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diff --git a/Thermal_Engineering_by_A._V._Arasu/ch4.ipynb b/Thermal_Engineering_by_A._V._Arasu/ch4.ipynb new file mode 100644 index 00000000..09c1bcde --- /dev/null +++ b/Thermal_Engineering_by_A._V._Arasu/ch4.ipynb @@ -0,0 +1,1482 @@ +{ + "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 +} |