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"source": [
"# Chapter 8 - Steam Nozzles and Turbines"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 - pg 8.47"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Final velocity of steam is (m/s) = 596.97\n",
"(b)Percentage reduction in velocity is (percent) = 7.87\n"
]
}
],
"source": [
"#calculate the Final velocity and percentage reduction in velocity\n",
"#Input data\n",
"P1=12.;#Pressure of Dry saturated steam entering a steam nozzle in bar\n",
"P2=1.5;#Discharge pressure of Dry saturated steam in bar\n",
"f=0.95;#Dryness fraction of the discharged steam\n",
"l=12.;#Heat drop lost in friction in percentage\n",
"hg1=2784.8;#Specific enthalpy of steam at 12 bar from steam tables in kJ/kg\n",
"hg2=2582.3;#Specific enthalpy of 0.95 dry steam at 1.5 bar from steam tables in kJ/kg\n",
"\n",
"#Calculations\n",
"hd=hg1-hg2;#Heat drop in kJ/kg\n",
"V1=44.72*(hd)**(0.5);#Velocity of steam at discharge from the nozzle in m/s\n",
"n=1-(l/100.);#Nozzle coefficient when 12 percent heat drop is lost in friction\n",
"V2=44.72*(n*hd)**(0.5);#Velocity of steam in m/s\n",
"percentV=((V2-550.)/V2)*100;#Percentage reduction in velocity\n",
"#Output\n",
"print '(a)Final velocity of steam is (m/s) = ',round(V2,2)\n",
"print '(b)Percentage reduction in velocity is (percent) = ',round(percentV,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 - pg 8.48"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Velocity (m/s) = 886.98\n",
"The mass of steam discharged,when the exit diameter of the nozzle is 12mm is (kg/hour) = 236.47\n",
"The answers given in textbook are wrong. Please check using a calculator\n"
]
}
],
"source": [
"#calculate the mass of steam\n",
"#Input data\n",
"P1=12.;#Initial pressure of dry saturated steam expanded in a nozzle in bar\n",
"P2=0.95;#Final pressure of dry saturated steam expanded in a nozzle in bar\n",
"f=10.;#Frictional loss in the nozzle of the total heat drop in percentage\n",
"d=12.;#Exit diameter of the nozzle in mm\n",
"hd=437.1;#Heat drop in kJ/kg from steam tables\n",
"q=0.859;#Dryness fraction of steam at discharge pressure\n",
"vg=1.777;#Specific volume of dry saturated steam at 0.95 bar\n",
"\n",
"#Calculations\n",
"n=1.-(f/100.);#Nozzle coefficient from moiller chart\n",
"V2=44.72*(n*hd)**(0.5);#Velocity of steam at nozzle exit in m/s\n",
"A=(3.14/4)*(0.012)**(2);#Area of the nozzle at the exit in mm**2\n",
"m=((A*V2)/(q*vg))*3600;#Mass of steam discharged through the nozzle per hour in kg/hour\n",
"\n",
"#Output\n",
"print 'Velocity (m/s) = ',round(V2,2)\n",
"print 'The mass of steam discharged,when the exit diameter of the nozzle is 12mm is (kg/hour) = ',round(m,2)\n",
"print 'The answers given in textbook are wrong. Please check using a calculator'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 - pg 8.49"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Throat area of steam nozzle is (cm^2) = 1.674\n",
"(b)Exit area of steam nozzle is (cm^2) = 2.016\n",
"(c)Exit velocity of the nozzle is (m/s) = 831.62\n"
]
}
],
"source": [
"#calculate the throat area of steam and exit area,exit velocity\n",
"#Input data\n",
"P1=12.;#Inlet pressure of steam nozzle in bar\n",
"T1=250.;#Inlet temperature of steam nozzle in degrees celcius\n",
"P2=2.;#Final pressure of the steam nozzle in bar\n",
"n=1.3;#Polytropic constant for superheated steam\n",
"St=6.831;#For isentropic expansion, entropy remains constant in kJ/kg\n",
"h1=2935.4#Enthalpy of steam at P1 from steam table in kJ/kg\n",
"ht=2860.;#Enthalpy of steam at pt in kJ/kg\n",
"vt=0.325;#Specific volume of steam at the throat conditions in m**3/kg\n",
"m=0.2;#Mass of steam discharged through the nozzle in kg/hour\n",
"q=0.947;#The dryness fraction of steam at exit from steam tables\n",
"hg=2589.6;#Enthalpy of steam at exit in kJ/kg\n",
"vs=0.8854;#Specific volume of saturated steam in m**3/kg\n",
"\n",
"#Calculations\n",
"pt=(P2/(n+1))**(n/(n-1))*P1;#Critical pressure ratio i.e.,Throat pressure in bar\n",
"Vt=(2*1000*(h1-ht))**(0.5);#Velocity of steam at throat in m/s\n",
"At=((m*vt)/Vt)*10**4;#Area of the throat in cm**2 from continuity equation\n",
"ve=q*vs;#Specific volume of steam at exit in m**3/kg\n",
"Ve=(2*1000*(h1-hg))**(0.5);#Velocity of steam at nozzle exit in m/s\n",
"Ae=((m*ve)/Ve)*10**4;#Exit area in cm**2\n",
"\n",
"#Output\n",
"print '(a)Throat area of steam nozzle is (cm^2) = ',round(At,3)\n",
"print '(b)Exit area of steam nozzle is (cm^2) = ',round(Ae,3)\n",
"print '(c)Exit velocity of the nozzle is (m/s) = ',round(Ve,2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 - pg 8.51"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Final exit velocity of steam is (m/s) = 785.2\n",
"(b)Cross sectional area of the nozzle at exit for maximum discharge is (mm^2) = 678.0\n"
]
}
],
"source": [
"#calculate the Final exit velocity, Cross sectional area\n",
"#Input data\n",
"P1=10.;#Pressure of steam in bar\n",
"f=0.9;#Dryness fraction of steam\n",
"At=350.;#Throat area in mm**2\n",
"Pb=1.4;#Back pressure in bar\n",
"h1=2574.8;#Enthalpy of steam at nozzle inlet from steam tables in kJ/kg\n",
"ft=0.87;#Dryness fraction of steam at throat pressure\n",
"fe=0.81;#Dryness fraction of steam at exit pressure\n",
"ht=2481.;#Enthalpy of steam at throat pressure at ft in kJ/kg\n",
"vt=0.285;#Specific volume of steam at throat in m**3/kg\n",
"he=2266.2;#Enthalpy of steam at exit conditions in kJ/kg\n",
"ve=1.001;#Specific volume of steam at exit conditions in m**3/kg\n",
"\n",
"#Calculations\n",
"Pt=0.582*P1;#Steam pressure at the throat in bar\n",
"hd=h1-ht;#Enthalpy drop upto the throat in kJ/kg\n",
"Vt=44.7*(hd)**(0.5);#Velocity of steam at the throat in m/s\n",
"hde=h1-he;#Enthalpy drop from nozzle entrance to exit in kJ/kg\n",
"Ve=44.7*(hde)**(0.5);#Velocity of steam at nozzle exit in m/s\n",
"Ae=(At*Vt*ve)/(Ve*vt);#Exit area of nozzle from the mass rate of flow equation in mm**2\n",
"\n",
"#Output\n",
"print '(a)Final exit velocity of steam is (m/s) = ',round(Ve,1)\n",
"print '(b)Cross sectional area of the nozzle at exit for maximum discharge is (mm^2) = ',round(Ae,0)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5 - pg 8.52"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(a)Velocity of steam at throat is (m/s) = 531.0\n",
"(b)Temperature of steam at the throat is (degrees celcius) = 202.8\n",
"(c)Cone angle of the divergent portion is (degrees) = 2.134\n"
]
}
],
"source": [
"#calculate the Velocity of steam at throat, temperature and cone angle\n",
"#Input data\n",
"import math\n",
"P1=7.;#Inlet pressure of a convergent divergent steam nozzle in bar\n",
"T1=275.;#Inlet temperature of the nozzle in degrees celcius\n",
"P2=1.;#Discharge pressure of steam in bar\n",
"l=60.;#Length of diverging portion of the nozzle in mm\n",
"dt=6.;#Diameter of the throat in mm\n",
"f1=10.;#Percent of total available enthalpy drop lost in friction in the diverging portion in percentage\n",
"h1=3006.9;#Enthalpy of steam at 7bar pressure and 275 degrees celcius in kJ/kg\n",
"ht=2865.9;#Enthalpy at the throat from Moiller chart in kJ/kg\n",
"he=2616.7;#Enthalpy at the exit from moiller chart in kJ/kg\n",
"vt=0.555;#Specific volume of steam at throat in m**3/kg\n",
"Tt=202.8;#Temperature of steam at throat in degrees celcius from moiller chart\n",
"ve=1.65;#Volume of steam at exit in m**3/kg\n",
"\n",
"#Calculations\n",
"Pt=0.546*P1;#The throat pressure for maximum discharge in bar\n",
"hd=h1-ht;#Enthalpy drop upto throat in kJ/kg\n",
"Vt=44.7*(hd)**(0.5);#Velocity of steam at throat in m/s\n",
"hid=h1-he;#Total isentropic drop from 7 bar,275 degrees celcius to 1 bar in kJ/kg\n",
"hda=(1-(f1/100.))*(hid);#Actual heat drop in kJ/kg\n",
"Ve=44.7*(hda)**(0.5);#Velocity at exit in m/s\n",
"At=(3.14/4)*(6./1000)**(2);#Throat area of the nozzle in m**2\n",
"m=(At*Vt)/vt;#Mass flow rate at nozzle throat in kg/s\n",
"Ae=((m*ve)/Ve)*10**4;#Exit area of the nozzle in cm**2\n",
"de=(((Ae*4)/3.14)**(0.5))*10;#Diameter of the nozzle at exit in mm\n",
"alpha=math.atan((de-dt)/(2*60))*180/math.pi;#Half of the cone angle of the nozzle in degrees\n",
"alpha1=2*alpha;#Cone angle of the nozzle in degrees\n",
"\n",
"#Output\n",
"print '(a)Velocity of steam at throat is (m/s) = ',round(Vt,0)\n",
"print '(b)Temperature of steam at the throat is (degrees celcius) =',Tt\n",
"print '(c)Cone angle of the divergent portion is (degrees) =',round(alpha1,3)\n"
]
}
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