet in m/s\n",
"b11=degrees(atan(C1/U1))#The blade angle at impeller inlet in degree\n",
"U2=(3.14*Dt*N)/60#Peripheral velocity of impeller top at outlet in m/s\n",
"T2=T1*(P)**((n-1)/n)#Final temperature of the air to the centrifugal compressor in K\n",
"Cx2=((Cp*(T2-T1))/U2)#The whirl component of absolute velocity in m/s\n",
"Wx2=U2-Cx2#The exit relative velocity in m/s\n",
"a2=degrees(atan(Cr2/Cx2))#The blade angle at inlet to casing in degree\n",
"b22=degrees(atan(Cr2/Wx2))#The blade angle at impeller outlet in degree\n",
"b1=Q1/(2*3.14*(Dh/2)*C1)#The breadth of impeller blade at inlet in m \n",
"V2=(P1*V1*T2)/(T1*P*P1)#Volume flow rate of air at exit in m**3/s\n",
"Q2=V2#Volume flow rate is equal to discharge in m**3/s\n",
"b2=Q2/(2*3.14*(Dt/2)*Cr2)#The breadth of impeller blade at outlet in m\n",
"\n",
"#output\n",
"print '(a)The blade and flow angles\\n (1)The blade angle at impeller inlet is %3.1f degree\\n (2)The blade angle at inlet to casing is %3.1f degree\\n (3)The blade angle at impeller outlet is %3.2f degree\\n(b)Breadth of the impeller blade at inlet and outlet\\n (1)The breadth of impeller blade at inlet is %3.3f m\\n (2)The Volume flow rate of air at exit is %3.2f m**3/s\\n (3)The breadth of impeller blade at outlet is %3.4f m'%(b11,a2,b22,b1,V2,b2)\n",
"\n",
"\n",
"#comments\n",
"#error in the first review is not printing the value of V2 which is corrected"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The blade and flow angles\n",
" (1)The blade angle at impeller inlet is 20.9 degree\n",
" (2)The blade angle at inlet to casing is 24.2 degree\n",
" (3)The blade angle at impeller outlet is 18.38 degree\n",
"(b)Breadth of the impeller blade at inlet and outlet\n",
" (1)The breadth of impeller blade at inlet is 0.177 m\n",
" (2)The Volume flow rate of air at exit is 15.26 m**3/s\n",
" (3)The breadth of impeller blade at outlet is 0.0675 m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.3 Page 97"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"m=14#The mass flow rate of air delivered to centrifugal compressor in kg/s\n",
"P01=1#The inlet stagnation pressure in bar\n",
"T01=288#The inlet stagnation temperature in K\n",
"P=4#The stagnation pressure ratio\n",
"N=200#The speed of centrifygal compressor in rps\n",
"ss=0.9#The slip factor\n",
"ps=1.04#The power input factor\n",
"ntt=0.8#The overall isentropic efficiency\n",
"r=1.4#The ratio of specific heats of air\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"pp=ss*ps*ntt#The pressure coefficient\n",
"U2=((Cp*T01*((P**((r-1)/r))-1))/pp)**(1/2)#Peripheral velocity of impeller top at outlet in m/s\n",
"D2=U2/(3.14*N)#The overall diameter of the impeller in m\n",
"\n",
"#output\n",
"print 'The overall diameter of the impeller is %.f cm'%(D2*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The overall diameter of the impeller is 69 cm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.4 Page 98"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import cos, pi, tan\n",
"#input data\n",
"D1=0.457#Impeller diameter at inlet in m\n",
"D2=0.762#Impeller diameter at exit in m\n",
"Cr2=53.4#Radial component of velocity at impeller exit in m/s\n",
"ss=0.9#Slip factor\n",
"N=11000#Impeller speed in rpm\n",
"P2=2.23#Static pressure at impeller exit in bar\n",
"T01=288#The inlet stagnation temperature in K\n",
"P01=1.013#The inlet stagnation pressure in bar\n",
"C1=91.5#Velocity of air leaving the guide vanes in m/s\n",
"a11=70#The angle at which air leaves the guide vanes in degrees\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"Cx1=C1*cos(a11*pi/180)#Inlet absolute velocity of air in tangential direction in m/s\n",
"Ca1=Cx1*tan(a11*pi/180)#Radial component of absolute velocity at inlet in m/s\n",
"U1=(3.14*D1*N)/(60)#Peripheral velocity of impeller at inlet in m/s\n",
"Wx1=U1-Cx1#Relative whirl component of velocity at inlet in m/s\n",
"W1=((Wx1**2)+(Ca1**2))**(1/2)#Relative velocity at inlet in m/s\n",
"T1=T01-((C1**2)/(2*Cp))#The inlet air temperature in K\n",
"a1=(r*R*T1)**(1/2)#The velocity of air in m/s\n",
"M1r=W1/a1#Initial relative mach number\n",
"U2=(3.14*D2*N)/60#Peripheral velocity of impeller top at exit in m/s\n",
"W=(ss*U2**2)-(U1*Cx1)#Work done by the compressor in kJ/kg\n",
"T02=(W/Cp)+T01#The outlet stagnation temperature in K\n",
"Cx21=ss*U2#Absolute whirl component of velocity with slip consideration in m/s\n",
"C2=((Cx21**2)+(Cr2**2))**(1/2)#The absolute velocity of air at exit in m/s\n",
"T2=T02-((C2**2)/(2*Cp))#The exit temperature of air in K\n",
"P02=P2*(T02/T2)**(r/(r-1))#The exit stagnation pressure of compressor in bar\n",
"nc=(T01/(T02-T01))*(((P02/P01)**((r-1)/r))-1)#Total head isentropic efficiency\n",
"\n",
"#output\n",
"print '(1)The inlet relative mach number is %3.3f\\n(2)The impeller total head efficiency is %0.1f %%'%(M1r,nc*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1)The inlet relative mach number is 0.732\n",
"(2)The impeller total head efficiency is 90.9 %\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.5 Page 100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"N=16500#The running speed ofradial blade of a centrifugal compressor in rpm\n",
"P=4#The total pressure ratio\n",
"P01=1#The atmospheric pressure in bar\n",
"T01=298#THe atmospheric temperature in K\n",
"Dh=0.16#The hub diameter at impeller eye in m\n",
"Ca=120#The axial velocity at inlet in m/s\n",
"C1=Ca#The absolute velocity at inlet in m/s\n",
"sp=0.7#The pressure coefficient\n",
"C3=120#The absolute velocity at diffuser exit in m/s\n",
"m=8.3#The mass flow rate in kg/s\n",
"nc=0.78#The adiabatic total-to-total efficiency\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"T1=T01-((C1**2)/(2*Cp))#The inlet temperature in K\n",
"P1=P01*(T1/T01)**(r/(r-1))#The inlet pressure in bar\n",
"d1=(P1*10**5)/(R*T1)#The inlet density of air in kg/m**3\n",
"Dt=(((4*m)/(3.14*d1*Ca))+(0.16**2))**(1/2)#The eye tip diameter in m\n",
"T=((T01)*((P**((r-1)/r))-1))/nc#The overall change in temperature in K\n",
"ssps=sp/nc#The product of slip factor and power factor\n",
"U2=(T*Cp/ssps)**(1/2)#Peripheral velocity of impeller top at exit in m/s\n",
"D2=(U2*60)/(3.14*N)#The impeller tip diameter in m\n",
"Uh=(3.14*Dh*N)/60#Peripheral velocity of eye hub in m/s\n",
"bh=degrees(atan(C1/Uh))#Blade angle at eye hub in degree\n",
"Ut=(3.14*Dt*N)/60#Peripheral velocity of eye tip in m/s\n",
"bt=degrees(atan(C1/Ut))#Blade angle at eye tip in degree\n",
"T03=T01+T#Temperature at the exit in K\n",
"T3=T03-((C3**2)/(2*Cp))#Exit static temperature in K\n",
"P3=(P*P01)*(T3/T03)**(r/(r-1))#Exit static pressure in bar\n",
"W=m*Cp*(T03-T01)*10**-6#Power required to drive the compressor in mW\n",
"#output\n",
"print '(a)The main dimensions of the impeller are\\n (1)Eye tip diameter is %3.3f m\\n (2)Impeller tip diameter is %3.3f m\\n (3)Blade angle at the eye hub is %3.2f degree\\n Blade angle at the eye tip is %3.2f degree\\n(b) (1)The static exit temperature is %3.1f K\\n (2)The static exit pressure is %3.3f bar\\n(c)The power required is %3.3f mW'%(Dt,D2,bh,bt,T3,P3,W)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The main dimensions of the impeller are\n",
" (1)Eye tip diameter is 0.325 m\n",
" (2)Impeller tip diameter is 0.528 m\n",
" (3)Blade angle at the eye hub is 40.98 degree\n",
" Blade angle at the eye tip is 23.15 degree\n",
"(b) (1)The static exit temperature is 476.5 K\n",
" (2)The static exit pressure is 3.796 bar\n",
"(c)The power required is 1.549 mW\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.6 Page 102"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin\n",
"#input data\n",
"Dt=0.25#Tip diameter of the eye in m\n",
"Dh=0.1#Hub diameter of the eye in m\n",
"N=120#Speed of the compressor in rps\n",
"m=5#Mass of the air handled in kg/s\n",
"P01=102#Inlet stagnation pressure in kPa\n",
"T01=335#Inlet total temperature in K\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"d1=(P01*10**3)/(R*T01)#Density at the inlet of inducer in kg/m**3\n",
"Dm=(Dh+Dt)/2#Mean impeller diameter in m\n",
"b=(Dt-Dh)/2#Impeller blade height in m\n",
"C1=m/(d1*3.14*Dm*b)#Axial velocity component at the inlet in m/s\n",
"T11=T01-((C1**2)/(2*Cp))#Inlet temperature in K\n",
"P11=P01*(T11/T01)**(r/(r-1))#Inlet pressure in kPa\n",
"d11=(P11*10**3)/(R*T11)#Inlet density with mean impeller diameter an blade height in kg/m**3\n",
"C11=m/(d11*3.14*Dm*b)#Axial velocity component at inlet using mean blade values in m/s\n",
"T12=T01-((C1**2)/(2*Cp))#Initial temperature using modified axial velocity in K\n",
"P12=P01*(T12/T01)**(r/(r-1))#Initial pressure at inlet usin modified axial velocity in kPa\n",
"d12=(P12*10**3)/(R*T12)#Inlet density with modified axial velocity in kg/m**3\n",
"C12=m/(d12*3.14*Dm*b)#Axial velocity component at inlet using modified axial velocity in m/s\n",
"U1=3.14*Dm*N#Peripheral velocity of impeller at inlet in m/s\n",
"b1=degrees(atan(C12/U1))#The blade angle at impeller inlet in degree\n",
"W11=C12/sin(b1*pi/180)#Relative velocity at inlet in m/s\n",
"Mr11=W11/(r*R*T12)**(1/2)#Initial relative mach number\n",
"Ca=C12#Axial velocity at IGV in m/s\n",
"W12=Ca#Relative velocity at inlet usin IGV in m/s\n",
"a1=degrees(atan(Ca/U1))#Air angle at IGV exit in degree\n",
"C13=Ca/sin(a1*pi/180)#The velocity of flow of air at inlet in m/s\n",
"T13=T01-((C13**2)/(2*Cp))#Initial temperature using IGV in K\n",
"Mr12=W12/(r*R*T13)**(1/2)#Initial relative mach number using IGV \n",
"\n",
"#output5\n",
"print '(1)Without using IGV\\n (a)The air angle at inlet of inducer blade is %3.2f degree\\n (b)The inlet relative mach number is %3.3f\\n(2)With using IGV\\n (a))The air angle at inlet of inducer blade is %3.2f degree\\n (b)The inlet relative mach number is %3.3f'%(b1,Mr11,a1,Mr12)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1)Without using IGV\n",
" (a)The air angle at inlet of inducer blade is 61.23 degree\n",
" (b)The inlet relative mach number is 0.377\n",
"(2)With using IGV\n",
" (a))The air angle at inlet of inducer blade is 61.23 degree\n",
" (b)The inlet relative mach number is 0.332\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.7 Page 105"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Cr2=28#Radial component of velocity at impeller exit in m/s\n",
"ss=0.9#The slip factor\n",
"U2=350#The impeller tip speed in m/s\n",
"A=0.08#The impeller area in m**2\n",
"nc=0.9#Total head isentropic efficiency\n",
"T01=288#The ambient air temperature in K\n",
"P01=1#The ambient air pressure in bar\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"Cx2=ss*U2#outlet absolute velocity of air in tangential direction in m/s\n",
"C2=((Cx2**2)+(Cr2**2))**(1/2)#Axial velocity component at the outlet in m/s\n",
"T=(ss*(U2**2))/Cp#Total change in temperature in K\n",
"T02=T+T01#The final ambient air temperature in K\n",
"T2=T02-((C2**2)/(2*Cp))#The actual final air temperature in K\n",
"M2=(C2)/(r*R*T2)**(1/2)#Exit absolute mach number\n",
"P=((1+(ss*T/T01))**(r/(r-1)))#The overall pressure ratio\n",
"P02=P*P01#The final ambient pressure in bar\n",
"P2=P02*(T2/T02)**(r/(r-1))#The absolute final pressure in bar\n",
"d2=(P2*10**5)/(R*T2)#The final density of air at exit in kg/m**3\n",
"m=d2*A*Cr2#The mass flow rate in kg/s\n",
"\n",
"#output\n",
"print '(a)The exit absolute mach number is %3.4f\\n(b)The mass flow rate is %3.4f kg/s'%(M2,m)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The exit absolute mach number is 0.8458\n",
"(b)The mass flow rate is 3.9423 kg/s\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.8 Page 107"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"Dh=0.175#Hub diameter of the eye in m\n",
"Dt=0.3125#Tip diameter of the eye in m\n",
"m=20#Mass of the air handled in kg/s\n",
"N=16000#Speed of the compressor in rpm\n",
"T01=288#The ambient air temperature in K\n",
"P01=100#The ambient air pressure in kPa\n",
"Ca=152#The axial component of inlet velocity of eye in m/s\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"\n",
"#calculations\n",
"A=(3.14/4)*((Dt**2)-(Dh**2))#Annulus area of flow at the impeller eye in m**2\n",
"Ut=(3.1415*Dt*N)/60#Impeller eye tip speed in m/s\n",
"Uh=(3.1415*Dh*N)/60#Impeller eye hub speed in m/s\n",
"a1=90-20#Blade angle at inlet in degree \n",
"C1=Ca/sin(a1*pi/180)#The air entry velocity into the impeller eye in m/s\n",
"T1=T01-((C1**2)/(2*Cp))#The actual inlet air temperature in K\n",
"P1=P01*(T1/T01)**(r/(r-1))#The actual inlet air pressure in kPa\n",
"d1=P1/(R*T1)#The initial density of air at entry in kg/m**3\n",
"b1h=degrees(atan(Ca/(Uh-(Ca/tan(a1*pi/180)))))#Impeller angle at the hub in degree\n",
"b1t=degrees(atan(Ca/(Ut-(Ca/tan(a1*pi/180)))))#Impeller angle at the tip of eye in degree\n",
"Cx1=Ca/tan(a1*pi/180)#Inlet absolute velocity of air in tangential direction in m/s\n",
"Wx1=Ut-Cx1#Relative whirl component of velocity at inlet in m/s\n",
"W1=((Wx1**2)+(Ca**2))**(1/2)#Relative velocity at inlet in m/s\n",
"Mr1=W1/(r*R*T1)**(1/2)#Maximum mach number at the eye\n",
"\n",
"#output\n",
"print '(a)\\n (1)The impeller eye tip speed is %3.2f m/s\\n (2)The impeller eye hub speed is %3.2f m/s\\n (3)The impeller angle at the hub is %i degree\\n (4)Impeller angle at the tip of eye is %3.2f degree\\n(b)The maximum mach number at the eye is %3.2f'%(Ut,Uh,b1h,b1t,Mr1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)\n",
" (1)The impeller eye tip speed is 261.79 m/s\n",
" (2)The impeller eye hub speed is 146.60 m/s\n",
" (3)The impeller angle at the hub is 59 degree\n",
" (4)Impeller angle at the tip of eye is 36.36 degree\n",
"(b)The maximum mach number at the eye is 0.77\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.9 Page 109"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"P1=100#The air in take pressure in kPa\n",
"T1=309#The air in take temperature in K\n",
"H=0.750#Pressure head developed in mm W.G\n",
"P=33#Input power to blower in kW\n",
"nb=0.79#Blower efficiency\n",
"nm=0.83#Mechanical efficiency\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"d=(P1*10**3)/(R*T1)#Density of air flow at inlet in kg/m**3\n",
"dP=dw*g*H#Total change in pressure in N/m**2\n",
"IW=dP/d#Ideal work done in J/kg\n",
"Wm=IW/nb#Actual work done per unit mass flow rate in J/kg\n",
"W=P*nm#Actual power input in kW\n",
"m=(W*10**3)/Wm#Mass flow rate in kg/s\n",
"Q=m/d#Volume flow rate in m**3/s\n",
"P2=P1+(dP/10**3)#The exit pressure of air in kPa\n",
"T2=T1+(Wm/(Cp))#The exit temperature of air in K\n",
"\n",
"#output\n",
"print '(a)The mass flow rate of air is %3.3f kg/s\\n(b)The volume flow rate of air is %3.2f m**3/s\\n(c)\\n (1)The exit pressure of air is %3.2f kPa\\n (2)The exit temperature of air is %3.2f K'%(m,Q,P2,T2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The mass flow rate of air is 3.316 kg/s\n",
"(b)The volume flow rate of air is 2.94 m**3/s\n",
"(c)\n",
" (1)The exit pressure of air is 107.36 kPa\n",
" (2)The exit temperature of air is 317.22 K\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.10 Page 110"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=0.075#Pressure developed by a fan in m W.G\n",
"D2=0.89#The impeller diameter in m\n",
"N=720#The running speed of the fan in rpm\n",
"b22=39#The blade air angle at the tip in degree\n",
"b2=0.1#The width of the impeller in m\n",
"Cr=9.15#The constant radial velocity in m/s\n",
"d=1.2#Density of air in kg/m**3\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"IW=(dw*g*H)/d#Ideal work done in J/kg\n",
"U2=(3.1415*D2*N)/60#The impeller tip speed in m/s\n",
"Wx2=Cr/tan(b22*pi/180)#Relative whirl component of velocity at outlet in m/s\n",
"Cx2=U2-(Wx2)#Outlet absolute velocity of air in tangential direction in m/s\n",
"Wm=U2*Cx2#Actual work done per unit mass flow rate in J/kg\n",
"nf=IW/Wm#Fan efficiency\n",
"Q=3.1415*D2*b2*Cr#The discharge of the air by fan in m**3/s\n",
"m=d*Q#Mass flow rate of the air by the fan in kg/s\n",
"W=m*Wm*10**-3#Power required to drive the fan in kW\n",
"R=1-(Cx2/(2*U2))#Stage reaction of the fan\n",
"sp=2*Cx2/U2#The pressure coefficient\n",
"\n",
"#output\n",
"print '(a)The fan efficiency is %0.1f %%\\n(b)The Discharge of air by the fan is %3.3f m**3/s\\n(c)The power required to drive the fan is %3.4f kW\\n(d)The stage reaction of the fan is %0.2f %%\\n(e)The pressure coefficient of the fan is %3.3f'%(nf*100,Q,W,R*100,sp)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The fan efficiency is 82.1 %\n",
"(b)The Discharge of air by the fan is 2.558 m**3/s\n",
"(c)The power required to drive the fan is 2.2919 kW\n",
"(d)The stage reaction of the fan is 66.84 %\n",
"(e)The pressure coefficient of the fan is 1.326\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.11 Page 111"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"\n",
"b22=30#The blade air angle at the tip in degrees\n",
"D2=0.466#The impeller diameter in m\n",
"Q=3.82#The discharge of the air by fan in m**3/s\n",
"m=4.29#Mass flow rate of the air by the fan in kg/s\n",
"H=0.063#Pressure developed by a fan in m W.G\n",
"pi2=0.25#Flow coefficient at impeller exit\n",
"W=3#Power supplied to the impeller in kW\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1005#The specific heat of air at constant pressure in J/kg.K\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=10**3#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"IW=Q*dw*g*H*(10**-3)#Ideal work done in kW\n",
"nf=IW/W#Fan efficiency\n",
"U2=(((W*10**3)/m)/(1-(pi2/tan(b22*pi/180))))**(1/2)#The impeller tip speed in m/s\n",
"Cr2=pi2*U2#The radial velocity at exit in m/s\n",
"Cx2=U2-(Cr2/tan(b22*pi/180))#Outlet absolute velocity of air in tangential direction in m/s\n",
"sp=2*Cx2/U2#Presuure coefficient of the fan\n",
"R=1-(Cx2/(2*U2))#Degree of reaction of the fan\n",
"N=(U2*60)/(3.141592*D2)#Rotational speed of the fan in rpm\n",
"b2=Q/(3.14*D2*Cr2)#Impeller width at the exit in m\n",
"\n",
"#output\n",
"print '(a)The fan efficiency is %0.1f %%\\n(b)The pressure coefficient is %3.3f\\n(c)The degree of reaction of the fan is %0.1f %%\\n(d)The rotational speed of the fan is %3.1f rpm\\n(e)The impeller width at exit is %0.1f cm'%(nf*100,sp,R*100,N,b2*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The fan efficiency is 78.7 %\n",
"(b)The pressure coefficient is 1.134\n",
"(c)The degree of reaction of the fan is 71.7 %\n",
"(d)The rotational speed of the fan is 1439.3 rpm\n",
"(e)The impeller width at exit is 29.7 cm\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.12 Page 113"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"N=3000#The running speed of the blower in rpm\n",
"D2=0.75#The impeller diameter in m\n",
"Cr2=57#The radial velocity at exit in m/s\n",
"Cx1=0#Inlet absolute velocity of air in tangential direction in m/s\n",
"DR=0.58#Degree of reaction of the blower\n",
"nc=0.75#Total-to-total efficiency\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1.005#The specific heat of air at constant pressure in J/kg.K\n",
"T01=298#The inlet stagnation temperature in K\n",
"P01=1*101.325#The inlet stagnation pressure in kPa\n",
"\n",
"#calculations\n",
"U2=(3.1415*D2*N)/60#The impeller tip speed in m/s\n",
"Cx2=2*(1-DR)*U2#Outlet absolute velocity of air in tangential direction in m/s\n",
"Wx2=U2-Cx2#Relative whirl component of velocity at outlet in m/s\n",
"b22=degrees(atan(Cr2/Wx2))#The blade air angle at the tip in degree\n",
"Wm=U2*Cx2*10**-3#Actual work done per unit mass flow rate when Cx1=0 in kW/(kg/s)\n",
"T=Wm/Cp#Total change in temperature in blower in K\n",
"P=(1+(nc*(T/T01)))**(r/(r-1))#Total pressure ratio in the blower\n",
"P02=P*P01#The outlet stagnation pressure from blower in kPa\n",
"\n",
"#output\n",
"print '(a)The exit blade angle is %3.1f degree\\n(b)The power input to the blower is %3.3f kW/(kg/s)\\n(c)The exit stagnation pressure is %3.2f kPa'%(b22,Wm,P02)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The exit blade angle is 71.7 degree\n",
"(b)The power input to the blower is 11.658 kW/(kg/s)\n",
"(c)The exit stagnation pressure is 112.06 kPa\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.13 Page 114"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D1=0.18#The impeller inner diameter in m\n",
"D2=0.2#The impeller outer diameter in m\n",
"C1=21#The absolute velocity at the entry in m/s\n",
"C2=25#The absolute velocity at the exit in m/s\n",
"W1=20#The relative velocity at the entry in m/s\n",
"W2=17#The relative velocity at the exit in m/s\n",
"N=1450#The running speed of the fan in rpm\n",
"m=0.5#The mass flow rate of the air in fan in kg/s\n",
"nm=0.78#The motor efficiency of the fan \n",
"d=1.25#The density of the air in kg/m**3\n",
"r=1.4#The ratio of specific heats of air\n",
"R=287#The universal gas constant in J/kg.K\n",
"Cp=1.005#The specific heat of air at constant pressure in J/kg.K\n",
"\n",
"#calculations\n",
"U1=(3.14*D1*N)/60#Peripheral velocity of impeller at inlet in m/s\n",
"U2=(3.14*D2*N)/60#The impeller tip speed in m/s\n",
"dH=(((U2**2)-(U1**2))/2)+(((W1**2)-(W2**2))/2)#The actual total rise in enthalpy in kJ/kg\n",
"dH0=dH+(((C2**2)-(C1**2))/2)#The stage total isentropic rise in enthalpy in kJ/kg\n",
"dP0=d*dH0#The stage total pressure rise in N/m**2\n",
"dP=d*dH#The actual total rise in pressure in N/m**2\n",
"R=dP/dP0#The degree of reaction of the fan\n",
"W=m*(dH0)#The work done by the fan per second in W\n",
"P=W/nm#The power input to the fan in W\n",
"\n",
"#output\n",
"print '(a)The stage total pressure rise is %3.1f N/m**2\\n(b)The degree of reaction of the fan is %3.3f\\n(c)The power input to the fan is %3.1f W'%(dP0,R,P)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The stage total pressure rise is 211.7 N/m**2\n",
"(b)The degree of reaction of the fan is 0.457\n",
"(c)The power input to the fan is 108.6 W\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 3.14 Page 116"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"dH=0.14#Rise in static pressure of the air by fan in m of water\n",
"N=650#The running speed of the fan in rpm\n",
"P=85*0.735#Power consumed by the fan in kW\n",
"H1=0.75#The static pressure of the air at the fan in m of Hg\n",
"T1=298#The static pressure at the fan of air in K\n",
"m=260#Mass flow rate of air in kg/min\n",
"dHg=13590#Density of mercury in kg/m**3\n",
"dw=1000#Density of water in kg/m**3\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"R=287#The universal gas constant in J/kg.K\n",
"\n",
"#calculations\n",
"P1=dHg*g*H1*10**-3#The inlet static pressure in kPa\n",
"dP=dw*g*dH*10**-3#The total change in static pressures at inlet and outlet in kPa\n",
"P2=P1+dP#The exit static pressure in kPa\n",
"d1=(P1*10**3)/(R*T1)#The inlet density of the air in kg/m**3\n",
"Q=m/d1#The volume flow rate of air in fan in m**3/min\n",
"\n",
"#output\n",
"print '(a)The exit static pressure of air in the fan is %3.2f kPa\\n(b)The volume flow rate of the air is %3.1f m**3/min'%(P2,Q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The exit static pressure of air in the fan is 101.36 kPa\n",
"(b)The volume flow rate of the air is 222.4 m**3/min\n"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}