{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 4 : Steam nozzles and Steam turbines"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.1 Page no : 161"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Throat area is 255 mm**2 \n",
"Exit area is 344 mm**2 \n",
"Mach number at exit is 1.49\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"P1 = 3.5;\t\t\t#Pressure at entry in MN/(m**2)\n",
"T1 = 773.;\t\t\t#Temperature at entry in K\n",
"P2 = 0.7;\t\t\t#Pressure at exit in MN/(m**2)\n",
"ma = 1.3;\t\t\t#mass flow rate of air in kg/s\n",
"y = 1.4;\t\t\t#Ratio of specific heats\n",
"R = 0.287;\t\t\t#Universal gas constant in KJ/Kg-K\n",
"\n",
"# Calculations\n",
"c = y/(y-1); \t\t\t#Ratio\n",
"Pt = ((2/(y+1))**c)*P1;\t\t\t#Throat pressure in MN/(m**2)\n",
"v1 = (R*T1)/(P1*1000);\t\t\t#Specific volume at entry in (m**3)/kg\n",
"Ct = ((2*c*P1*v1*(1-((Pt/P1)**(1/c))))**0.5)*1000;\t\t\t#Velocity at throat in m/s\n",
"vt = v1*((P1/Pt)**(1/y));\t\t\t#Specific volume at throat in (m**3)/kg\n",
"At = ((ma*vt)/Ct)*(10**6);\t\t\t#Area of throat in (mm**2)\n",
"C2 = ((2*c*P1*v1*(1-((P2/P1)**(1/c))))**0.5)*1000;\t\t\t#Velocity at exit in m/s\n",
"v2 = v1*((P1/P2)**(1/y));\t\t\t#Specific volume at exit in (m**3)/kg\n",
"A2 = ((ma*v2)/C2)*(10**6);\t\t\t#Area of exit in (mm**2)\n",
"M = C2/Ct;\t\t\t #Mach number at exit\n",
"\n",
"# Results\n",
"print 'Throat area is %3.0f mm**2 \\\n",
"\\nExit area is %3.0f mm**2 \\\n",
"\\nMach number at exit is %3.2f'%(At,A2,M)\n",
"\n",
"# rounding off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.2 Page no : 163"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Increase in temperature is 356 K \n",
"Increase in pressure is 2.46 MN/m**2 \n",
"Increase in internal energy is 255 kJ/kg\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"T1 = 273.;\t\t\t#Temperature at section 1 in K\n",
"P1 = 140.;\t\t\t#Pressure at section 1 in KN/(m**2)\n",
"v1 = 900.;\t\t\t#Velocity at section 1 in m/s\n",
"v2 = 300.;\t\t\t#Velocity at section 2 in m/s\n",
"Cp = 1.006;\t\t\t#Specific heat at constant pressure in kJ/kg-K\n",
"Cv = 0.717;\t\t\t#Specific heat at constant volume in kJ/kg-K\n",
"y = 1.4;\t\t\t#Ratio of specific heats\n",
"\n",
"# Calculations\n",
"c = y/(y-1);\t\t\t#Ratio\n",
"R = Cp-Cv;\t\t\t#Universal gas constant in KJ/Kg-K\n",
"T2 = T1-(((v2)**2-(v1)**2)/(2000*c*R));\t\t\t#Temperature at section 2 in K\n",
"DT = T2-T1;\t\t\t#Increase in temperature in K\n",
"P2 = P1*((T2/T1)**c);\t\t\t#Pressure at section 2 in KN/(m**2)\n",
"DP = (P2-P1)/1000;\t\t\t#Increase in pressure in MN/(m**2)\n",
"IE = Cv*(T2-T1);\t\t\t#Increase in internal energy in kJ/kg\n",
"\n",
"# Results\n",
"print 'Increase in temperature is %3.0f K \\\n",
"\\nIncrease in pressure is %3.2f MN/m**2 \\\n",
"\\nIncrease in internal energy is %3.0f kJ/kg'%(DT,DP,IE)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.3 Page no : 163"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Throat area is 2888 mm**2 \n",
"Exit area is 4280 mm**2 \n",
"Degree of undercooling at exit is 10.3 K\n"
]
}
],
"source": [
"\n",
"\n",
"# Variables\n",
"P1 = 2;\t\t\t#Pressure at entry in MN/(m**2)\n",
"T1 = 598;\t\t\t#Temperature at entry in K\n",
"P2 = 0.36;\t\t\t#Pressure at exit in MN/(m**2)\n",
"m = 7.5;\t\t\t#mass flow rate of steam in kg/s\n",
"n = 1.3;\t\t\t#Adiabatic gas constant\n",
"v1 = 0.132;\t\t\t#Volume at entry in (m**3)/kg from steam table\n",
"Ts = 412.9;\t\t\t#Saturation temperature in K\n",
"\n",
"# Calculations\n",
"c = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**c)*P1;\t\t\t#Throat pressure in MN/(m**2)\n",
"Ct = ((2*c*P1*v1*(1-((Pt/P1)**(1/c))))**0.5)*1000;\t\t\t#Velocity at throat in m/s\n",
"vt = v1*((P1/Pt)**(1/n));\t\t\t#Specific volume at throat in (m**3)/kg\n",
"At = ((m*vt)/Ct)*(10**6);\t\t\t#Area of throat in (mm**2)\n",
"C2 = ((2*c*P1*v1*(1-((P2/P1)**(1/c))))**0.5)*1000;\t\t\t#Velocity at exit in m/s\n",
"v2 = v1*((P1/P2)**(1/n));\t\t\t#Specific volume at exit in (m**3)/kg\n",
"A2 = ((m*v2)/C2)*(10**6);\t\t\t#Area of exit in (mm**2)\n",
"T2 = T1*((P2/P1)**(1/c));\t\t\t#Temperature at exit in K\n",
"D = Ts-T2;\t\t\t#Degree of undercooling at exit in K\n",
"\n",
"# Results\n",
"print 'Throat area is %3.0f mm**2 \\\n",
"\\nExit area is %3.0f mm**2 \\\n",
"\\nDegree of undercooling at exit is %3.1f K'%(At,round(A2,-1),D)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.4 Page no : 165"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Throat velocity is 548 m/s \n",
"Exit velocity is 800 m/s \n",
"Throat area is 3210 mm**2 \n",
"Exit area is 6050 mm**2 \n"
]
}
],
"source": [
"\n",
"\n",
"# Variables\n",
"P1 = 2.2;\t\t\t#Pressure at entry in MN/(m**2)\n",
"T1 = 533.;\t\t\t#Temperature at entry in K\n",
"P2 = 0.4;\t\t\t#Pressure at exit in MN/(m**2)\n",
"m = 11.;\t\t\t#mass flow rate of steam in kg/s\n",
"n = 0.85;\t\t\t#Efficiency of expansion\n",
"h1 = 2940.;\t\t\t#Enthalpy at entrance in kJ/kg from Moiller chart\n",
"ht = 2790.;\t\t\t#Enthalpy at throat in kJ/kg from Moiller chart\n",
"h2s = 2590.;\t\t\t#Enthalpy below exit level in kJ/kg from Moiller chart\n",
"vt = 0.16;\t\t\t#Throat volume in (m**3)/kg\n",
"v2 = 0.44;\t\t\t#Volume at exit in (m**3)/kg\n",
"\n",
"# Calculations\n",
"Ct = (2000*(h1-ht))**0.5;\t\t\t#Throat velocity in m/s\n",
"h2 = ht-(0.85*(ht-h2s));\t\t\t#Enthalpy at exit in kJ/kg\n",
"C2 = (2000*(h1-h2))**0.5;\t\t\t#Exit velocity in m/s\n",
"At = ((m*vt)/Ct)*(10**6);\t\t\t#Area of throat in (mm**2)\n",
"A2 = ((m*v2)/C2)*(10**6);\t\t\t#Area of exit in (mm**2)\n",
"\n",
"# Results\n",
"print 'Throat velocity is %3.0f m/s \\\n",
"\\nExit velocity is %3.0f m/s \\\n",
"\\nThroat area is %3.0f mm**2 \\\n",
"\\nExit area is %3.0f mm**2 '%(Ct,C2,round(At,-1),A2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.5 Page no : 166"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cross section of nozzle is 26.7 mm * 8.9 mm \n",
"Degree of undercooling is 35.8 K and Degree of supersaturation is 2.58 \n",
"Loss in available heat drop due to irreversibility is 6.16 kJ/kg \n",
"Increase in entropy is 0.01390 kJ/kg-K \n",
"Ratio of mass flow rate with metastable expansion to the thermal expansion is 1.065\n"
]
}
],
"source": [
"\n",
"\n",
"# Variables\n",
"P1 = 35.;\t\t\t#Pressure at entry in bar\n",
"T1 = 573.;\t\t\t#Temperature at entry in K\n",
"P2 = 8.;\t\t\t#Pressure at exit in bar\n",
"Ts = 443.4;\t\t\t#Saturation temperature in K\n",
"Ps = 3.1;\t\t\t#Saturation pressure in bar\n",
"m = 5.2;\t\t\t#mass flow rate of steam in kg/s\n",
"n = 1.3;\t\t\t#Adiabatic gas consmath.tant\n",
"v1 = 0.06842;\t\t\t#Specific volume at entry in (m**3)/kg from steam table\n",
"v3 = 0.2292;\t\t\t#Specific volume at exit in (m**3)/kg from steam table\n",
"h1 = 2979.;\t\t\t#Enthalpy in kJ/kg from Moiller chart\n",
"h3 = 2673.3;\t\t\t#Enthalpy in kJ/kg from Moiller chart\n",
"\n",
"# Calculations\n",
"c = n/(n-1);\t\t\t#Ratio\n",
"C2 = ((2*c*P1*(10**5)*v1*(1-((P2/P1)**(1/c))))**0.5);\t\t\t#Velocity at exit in m/s\n",
"v2 = v1*((P1/P2)**(1/n));\t\t\t#Specific volume at exit in (m**3)/kg\n",
"A2 = ((m*v2)/C2)*(10**4);\t\t\t#Area of exit in (cm**2)\n",
"a = ((A2/18)**0.5)*10;\t\t\t#Length in mm\n",
"b = 3*a;\t\t\t#Breadth in mm\n",
"T2 = T1*((P2/P1)**(1/c));\t\t\t#Temperature at exit in K\n",
"D = Ts-T2;\t\t\t#Degree of undercooling in K\n",
"Ds = P2/Ps;\t\t\t#Degree of supersaturation\n",
"hI = h1-h3;\t\t\t#Isentropic enthalpy drop in kJ/kg\n",
"ha = (C2**2)/2000;\t\t\t#Actual enthalpy drop in kJ/kg\n",
"QL = hI-ha;\t\t\t#Loss in available heat in kJ/kg\n",
"DS = QL/Ts;\t\t\t#Increase in entropy in kJ/kg-K\n",
"C3 = (2000*(h1-h3))**0.5;\t\t\t#Exit velocity from nozzle\n",
"mf = ((A2*C3*(10**-4))/v3);\t\t\t#Mass flow rate in kg/s\n",
"Rm = m/mf;\t\t\t#Ratio of mass rate\n",
"\n",
"# Results\n",
"print 'Cross section of nozzle is %3.1f mm * %3.1f mm \\\n",
"\\nDegree of undercooling is %3.1f K and Degree of supersaturation is %3.2f \\\n",
"\\nLoss in available heat drop due to irreversibility is %3.2f kJ/kg \\\n",
"\\nIncrease in entropy is %3.5f kJ/kg-K \\\n",
"\\nRatio of mass flow rate with metastable expansion to the thermal expansion is %3.3f'%(b,a,D,Ds,QL,DS,Rm)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.6 Page no : 169"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nozzle efficiency is 88.9 percent \n",
"Exit area is 7000 mm**2 \n",
"Throat velocity is 529 m/s\n"
]
}
],
"source": [
"\n",
"import math\n",
"\n",
"# Variables\n",
"m = 14.;\t\t\t#Mass flow rate of steam in kg/s\n",
"P1 = 3.;\t\t\t#Pressure of Steam in MN/(m**2)\n",
"T1 = 300.;\t\t\t#Steam temperature in oC\n",
"h1 = 2990.;\t\t\t#Enthalpy at point 1 in kJ/kg\n",
"h2s = 2630.;\t\t\t#Enthalpy at point 2s in kJ/kg\n",
"ht = 2850.;\t\t\t#Enthalpy at point t in kJ/kg\n",
"n = 1.3;\t\t\t#Adiabatic gas consmath.tant\n",
"C2 = 800.;\t\t\t#Exit velocity in m/s\n",
"v2 = 0.4;\t\t\t#Specific volume at exit in (m**3)/kg\n",
"\n",
"# Calculations\n",
"x = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**x)*P1;\t\t\t#Temperature at point t in MN/(m**2)\n",
"h2 = h1-((C2**2)/2000);\t\t\t#Exit enthalpy in kJ/kg\n",
"nN = ((h1-h2)/(h1-h2s))*100;\t\t\t#Nozzle efficiency\n",
"A2 = ((m*v2)/C2)*(10**6);\t\t\t#Exit area in (mm**2)\n",
"Ct = math.sqrt(2*(h1-ht)*10**3);\t\t\t#Throat velocity in m/s\n",
"\n",
"# Results\n",
"print 'Nozzle efficiency is %3.1f percent \\\n",
"\\nExit area is %3.0f mm**2 \\\n",
"\\nThroat velocity is %3.0f m/s'%(nN,A2,Ct)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.7 Page no : 170"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Throat area is 388 mm**2 \n",
"Exit area is 1275 mm**2 \n",
"Steam quality at exit is 95 percent\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"P1 = 10.;\t\t\t#Pressure at point 1 in bar\n",
"P2 = 0.5;\t\t\t#Pressure at point 2 in bar\n",
"h1 = 3050.;\t\t\t#Enthalpy at point 1 in kJ/kg\n",
"h2s = 2480.;\t\t\t#Enthalpy at point 2s in kJ/kg\n",
"ht = 2910.;\t\t\t#Enthalpy at throat in kJ/kg\n",
"n = 1.3;\t\t\t#Adiabatic gas constant\n",
"r = 0.1;\t\t\t#Total available heat drop\n",
"v1 = 0.258;\t\t\t#Specific volume at point 1 in (m**3)/kg\n",
"h2f = 340.6;\t\t\t#Enthalpy for exit pressure from steam tables in kJ/kg\n",
"hfg = 2305.4;\t\t\t#Enthalpy for exit pressure from steam tables in kJ/kg\n",
"m = 0.5;\t\t\t#Mass flow rate in kg/s\n",
"\n",
"# Calculations\n",
"x = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**x)*P1;\t\t\t#Temperature at throat in bar\n",
"h2 = h2s+(r*(h1-h2s));\t\t\t#Enthalpy at point 2 in kJ/kg\n",
"vt = ((P1/Pt)**(1/n))*v1;\t\t\t#Specific volume at throat in (m**3)/kg\n",
"v2 = ((P1/P2)**(1/n))*v1;\t\t\t#Specific volume at point 2 in (m**3)/kg\n",
"Ct = math.sqrt(2000*(h1-ht));\t\t\t#Throat velocity in m/s\n",
"At = ((m*vt)/Ct)*(10**6);\t\t\t#Throat area in (mm**2)\n",
"C2 = math.sqrt(2000*(h1-h2));\t\t\t#Exit velocity in m/s\n",
"A2 = ((m*v2)/C2)*(10**6);\t\t\t#Exit area in (mm**2)\n",
"x2 = ((h2-h2f)/hfg)*100;\t\t\t#Steam quality at exit\n",
"\n",
"# Results\n",
"print 'Throat area is %d mm**2 \\\n",
"\\nExit area is %d mm**2 \\\n",
"\\nSteam quality at exit is %3.0f percent'%(At,A2,x2)\n",
"\n",
"# rounding off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.8 Page no : 171"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum discharge is 13.294 kg/min \n",
"Exit area is 493.8 mm**2\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"P1 = 3.5;\t\t\t#Dry saturated steam in bar\n",
"P2 = 1.1;\t\t\t#Exit pressure in bar\n",
"At = 4.4;\t\t\t#Throat area in cm**2\n",
"h1 = 2731.6;\t\t\t#Enthalpy at P1 in kJ/kg\n",
"v1 = 0.52397;\t\t\t#Specific volume at P1 in m**3/kg\n",
"n = 1.135;\t\t\t#Adiabatic gas constant\n",
"ht = 2640.;\t\t\t#Enthalpy at Pt in kJ/kg\n",
"vt = 0.85;\t\t\t#Specific volume at throat in m**3/kg\n",
"h2 = 2520.;\t\t\t#Enthalpy at P2 in kJ/kg\n",
"v2 = 1.45;\t\t\t#Specific volume at P2 in m**3/kg\n",
"\n",
"# Calculations\n",
"x = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**x)*P1;\t\t\t#Throat pressure in bar\n",
"Ct = math.sqrt(2000*(h1-ht));\t\t\t#Throat velocity in m/s\n",
"mmax = ((At*Ct*(10**-4))/vt)*60;\t\t\t#Maximum discharge in kg/min\n",
"C2 = math.sqrt(2000*(h1-h2));\t\t\t#Exit velocity in m/s\n",
"A2 = ((mmax*v2)/(C2*60))*(10**6);\t\t\t#Exit area in mm**2\n",
"\n",
"# Results\n",
"print 'Maximum discharge is %3.3f kg/min \\\n",
"\\nExit area is %3.1f mm**2'%(mmax,A2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.9 Page no : 172"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Since throat pressure is greater than exit pressure,nozzle used is convergent-divergent nozzle \n",
"Minimum area of nozzle required is 2.14e-03 m**2\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"P1 = 10.;\t\t\t#Pressure at point 1 in bar\n",
"T1 = 200.;\t\t\t#Temperature at point 1 in oC\n",
"P2 = 5.;\t\t\t#Pressure at point 2 in bar\n",
"n = 1.3;\t\t\t#Adiabatic gas consmath.tant\n",
"h1 = 2830.;\t\t\t#Enthalpy at P1 in kJ/kg\n",
"ht = 2710.;\t\t\t#Enthalpy at point Pt in kJ/kg\n",
"vt = 0.35;\t\t\t#Specific volume at Pt in m**3/kg\n",
"m = 3. \t\t\t#Nozzle flow in kg/s\n",
"\n",
"# Calculations\n",
"x = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**x)*P1;\t\t\t#Throat pressure in bar\n",
"Ct = math.sqrt(2000*(h1-ht));\t\t\t#Throat velocity in m/s\n",
"At = (m*vt)/Ct;\t\t\t#Throat area in m**2\n",
"\n",
"# Results\n",
"print 'Since throat pressure is greater than exit pressure,nozzle used is\\\n",
" convergent-divergent nozzle \\\n",
" \\nMinimum area of nozzle required is %.2e m**2'%(At)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.10 Page no : 173"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Throat velocity is 443.27 m/s \n",
"Mass flow rate of steam is 1549.90 kg/m**2\n"
]
}
],
"source": [
"import math \n",
"\n",
"# Variables\n",
"P1 = 10.5;\t\t\t#Pressure at point 1 in bar\n",
"x1 = 0.95;\t\t\t#Dryness fraction\n",
"n = 1.135;\t\t\t#Adiabatic gas constant\n",
"P2 = 0.85;\t\t\t#Pressure at point 2 in bar\n",
"vg = 0.185;\t\t\t#Specific volume in m**3/kg\n",
"\n",
"\n",
"# Calculations\n",
"c = n/(n-1);\t\t\t#Ratio\n",
"Pt = round(((2/(n+1))**c)*P1,2);\t\t\t#Throat pressure in MN/(m**2)\n",
"v1 = round(x1*vg,3);\t\t\t#Specific volume at point 1 in m**3/kg\n",
"Ct = round(math.sqrt((2*n*P1*v1*(10**5)/(n+1))),2);\t\t\t#Velocity at throat in m/s\n",
"vt = round(((P1/Pt)*(v1**n))**(1/1.135),3);\t\t\t#Specific volume at throat in m**3/kg\n",
"m = Ct/vt;\t\t\t#Mass flow rate per unit throat area in kg/(m**2)\n",
"\n",
"# Results\n",
"print 'Throat velocity is %3.2f m/s \\\n",
"\\nMass flow rate of steam is %3.2f kg/m**2'%(Ct,m)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.11 Page no : 174"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Degree of supersaturation is 4.98 \n",
"Degree of undercooling 50 C\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"P1 = 10.;\t\t\t#Pressure at point 1 in bar\n",
"T1 = 452.9;\t\t\t#Temperature at point 1 in K\n",
"P2 = 4.;\t\t\t#Pressure at point 2 in bar\n",
"n = 1.3;\t\t\t#Adiabatic gas constant\n",
"Ps = 0.803;\t\t\t#Saturation pressure at T2 in bar\n",
"Ts = 143.6;\t\t\t#Saturation temperature at P2 in oC\n",
"# Calculations\n",
"x = (n-1)/n;\t\t\t#Ratio\n",
"T2 = ((P2/P1)**x)*T1;\t\t\t#Temperature at point 2 in K\n",
"Ds = P2/Ps;\t\t\t#Degree of supersaturation\n",
"Du = Ts-(T2-273);\t\t\t#Degree of undercooling\n",
"\n",
"# Results\n",
"print 'Degree of supersaturation is %3.2f \\\n",
"\\nDegree of undercooling %3.0f C'%(Ds,Du)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.12 Page no : 174"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Quantity of steam used per second is 0.012 kg/s \n",
"Exit velocity of steam is 816.09 m/s\n"
]
}
],
"source": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"P1 = 9.;\t\t\t#Pressure at point 1 in bar\n",
"P2 = 1.;\t\t\t#Pressure at point 2 in bar\n",
"Dt = 0.0025;\t\t\t#Throat diameter in m\n",
"nN = 0.9;\t\t\t#Nozzle efficiency\n",
"n = 1.135;\t\t\t#Adiabatic gas constant\n",
"h1 = 2770.;\t\t\t#Enthalpy at point 1 in kJ/kg\n",
"ht = 2670.;\t\t\t#Throat enthlapy in kJ/kg\n",
"h3 = 2400.;\t\t\t#Enthlapy at point 2 in kJ/kg\n",
"x2 = 0.96;\t\t\t#Dryness fraction 2\n",
"vg2 = 0.361;\t\t\t#Specific volume in m**3/kg\n",
"\n",
"# Calculations\n",
"x = n/(n-1);\t\t\t#Ratio\n",
"Pt = ((2/(n+1))**x)*P1;\t\t\t#Throat pressure in bar\n",
"Ct = math.sqrt(2000*(h1-ht)*nN);\t\t\t#Throat velocity in m/s\n",
"At = (3.147*2*(Dt**2))/4;\t\t\t#Throat area in m**2\n",
"vt = x2*vg2;\t\t\t#Specific volume at throat in m**3/kg\n",
"m = (At*Ct)/vt;\t\t\t#Mass flow rate of steam in kg/s\n",
"hact = nN*(h1-h3);\t\t\t#Actual enthalpy drop in kJ/kg\n",
"C2 = math.sqrt(2000*hact);\t\t\t#Exit velocity of steam in m/s\n",
"\n",
"# Results\n",
"print 'Quantity of steam used per second is %3.3f kg/s \\\n",
"\\nExit velocity of steam is %3.2f m/s'%(m,C2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.13 Page no : 202"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blade angles are 33 degrees, 33 degrees \n",
"Tangential force on blades is 840 N \n",
"Axial thrust is 0 \n",
"Diagram power is 336 kW \n",
"Diagram efficiency 89.6 percent\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"C1 = 1000.;\t\t\t#Steam velocity in m/s\n",
"a1 = 20.;\t\t\t#Nozzle angle in degrees\n",
"U = 400.;\t\t\t#Mean blade speed in m/s\n",
"m = 0.75;\t\t\t#Mass flow rate of steam in kg/s\n",
"b1 = 33.;\t\t\t#Blade angle at inlet from the velocity triangle in degrees\n",
"b2 = b1;\t\t\t#Blade angle at exit from the velocity triangle in degrees\n",
"Cx = 1120.;\t\t\t#Change in whirl velocity from the velocity triangle in m/s\n",
"Ca = 0;\t\t \t#Change in axial velocity from the velocity triangle in m/s\n",
"\n",
"# Calculations\n",
"Fx = m*Cx;\t\t \t #Tangential force on blades in N\n",
"Fy = m*Ca;\t\t\t #Axial thrust in N\n",
"W = (m*Cx*U)/1000;\t\t\t#Diagram power in kW\n",
"ndia = ((2*U*Cx)/(C1**2))*100;\t\t\t#Diagram efficiency\n",
"\n",
"# Results\n",
"print 'Blade angles are %3.0f degrees, %3.0f degrees \\\n",
"\\nTangential force on blades is %3.0f N \\\n",
"\\nAxial thrust is %3.0f \\\n",
"\\nDiagram power is %3.0f kW \\\n",
"\\nDiagram efficiency %3.1f percent'%(b1,b2,Fx,Fy,W,ndia)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.14 Page no : 203"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Power developed is 3800 kW \n",
"Blade efficiency is 78.7 percent \n",
"Steam consumed is 9.46 kg/kWh\n"
]
}
],
"source": [
"# Variables\n",
"D = 2.5;\t\t\t#Mean diameter of blade ring in m\n",
"N = 3000.;\t\t\t#Speed in rpm\n",
"a1 = 20.;\t\t\t#Nozzle angle in degrees\n",
"r = 0.4;\t\t\t#Ratio blade velocity to steam velocity\n",
"Wr = 0.8;\t\t\t#Blade friction factor\n",
"m = 10.;\t\t\t#Steam flow in kg/s\n",
"x = 3.;\t \t\t#Sum in blade angles in degrees\n",
"b1 = 32.5;\t\t\t#Blade angle at inlet from the velocity triangle in degrees\n",
"W1 = 626.7;\t\t\t#Relative velocity at inlet from the velocity triangle in m/s\n",
"Cx = 967.;\t\t\t#Change in whirl velocity from the velocity triangle in m/s\n",
"\n",
"# Calculations\n",
"U = (3.147*D*N)/60;\t\t\t#Blade velocity in m/s\n",
"C1 = U/r;\t\t\t#Steam velocity in m/s\n",
"b2 = b1-x;\t\t\t#Blade angle at exit in degrees\n",
"W2 = Wr*W1;\t\t\t#Relative velocity at outlet from the velocity triangle in m/s\n",
"W = (m*Cx*U)/1000;\t\t\t#Power developed in kW\n",
"ndia = ((2*U*Cx)/(C1**2))*100;\t\t\t#Blade efficiency\n",
"sc = (m*3600)/W;\t\t\t#Steam consumption in kg/kWh\n",
"\n",
"# Results\n",
"print 'Power developed is %3.0f kW \\\n",
"\\nBlade efficiency is %3.1f percent \\\n",
"\\nSteam consumed is %3.2f kg/kWh'%(round(W,-1),ndia,sc)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.15 Page no : 204"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blading efficiency is 68.3 percent \n",
"Blade velocity co-efficient is 0.49\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"m = 3.;\t \t\t#Mass flow rate of steam in kg/s\n",
"C1 = 425.;\t\t\t#Steam velocity in m/s\n",
"r = 0.4;\t\t\t#Ratio of blade speed to jet speed\n",
"W = 170.;\t\t\t#Stage output in kW\n",
"IL = 15.;\t\t\t#Internal losses in kW\n",
"a1 = 16.;\t\t\t#Nozzle angle in degrees\n",
"b2 = 17.;\t\t\t#Blade angle at exit in degrees\n",
"W1 = 265.;\t\t\t#Relative velocity at inlet from the velocity triangle in m/s\n",
"W2 = 130.;\t\t\t#Relative velocity at outlet from the velocity triangle in m/s\n",
"\n",
"# Calculations\n",
"U = C1*r;\t\t\t#Blade speed in m/s\n",
"P = (W+IL)*1000;\t\t\t#Total power developed in W\n",
"Cx = P/(m*W);\t\t\t#Change in whirl velocity in m/s\n",
"ndia = ((2*U*Cx)/(C1**2))*100;\t\t\t#Blading efficiency\n",
"Wr = W2/W1;\t\t\t#Blade velocity co-efficient\n",
"\n",
"# Results\n",
"print 'Blading efficiency is %3.1f percent \\\n",
"\\nBlade velocity co-efficient is %3.2f'%(ndia,Wr)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.16 Page no : 205"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blade angles assumed are 34 degrees, 41 degrees \n",
"Power developed by turbine is 52.8 kW\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"C1 = 375.;\t\t\t#Steam velocity in m/s\n",
"a1 = 20.;\t\t\t#Nozzle angle\n",
"U = 165.;\t\t\t#Blade speed in m/s\n",
"m = 1.;\t\t\t#Mass flow rate of steam in kg/s\n",
"Wr = 0.85;\t\t\t#Blade friction factor\n",
"Ca1 = 130.;\t\t\t#Axial velocity at inlet from the velocity triangle in m/s\n",
"Ca2 = Ca1;\t\t\t#Axial velocity at outlet in m/s\n",
"W1 = 230.;\t\t\t#Relative velocity at inlet from the velocity triangle in m/s\n",
"Cx = 320.;\t\t\t#Change in whirl velocity from the velocity triangle in m/s\n",
"\n",
"# Calculations\n",
"b2 = 41;\t\t\t#Blade angle at exit from the velocity triangle in degrees\n",
"b1 = 34;\t\t\t#Blade angle at exit from the velocity triangle in degrees\n",
"W = (m*Cx*U)/1000;\t\t\t#Power developed by turbine in kW\n",
"\n",
"# Results\n",
"print 'Blade angles assumed are %3.0f degrees, %3.0f degrees \\\n",
"\\nPower developed by turbine is %3.1f kW'%(b1,b2,W)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.17 Page no : 206"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nozzle angle is 19 degrees \n",
"Blade angles are 33 degrees, 36 degrees\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"m = 2.;\t\t\t#Mass flow rate of steam in kg/s\n",
"W = 130.;\t\t\t#Turbine power in kW\n",
"U = 175.;\t\t\t#Blade velocity in m/s\n",
"C1 = 400.;\t\t\t#Steam velocity in m/s\n",
"Wr = 0.9;\t\t\t#Blade friction factor\n",
"W1 = 240.;\t\t\t#Realtive velocity at inlet from the velocity triangle in m/s\n",
"\n",
"# Calculations\n",
"Cx1 = (W*1000)/(m*U);\t\t\t#Whirl velocity at inlet in m/s\n",
"W2 = Wr*W1;\t\t\t#Realtive velocity at outlet from the velocity triangle in m/s\n",
"a1 = 19;\t\t\t#Nozzle angle from the velocity triangle in degrees\n",
"b1 = 33;\t\t\t#Blade angle at inlet from the velocity triangle in degrees\n",
"b2 = 36;\t\t\t#Blade angle at outlet from the velocity triangle in degrees\n",
"\n",
"# Results\n",
"print 'Nozzle angle is %3.0f degrees \\\n",
"\\nBlade angles are %3.0f degrees, %3.0f degrees'%(a1,b1,b2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.18 Page no : 207"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Diagram efficiency is 76.2 percent\n"
]
}
],
"source": [
"# find Diagram efficiency\n",
"\n",
"# Variables\n",
"U = 150.;\t\t\t#Blade speed in m/s\n",
"m = 3.;\t\t\t#Mass flow rate of steam in kg/s\n",
"P = 10.5;\t\t\t#Pressure in bar\n",
"r = 0.21;\t\t\t#Ratio blade velocity to steam velocity\n",
"a1 = 16.;\t\t\t#Nozzle angle in first stage in degrees\n",
"b2 = 20.;\t\t\t#Blade angle at exit in first stage in degrees\n",
"a3 = 24.;\t\t\t#Nozzle angle in second stage in degrees\n",
"b4 = 32.;\t\t\t#Blade angle at exit in second stage in degrees\n",
"Wr = 0.79;\t\t\t#Blade friction factor for first stage\n",
"Wr2 = 0.88;\t\t\t#Blade friction factor for second stage\n",
"Cr = 0.83;\t\t\t#Blade velocity coefficient\n",
"W1 = 570.;\t\t\t#Relative velocity at inlet from the velocity triangle for first stage in m/s\n",
"C2 = 375.;\t\t\t#Velocity in m/s\n",
"W3 = 185.;\t\t\t#Relative velocity at inlet from the velocity triangle for second stage in m/s\n",
"\n",
"# Calculations\n",
"C1 = U/r;\t\t\t#Steam speed at exit in m/s\n",
"W2 = Wr*W1;\t\t\t#Relative velocity at outlet for first stage in m/s\n",
"C3 = Cr*C2;\t\t\t#Steam velocity at inlet for second stage in m/s\n",
"W4 = Wr2*W3;\t\t\t#Relative velocity at exit for second stage in m/s\n",
"DW1 = W1+W2;\t\t\t#Change in relative velocity for first stage in m/s\n",
"DW2 = 275;\t\t\t#Change in relative velocity from the velocity triangle for second stage in m/s\n",
"ndia = ((2*U*(DW1+DW2))/(C1**2))*100;\t\t\t#Diagram efficiency\n",
"\n",
"# Results\n",
"print 'Diagram efficiency is %3.1f percent'%(ndia)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.19 Page no : 208"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blade speed is 124.7 m/s \n",
"Blade tip angles of the fixed blade are 17 degrees and 43 degrees \n",
"Diagram efficiency is 79.5 percent\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"b1 = 30.;\t\t\t#Blade angle at inlet in first stage in degrees\n",
"b2 = 30.;\t\t\t#Blade angle at exit in first stage in degrees\n",
"b3 = 30.;\t\t\t#Blade angle at inlet in second stage in degrees\n",
"b4 = 30.;\t\t\t#Blade angle at exit in second stage in degrees\n",
"t1 = 240.;\t\t\t#Temperature at entry in oC\n",
"P1 = 11.5;\t\t\t#Pressure at entry in bar\n",
"P2 = 5.;\t\t\t#Pressure in wheel chamber in bar\n",
"vl = 10.;\t\t\t#Loss in velocity in percent\n",
"h = 155.;\t\t\t#Enthalpy at P2 in kJ/kg\n",
"W4 = 17.3;\t\t\t#Relative velocity at exit from the velocity triangle for second stage in m/s\n",
"a4 = 90.;\t\t\t#Nozzle angle in second stage in degrees\n",
"C3 = 33.;\t\t\t#Steam velocity at inlet from the velocity triangle for second stage in m/s\n",
"W2 = 49.;\t\t\t#Relative velocity at outlet from the velocity triangle for first stage in m/s\n",
"x = 15.;\t\t\t#Length of AB assumed for drawing velocity triangle in mm\n",
"y = 67.;\t\t\t#Length of BC from the velocity triangle in mm\n",
"\n",
"# Calculations\n",
"C1 = math.sqrt(2000*h);\t\t\t#Velocity of steam in m/s\n",
"W3 = W4/0.9;\t\t\t#Relative velocity at inlet for second stage in m/s\n",
"C2 = C3/0.9;\t\t\t#Velocity in m/s\n",
"W1 = W2/0.9;\t\t\t#Relative velocity at inlet for first stage in m/s\n",
"C1n = C1/y;\t\t\t#Velocity of steam in m/s\n",
"U = x*C1n;\t\t\t#Blade speed in m/s\n",
"a3 = 17.;\t\t\t#Nozzle angle in second stage from the velocity triangle in degrees\n",
"a2 = 43.;\t\t\t#Nozzle angle from the velocity triangle in degrees\n",
"DW1 = 731.5;\t\t\t#Change in relative velocity from the velocity triangle for first stage in m/s\n",
"DW2 = 257.5;\t\t\t#Change in relative velocity from the velocity triangle for second stage in m/s\n",
"ndia = ((2*U*(DW1+DW2))/(C1**2))*100;\t\t\t#Diagram efficiency\n",
"\n",
"# Results\n",
"print 'Blade speed is %3.1f m/s \\\n",
"\\nBlade tip angles of the fixed blade are %3.0f degrees and %3.0f degrees \\\n",
"\\nDiagram efficiency is %3.1f percent'%(U,a3,a2,ndia)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.20 Page no : 210"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blade speed is 160.5 m/s \n",
"Power developed by the turbine is 530.66 kW\n"
]
}
],
"source": [
"\n",
"# Variables\n",
"C1 = 600.;\t\t\t#Steam velocity in m/s\n",
"b1 = 30.;\t\t\t#Blade angle at inlet in first stage in degrees\n",
"b2 = 30.;\t\t\t#Blade angle at exit in first stage in degrees\n",
"b3 = 30.;\t\t\t#Blade angle at inlet in second stage in degrees\n",
"b4 = 30.;\t\t\t#Blade angle at exit in second stage in degrees\n",
"a4 = 90.;\t\t\t#Nozzle angle in second stage in degrees\n",
"m = 3.;\t\t\t#Mass of steam in kg/s\n",
"x = 15.;\t\t\t#Length for drawing velocity triangle in mm\n",
"y = 56.;\t\t\t#Length of BC from the velocity triangle in mm\n",
"\n",
"# Calculations\n",
"C1n = round(C1/y,1);\t\t\t#Velocity of steam in m/s\n",
"U = round(x*C1n,1);\t\t\t#Blade speed in m/s\n",
"l = 103.;\t\t\t#Length from velocity triangle in mm\n",
"P = (m*l*C1n*U)/1000;\t\t\t#Power developed in kW\n",
"\n",
"# Results\n",
"print 'Blade speed is %3.1f m/s \\\n",
"\\nPower developed by the turbine is %3.2f kW'%(U,P)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.21 Page no : 211"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean diameter of drum is 963 mm \n",
"Volume of steam flowing per second is 8.18 m**3/s\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"N = 400.;\t\t\t#Speed in rpm\n",
"m = 8.33;\t\t\t#Mass of steam in kg/s\n",
"P = 1.6;\t\t\t#Pressure of steam in bar\n",
"x = 0.9;\t\t\t#Dryness fraction\n",
"W = 10.;\t\t\t#Stage power in kW\n",
"r = 0.75;\t\t\t#Ratio of axial flow velocity to blade velocity\n",
"a1 = 20.;\t\t\t#Nozzle angle at inlet in degrees\n",
"a2 = 35.;\t\t\t#Nozzle angle at exit in degrees\n",
"b1 = a2;\t\t\t#Blade tip angle at exit in degrees\n",
"b2 = a1;\t\t\t#Blade tip angle at inlet in degrees\n",
"a = 25.;\t\t\t#Length of AB from velocity triangle in mm\n",
"vg = 1.091;\t\t\t#Specific volume of steam from steam tables in (m**3)/kg\n",
"\n",
"# Calculations\n",
"Cx = 73.5;\t\t\t#Change in whirl velocity from the velocity triangle by measurement in mm\n",
"y = Cx/a;\t\t\t#Ratio of change in whirl velocity to blade speed\n",
"U = math.sqrt((W*1000)/(m*y));\t\t\t#Blade speed in m/s\n",
"D = ((U*60)/(3.147*N))*1000;\t\t\t#Mean diameter of drum in mm\n",
"v = m*x*vg;\t\t\t#Volume flow rate of steam in (m**3)/s\n",
"\n",
"# Results\n",
"print 'Mean diameter of drum is %3.0f mm \\\n",
"\\nVolume of steam flowing per second is %3.2f m**3/s'%(D,v)\n",
"\n",
"# rounding off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.22 Page no : 212"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Drum diameter is 1.030 m \n",
"Blade height is 78 mm\n"
]
}
],
"source": [
"\n",
"import math\n",
"\n",
"# Variables\n",
"N = 300.;\t\t\t#Speed in rpm\n",
"m = 4.28;\t\t\t#Mass of steam in kg/s\n",
"P = 1.9;\t\t\t#Pressure of steam in bar\n",
"x = 0.93;\t\t\t#Dryness fraction\n",
"W = 3.5;\t\t\t#Stage power in kW\n",
"r = 0.72;\t\t\t#Ratio of axial flow velocity to blade velocity\n",
"a1 = 20.;\t\t\t#Nozzle angle at inlet in degrees\n",
"b2 = a1;\t\t\t#Blade tip angle at inlet in degrees\n",
"l = 0.08;\t\t\t#Tip leakage steam\n",
"vg = 0.929;\t\t\t#Specific volume of steam from steam tables in (m**3)/kg\n",
"\n",
"# Calculations\n",
"mact = m-(m*l);\t\t\t#Actual mass of steam in kg/s\n",
"a = (3.147*N)/60;\t\t\t#Ratio of blade velocity to mean dia\n",
"b = r*a;\t\t\t#Ratio of axial velocity to mean dia\n",
"c = 46;\t\t\t#Ratio of change in whirl velocity to mean dia\n",
"D = math.sqrt((W*1000)/(mact*c*a));\t\t\t#Mean dia in m\n",
"Ca = b*D;\t\t\t#Axial velocity in m/s\n",
"h = ((mact*x*vg)/(3.147*D*Ca))*1000;\t\t\t#Blade height in mm\n",
"D1 = D-(h/1000);\t\t\t#Drum dia in m\n",
"\n",
"# Results\n",
"print 'Drum diameter is %3.3f m \\\n",
"\\nBlade height is %3.0f mm'%(D1,h)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.23 Page no : 214"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rotor blade angles are 58.56 degrees and 58.56 degrees \n",
"Flow coefficient is 0.611 \n",
"Blade loading coefficient is 2 \n",
"Power developed is 13.8 MW\n"
]
}
],
"source": [
"import math\n",
"# Variables\n",
"P0 = 800.;\t\t\t#Steam pressure in kPa\n",
"P2 = 100.;\t\t\t#Pressure at point 2 in kPa\n",
"T0 = 973.;\t\t\t#Steam temperature in K\n",
"a1 = 73.;\t\t\t#Nozzle angle in degrees\n",
"ns = 0.9;\t\t\t#Steam efficiency\n",
"m = 35.;\t\t\t#Mass flow rate in kg/s\n",
"Cp = 1.005;\t\t\t#Specific heat at constant pressure in kJ/kg-K\n",
"y = 1.4;\t\t\t#Ratio of specific heats\n",
"\n",
"# Calculations\n",
"tanb1 = math.tan(math.radians(a1))/2;\t\t\t#Blade angle at inlet in degrees\n",
"b1 = math.degrees(math.atan(tanb1))\n",
"b2 = b1;\t\t\t#Blade angle at exit in degrees\n",
"p = 2/math.tan(math.radians(a1));\t\t\t#Flow coefficient\n",
"s = p*(math.tan(math.radians(b1))+math.tan(math.radians(b2)));\t\t\t#Blade loading coefficient\n",
"Dh = ns*Cp*T0*(1-((P2/P0)**((y-1)/y)));\t\t\t#Difference in enthalpies in kJ/kg\n",
"W = (m*Dh)/1000;\t\t\t#Power developed in MW\n",
"\n",
"# Results\n",
"print 'Rotor blade angles are %3.2f degrees and %3.2f degrees \\\n",
"\\nFlow coefficient is %3.3f \\\n",
"\\nBlade loading coefficient is %3.0f \\\n",
"\\nPower developed is %3.1f MW'%(b1,b2,p,s,W)\n",
"\n",
"# answer in book is wrong for W. please check."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.24 Page no : 215"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rotor blade angles for first stage are 53.95 degrees and 53.95 degrees \n",
"Rotor blade angles for second stage are 53.95 degrees and 53.95 degrees \n",
"Power developed is 9.90 MW \n",
"Final state of steam at first stage is 3306.52 kJ/kg \n",
"Final state of steam at second stage is 3257.00 kJ/kg \n",
"Blade height at first stage is 0.0114 m \n",
"Blade height at second stage is 0.0139 m\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"P0 = 100.;\t\t\t#Steam pressure in bar\n",
"T0 = 773.;\t\t\t#Steam temperature in K\n",
"a1 = 70.;\t\t\t#Nozzle angle in degrees\n",
"ns = 0.78;\t\t\t#Steam efficiency\n",
"m = 100.;\t\t\t#Mass flow rate of steam in kg/s\n",
"D = 1.;\t\t\t#Turbine diameter in m\n",
"N = 3000.;\t\t\t#Turbine speed in rpm\n",
"h0 = 3370.;\t\t\t#Steam enthalpy from Moiller chart in kJ/kg\n",
"v2 = 0.041;\t\t\t#Specific volume at P2 from steam tables in (m**3)/kg\n",
"v4 = 0.05;\t\t\t#Specific volume at P4 from steam tables in (m**3)/kg\n",
"\n",
"# Calculations\n",
"U = (3.147*D*N)/60;\t\t\t#Blade speed in m/s\n",
"C1 = (2*U)/math.sin(math.radians(a1));\t\t\t#Steam speed in m/s\n",
"b1 = math.tan(math.radians(a1))/2;\t\t\t#Blade angle at inlet for first stage in degrees\n",
"b1 = math.degrees(math.atan(b1))\n",
"b2 = b1;\t\t\t#Blade angle at exit for first stage in degrees\n",
"b3 = b1;\t\t\t#Blade angle at inlet for second stage in degrees\n",
"b4 = b2;\t\t\t#Blade angle at exit for second stage in degrees\n",
"Wt = (4*m*(U**2))/(10**6);\t\t\t#Total workdone in MW\n",
"Dh = (2*(U**2))/1000;\t\t\t#Difference in enthalpies in kJ/kg\n",
"Dhs = Dh/ns;\t\t\t#Difference in enthalpies in kJ/kg\n",
"h2 = h0-Dh;\t\t\t#Enthalpy at point 2 in kJ/kg\n",
"h2s = h0-Dhs;\t\t\t#Enthalpy at point 2s in kJ/kg\n",
"Dh2 = (2*(U**2))/1000;\t\t\t#Difference in enthalpies in kJ/kg\n",
"Dh2s = Dh2/ns;\t\t\t#Difference in enthalpies in kJ/kg\n",
"h4 = h2-Dh2;\t\t\t#Enthalpy at point 4 in kJ/kg\n",
"h4s = h2-Dh2s;\t\t\t#Enthalpy at point 4s in kJ/kg\n",
"Ca = C1*math.cos(math.radians(a1));\t\t\t#Axial velocity in m/s\n",
"hI = (m*v2)/(math.pi*D*Ca);\t\t\t#Blade height at first stage in m/s\n",
"hII = (m*v4)/(math.pi*D*Ca);\t\t\t#Blade height at second stage in m/s\n",
"\n",
"# Results\n",
"print 'Rotor blade angles for first stage are %3.2f degrees and %3.2f degrees \\\n",
"\\nRotor blade angles for second stage are %3.2f degrees and %3.2f degrees \\\n",
"\\nPower developed is %3.2f MW \\\n",
"\\nFinal state of steam at first stage is %3.2f kJ/kg \\\n",
"\\nFinal state of steam at second stage is %3.2f kJ/kg \\\n",
"\\nBlade height at first stage is %3.4f m \\\n",
"\\nBlade height at second stage is %3.4f m'%(b1,b2,b3,b4,Wt,h2s,h4s,hI,hII)\n",
"\n",
"# rounding off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.25 Page no : 218"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rotor blade angles for first stage are 64.11 degrees and 64.11 degrees \n",
"Rotor blade angles for second stage are 34.48 degrees and 34.48 degrees \n",
"Power developed is 19.81 MW \n",
"Final state of steam at first stage is 3171.9 kJ/kg \n",
"Final state of steam at second stage is 3065.27 kJ/kg \n",
"Rotor blade height is 0.0146 m\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"P0 = 100.;\t\t\t#Steam pressure in bar\n",
"T0 = 773.;\t\t\t#Steam temperature in K\n",
"a1 = 70.;\t\t\t#Nozzle angle in degrees\n",
"ns = 0.78;\t\t\t#Steam efficiency\n",
"m = 100.;\t\t\t#Mass flow rate of steam in kg/s\n",
"D = 1.;\t\t\t#Turbine diameter in m\n",
"N = 3000.;\t\t\t#Turbine speed in rpm\n",
"h0 = 3370.;\t\t\t#Steam enthalpy from Moiller chart in kJ/kg\n",
"P4 = 27.;\t\t\t#Pressure at point 4 in bar\n",
"T4 = 638.;\t\t\t#Temperature at point 4 in K\n",
"v4 = 0.105;\t\t\t#Specific volume at P4 from mollier chart in (m**3)/kg\n",
"ns = 0.65;\t\t\t#Stages efficiency\n",
"\n",
"# Calculations\n",
"U = (3.147*D*N)/60;\t\t\t#Blade speed in m/s\n",
"C1 = (4*U)/math.sin(math.radians(a1));\t\t\t#Steam speed in m/s\n",
"Ca = C1*math.cos(math.radians(a1));\t\t\t#Axial velocity in m/s\n",
"tanb1 = (3*U)/Ca;\t\t\t#Blade angle at inlet for first stage in degrees\n",
"b1 = math.degrees(math.atan(tanb1))\n",
"b2 = b1;\t\t\t#Blade angle at exit for first stage in degrees\n",
"b4 = math.degrees(math.atan(U/Ca));\t\t\t#Blade angle at exit for second stage in degrees\n",
"b3 = b4;\t\t\t#Blade angle at inlet for second stage in degrees\n",
"WI = m*6*(U**2);\t\t\t#Power developed in first stage in MW\n",
"WII = m*2*(U**2);\t\t\t#Power developed in second stage in MW\n",
"W = (WI+WII)/(10**6);\t\t\t#Total power developed in MW\n",
"Dh = (W*1000)/100;\t\t\t#Difference in enthalpies in kJ/kg\n",
"Dhs = (W*1000)/(ns*100);\t\t\t#Difference in enthalpies in kJ/kg\n",
"h4 = h0-Dh;\t\t\t#Enthalpy at point 4 in kJ/kg\n",
"h4s = h0-Dhs;\t\t\t#Enthalpy at point 4s in kJ/kg\n",
"h = (m*v4)/(3.147*D*Ca);\t\t\t#Rotor blade height in m\n",
"\n",
"\n",
"# Results\n",
"print 'Rotor blade angles for first stage are %3.2f degrees and %3.2f degrees \\\n",
"\\nRotor blade angles for second stage are %3.2f degrees and %3.2f degrees \\\n",
"\\nPower developed is %3.2f MW \\\n",
"\\nFinal state of steam at first stage is %3.1f kJ/kg \\\n",
"\\nFinal state of steam at second stage is %3.2f kJ/kg \\\n",
"\\nRotor blade height is %3.4f m'%(b1,b2,b3,b4,W,h4,h4s,h)\n",
"\n",
"# rounding off error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.26 Page no : 221"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blade angle at inlet is 10 degrees \n",
"Blade angle at exit is 60 degrees\n"
]
}
],
"source": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"a1 = 30.;\t\t\t#Nozzle angle in degrees\n",
"Ca = 180.;\t\t\t#Axial velocity in m/s\n",
"U = 280.;\t\t\t#Rotor blade speed in m/s\n",
"R = 0.5;\t\t\t#Degree of reaction\n",
"\n",
"# Calculations\n",
"a1n = 90-a1;\t\t\t#Nozzle angle measured from axial direction in degrees\n",
"Cx1 = Ca*math.tan(math.radians(a1n));\t\t\t#Whirl velocity in m/s\n",
"b1 = math.degrees(math.atan((Cx1-U)/Ca));\t\t\t#Blade angle at inlet in degrees\n",
"b2 = a1n;\t\t\t#Blade angle at exit in degrees\n",
"\n",
"# Results\n",
"print 'Blade angle at inlet is %3.0f degrees \\\n",
"\\nBlade angle at exit is %3.0f degrees'%(b1,b2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4.27 Page no : 222"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rotor blade angles are 0 degrees and 70 degrees \n",
"Power developed is 1.92 MW \n",
"Isentropic enthalpy drop is 30.12 kJ/kg\n"
]
}
],
"source": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"P0 = 800.;\t\t\t#Steam pressure in kPa\n",
"T0 = 900.;\t\t\t#Steam temperature in K\n",
"a1 = 70.;\t\t\t#Nozzle angle in degrees\n",
"ns = 0.85;\t\t\t#Steam efficiency\n",
"m = 75.;\t\t\t#Mass flow rate of steam in kg/s\n",
"R = 0.5;\t\t\t#Degree of reaction\n",
"U = 160.;\t\t\t#Blade speed in m/s\n",
"\n",
"# Calculations\n",
"C1 = U/math.sin(a1);\t\t\t#Steam speed in m/s\n",
"Ca = C1*math.cos(a1);\t\t\t#Axial velocity in m/s\n",
"b1 = 0;\t\t\t #Blade angle at inlet from velocity triangle in degrees\n",
"b2 = a1; \t\t\t#Blade angle at exit in degrees\n",
"a2 = b1;\t\t\t #Nozzle angle in degrees\n",
"W = (m*(U**2))/(10**6);\t\t\t#Power developed in MW\n",
"Dhs = (W*1000)/(ns*m);\t\t\t#Isentropic enthalpy drop in kJ/kg\n",
"\n",
"# Results\n",
"print 'Rotor blade angles are %3.0f degrees and %3.0f degrees \\\n",
"\\nPower developed is %3.2f MW \\\n",
"\\nIsentropic enthalpy drop is %3.2f kJ/kg'%(b1,b2,W,Dhs)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}