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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 11: The steam engine"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.1: bore_stroke_and_speed.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.1')\n",
+"\n",
+"// aim : To determine the \n",
+"// (a) bore of the cylinder\n",
+"// (b) piston stroke\n",
+"// (c) speed of the engine\n",
+"\n",
+"// Given values\n",
+"P_req = 60;// power required to develop, [kW]\n",
+"P = 1.25;// boiler pressure, [MN/m^2]\n",
+"Pb = .13;// back pressure, [MN/m^2]\n",
+"cut_off = .3;// [stroke]\n",
+"k = .82;// diagram factor\n",
+"n = .78;// mechanical efficiency\n",
+"LN = 3;// mean piston speed, [m/s]\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"r = 1/cut_off;// expansion ratio\n",
+"Pm = P/r*(1+log(r))-Pb;// mean effective pressure, [MN/m^2]\n",
+"P_ind = P_req/n;// Actual indicated power developed, [kW]\n",
+"P_the = P_ind/k;// Theoretical indicated power developed, [kW]\n",
+"\n",
+"// using indicated_power=Pm*LN*A\n",
+"// Hence\n",
+"A = P_the/(Pm*LN)*10^-3;// piston area,[m^2]\n",
+"d = sqrt(4*A/%pi)*10^3;// bore ,[mm]\n",
+"mprintf('\n (a) The bore of the cylinder is = %f mm\n',d);\n",
+"\n",
+"// (b)\n",
+"// given that stroke is 1.25 times bore\n",
+"L = 1.25*d;// [mm]\n",
+"mprintf('\n (b) The piston stroke is = %f mm\n',L);\n",
+"\n",
+"// (c)\n",
+"// LN=mean piston speed, where L is stroke in meter and N is 2*rev/s,(since engine is double_acting)\n",
+"// hence\n",
+"rev_per_sec = LN/(2*L*10^-3);// [rev/s]\n",
+"\n",
+"rev_per_min = rev_per_sec*60;// [rev/min]\n",
+"mprintf('\n (c) The speed of the engine is = %f rev/min\n',rev_per_min);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.2: diameter_and_stroke.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.2')\n",
+"\n",
+"// aim : To determine the \n",
+"// (a) the diameter of the cylinder\n",
+"// (b) piston stroke\n",
+"// (c) actual steam consumption and indicated thermal efficiency\n",
+"\n",
+"// Given values\n",
+"P = 900;// inlet pressure, [kN/m^2]\n",
+"Pb = 140;// exhaust pressure, [kN/m^2]\n",
+"cut_off =.4;// [stroke]\n",
+"k = .8;// diagram factor\n",
+"rs = 1.2;// stroke to bore ratio\n",
+"N = 4;// engine speed, [rev/s]\n",
+"ip = 22.5;// power output from the engine, [kW]\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"r = 1/cut_off;// expansion ratio\n",
+"Pm = P/r*(1+log(r))-Pb;// mean effective pressure, [kN/m^2]\n",
+"Pm = Pm*k;// actual mean effective pressure, [kN/m^2]\n",
+"\n",
+"// using ip=Pm*L*A*N\n",
+"// and L=r*d; where L is stroke and d is bore\n",
+"d = (ip/(Pm*rs*%pi/4*2*N))^(1/3);// diameter of the cylinder, [m]\n",
+"\n",
+"mprintf('\n (a) The diameter of the cylinder is = %f mm\n',d*1000);\n",
+"\n",
+"// (b)\n",
+"L = rs*d;// stroke, [m]\n",
+"mprintf('\n (b) The piston stroke is = %f mm\n',L*1000);\n",
+"\n",
+"// (c)\n",
+"SV = %pi/4*d^2*L;// stroke volume, [m^3]\n",
+"V = SV*cut_off*2*240*60;// volume of steam consumed per hour, [m^3]\n",
+"v = .2148;// specific volume at 900 kN/m^2, [m^3/kg]\n",
+"SC = V/v;// steam consumed/h, [kg]\n",
+"ASC = 1.5*SC;// actual steam consumption/h, [kg]\n",
+"mprintf('\n (c) The actual steam consumption/h is = %f kg\n',ASC);\n",
+"\n",
+"m_dot = ASC/3600;// steam consumption,[kg/s] \n",
+"// from steam table\n",
+"hg = 2772.1;// specific enthalpy of inlet steam, [kJ/kg]\n",
+"hfe = 458.4;// specific liquid enthalpy at exhaust pressure, [kJ/kg]\n",
+"\n",
+"ITE = ip/(m_dot*(hg-hfe));// indicated thermal efficiency\n",
+"mprintf('\n The indicated thermal efficiency is = %f percent\n',ITE*100);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.3: diagram_factor_and_indicated_thermal_efficiency.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.3');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) the diagram factor\n",
+"// (b) the indicated thermal efficiency of the engine\n",
+"\n",
+"// given values\n",
+"d = 250*10^-3;// cylinder diameter, [m]\n",
+"L = 375*10^-3;// length of stroke, [m]\n",
+"P = 1000;// steam pressure , [kPa]\n",
+"x = .96;// dryness fraction of steam\n",
+"Pb = 55;// exhaust pressure, [kPa]\n",
+"r = 6;// expansion ratio\n",
+"ip = 45;// indicated power developed, [kW]\n",
+"N = 3.5;// speed of engine, [rev/s]\n",
+"m = 460;// steam consumption, [kg/h]\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"Pm = P/r*(1+log(r))-Pb;// [kN/m^3]\n",
+"A = %pi*(d)^2/4;// area, [m^2]\n",
+"tip = Pm*L*A*N*2;// theoretical indicated power, [kW]\n",
+"k = ip/tip;// diagram factor\n",
+"mprintf('\n (a) The diagram factor is = %f\n',k);\n",
+"\n",
+"// (b)\n",
+"// from steam table at 1 MN/m^2\n",
+"hf = 762.6;// [kJ/kg]\n",
+"hfg = 2013.6;// [kJ/kg]\n",
+"// so \n",
+"h1 = hf+x*hfg;// specific enthalpy of steam at 1MN/m^2, [kJ/kg]\n",
+"// minimum specific enthalpy in engine at 55 kPa \n",
+"hf = 350.6;// [kJ/kg]\n",
+"// maximum energy available in engine is\n",
+"h = h1-hf;// [kJ/kg]\n",
+"ITE = ip/(m*h/3600)*100;// indicated thermal efficiency\n",
+"mprintf('\n (b) The indicated thermal efficiency is = %f percent\n ',ITE);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.4: steam_consumption.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.4');\n",
+"\n",
+"// aim : To determine\n",
+"// steam consumption\n",
+"\n",
+"// given values\n",
+"P1 = 11;// power, [kW]\n",
+"m1 = 276;// steam use/h when developing power P1,[kW]\n",
+"ip = 8;// indicated power output, [kW]\n",
+"B = 45;// steam used/h at no load, [kg]\n",
+"\n",
+"// solution\n",
+"// using graph of Fig.11.9 \n",
+"A = (m1-B)/P1;// slop of line, [kg/kWh]\n",
+"W = A*ip+B;// output, [kg/h]\n",
+"mprintf('\n The steam consumption is = %f kg/h\n ',W);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.5: pressure_power_output_and_steam_consumption.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.5');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) the intermediate pressure\n",
+"// (b) the indicated power output\n",
+"// (c) the steam consumption of the engine\n",
+"\n",
+"// given values\n",
+"P1 = 1400;// initial pressure, [kN/m^2]\n",
+"x = .9;// dryness fraction\n",
+"P5 = 35;// exhaust pressure\n",
+"k = .8;// diagram factor of low-pressure cylindaer\n",
+"L = 350*10^-3;// stroke of both the cylinder, [m]\n",
+"dhp = 200*10^-3;// diameter of high pressure cylinder, [m]\n",
+"dlp = 300*10^-3;// diameter of low-pressure cylinder, [m]\n",
+"N = 300;// engine speed, [rev/min]\n",
+"\n",
+"// solution\n",
+"// taking reference Fig.11.13\n",
+"Ahp = %pi/4*dhp^2;// area of high-pressure cylinder, [m^2]\n",
+"Alp = %pi/4*dlp^2;// area of low-pressure cylinder, [m^2]\n",
+"// for equal initial piston loads\n",
+"// (P1-P7)Ahp=(P7-P5)Alp\n",
+"deff('[x]=f(P7)','x=(P1-P7)*Ahp-(P7-P5)*Alp');\n",
+"P7 = fsolve(0,f);// intermediate pressure, [kN/m^2]\n",
+"mprintf('\n (a) The intermediate pressure is = %f kN/m^2\n ',P7);\n",
+"\n",
+"// (b)\n",
+"V6 = Ahp*L;// volume of high-pressure cylinder, [m^3]\n",
+"P2 = P1;\n",
+"P6 = P7;\n",
+"// using P2*V2=P6*V6\n",
+"V2 = P6*V6/P2; // [m^3]\n",
+"V1 = Alp*L;// volume of low-pressure cylinder, [m^3]\n",
+"R = V1/V2;// expansion ratio\n",
+"Pm = P1/R*(1+log(R))-P5;// effective pressure of low-pressure cylinder, [kn/m^2]\n",
+"Pm = k*Pm;// actual effective pressure, [kN/m^2]\n",
+"ip = Pm*L*Alp*N*2/60;// indicated power, [kW]\n",
+"mprintf('\n (b) The indicated power is = %f kW\n',ip);\n",
+"\n",
+"// (c) \n",
+"COV = V1/ R;// cut-off volume in high-pressure cylinder, [m^3]\n",
+"V = COV*N*2*60;// volume of steam admitted/h\n",
+"// from steam table\n",
+"vg = .1407;// [m^3/kg]\n",
+"AV = x*vg;// specific volume of admission steam, [m^3/kg]\n",
+"m = V/AV;// steam consumption, [kg/h]\n",
+"mprintf('\n (c) The steam consumption of the engine is = %f kg/h\n',m);\n",
+"\n",
+"// End "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.6: power_output_diameter_and_intermediate_pressure.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.6');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) the indicated power output\n",
+"// (b) the diameter of high-pressure cylinder of the engine\n",
+"// (c) the intermediate pressure\n",
+"\n",
+"// given values\n",
+"P = 1100;// initial pressure, [kN/m^2]\n",
+"Pb = 28;// exhaust pressure\n",
+"k = .82;// diagram factor of low-pressure cylindaer\n",
+"L = 600*10^-3;// stroke of both the cylinder, [m]\n",
+"dlp = 600*10^-3;// diameter of low-pressure cylinder, [m]\n",
+"N = 4;// engine speed, [rev/s]\n",
+"R = 8;// expansion ratio\n",
+"\n",
+"// solution\n",
+"// taking reference Fig.11.13\n",
+"// (a)\n",
+"Pm = P/R*(1+log(R))-Pb;// effective pressure of low-pressure cylinder, [kn/m^2]\n",
+"Pm = k*Pm;// actual effective pressure, [kN/m^2]\n",
+"Alp = %pi/4*dlp^2;// area of low-pressure cylinder, [m^2]\n",
+"ip = Pm*L*Alp*N*2;// indicated power, [kW]\n",
+"mprintf('\n (a) The indicated power is = %f kW\n',ip);\n",
+"\n",
+"// (b)\n",
+"// work done by both cylinder is same as area of diagram\n",
+"w = Pm*Alp*L;// [kJ]\n",
+"W = w/2;// work done/cylinder, [kJ]\n",
+"V2 = Alp*L/8;// volume, [m63]\n",
+"P2 = P;// [kN/m^2]\n",
+"// using area A1267=P2*V2*log(V6/V2)=W\n",
+"V6 = V2*exp(W/(P2*V2));// intermediate volume, [m^3]\n",
+"// using Ahp*L=%pi/4*dhp^2*L=V6\n",
+"dhp = sqrt(V6*4/L/%pi);// diameter of high-pressure cylinder, [m]\n",
+"mprintf('\n (b) The diameter of high-pressure cylinder is = %f mm\n',dhp*1000);\n",
+"\n",
+"// (c)\n",
+"// using P2*V2=P6*V6\n",
+"P6 = P2*V2/V6; // intermediate pressure, [kN/m^2]\n",
+"mprintf('\n (c) The intermediate opressure is = %f kN/m^2\n',P6);\n",
+"\n",
+"// End "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.7: speed_and_diameter.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.7');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) The speed of the engine\n",
+"// (b) the diameter of the high pressure cylinder\n",
+"\n",
+"// given values\n",
+"ip = 230;// indicated power, [kW]\n",
+"P = 1400;// admission pressure, [kN/m^2]\n",
+"Pb = 35;// exhaust pressure, [kN/m^2]\n",
+"R = 12.5;// expansion ratio\n",
+"d1 = 400*10^-3;// diameter of low pressure cylinder, [m]\n",
+"L = 500*10^-3;// stroke of both the cylinder, [m]\n",
+"k = .78;// diagram factor\n",
+"rv = 2.5;// expansion ratio of high pressure cylinder\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"Pm = P/R*(1+log(R))-Pb;// mean effective pressure in low pressure cylinder, [kN/m^2]\n",
+"ipt = ip/k;// theoretical indicated power, [kw]\n",
+"// using ip=Pm*L*A*N\n",
+"A = %pi/4*d1^2;// area , [m^2]\n",
+"N = ipt/(Pm*L*A*2);// speed, [rev/s]\n",
+"mprintf('\n (a) The engine speed is = %f rev/s\n',N);\n",
+"\n",
+"// (b)\n",
+"Vl = A*L;// volume of low pressure cylinder, [m^3]\n",
+"COV = Vl/R;// cutt off volume of hp cylinder, [m^3]\n",
+"V = COV*rv;// total volume, [m^3]\n",
+"\n",
+"// V = %pi/4*d^2*L, so\n",
+"d = sqrt(4*V/%pi/L);// diameter of high pressure cylinder, [m]\n",
+"mprintf('\n (b) The diameter of the high pressure cylinder is = %f mm\n',d*1000);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.8: mean_effective_pressures_diagram_factor_and_indicated_power.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.8');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) the actual and hypothetical mean effective pressures referred to the low-pressure cylinder\n",
+"// (b) the overall diagram factor\n",
+"// (c) the indicated power \n",
+"\n",
+"// given values\n",
+"P = 1100;// steam supply pressure, [kN/m^2]\n",
+"Pb = 32;// back pressure, [kN/m^2]\n",
+"d1 = 300*10^-3;// cylinder1 diameter, [m]\n",
+"d2 = 600*10^-3;// cylinder2 diameter, [m]\n",
+"L = 400*10^-3;// common stroke of both cylinder, [m]\n",
+"\n",
+"A1 = 12.5;// average area of indicated diagram for HP, [cm^2]\n",
+"A2 = 11.4;// average area of indicated diagram for LP, [cm^2]\n",
+"\n",
+"P1 = 270;// indicator calibration, [kN/m^2/ cm]\n",
+"P2 = 80;// spring calibration, [kN/m^2/ cm]\n",
+"N = 2.7;// engine speed, [rev/s]\n",
+"l = .75;// length of both diagram, [m]\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"// for HP cylinder\n",
+"Pmh = P1*A1/7.5;// [kN/m^2]\n",
+"F = Pmh*%pi/4*d1^2;// force on HP, [kN]\n",
+"PmH = Pmh*(d1/d2)^2;// pressure referred to LP cylinder, [kN/m^2]\n",
+"PmL = P2*A2/7.5;// pressure for LP cylinder, [kN/m^2]\n",
+"PmA = PmH+PmL;// actual effective pressure referred to LP cylinder, [kN/m^2]\n",
+"\n",
+"Ah = %pi/4*d1^2;// area of HP cylinder, [m^2]\n",
+"Vh = Ah*L;// volume of HP cylinder, [m^3]\n",
+"CVh = Vh/3;// cut-off volume of HP cylinder, [m^3]\n",
+"Al = %pi/4*d2^2;// area of LP cylinder, [m^2]\n",
+"Vl = Al*L;// volume of LP cylinder, [m^3]\n",
+"\n",
+"R = Vl/CVh;// expansion ratio\n",
+"Pm = P/R*(1+log(R))-Pb;// hypothetical mean effective pressure referred to LP cylinder, [kN/m^2]\n",
+"\n",
+"mprintf('\n (a) The actual mean effective pressure referred to LP cylinder is = %f kN/m^2\n',PmA);\n",
+"mprintf('\n The hypothetical mean effective pressure referred to LP cylinder is = %f kN/m^2\n',Pm);\n",
+"\n",
+"// (a)\n",
+"ko = PmA/Pm;// overall diagram factor\n",
+"mprintf('\n (b) The overall diagram factor is = %f\n',ko);\n",
+"\n",
+"// (c) \n",
+"ip = PmA*L*Al*N*2;// indicated power, [kW]\n",
+"mprintf('\n (c) The indicated power is = %f kW\n',ip);\n",
+"\n",
+"// End"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.9: EX11_9.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear;\n",
+"clc;\n",
+"disp('Example 11.9');\n",
+"\n",
+"// aim : To determine\n",
+"// (a) the actual and hypothetical mean effective pressures referred to the low-pressure cylinder\n",
+"// (b) the overall diagram factor\n",
+"// (c) the pecentage of the total indicated power developed in each cylinder\n",
+"\n",
+"// given values\n",
+"P = 1400;// steam supply pressure, [kN/m^2]\n",
+"Pb = 20;// back pressure, [kN/m^2]\n",
+"Chp = .6;// cut-off in HP cylinder, [stroke]\n",
+"dh = 300*10^-3;// HP diameter, [m]\n",
+"di = 500*10^-3;// IP diameter, [m]\n",
+"dl = 900*10^-3;// LP diameter, [m]\n",
+"\n",
+"Pm1 = 590;// actual pressure of HP cylinder, [kN/m^2]\n",
+"Pm2 = 214;// actual pressure of IP cylinder, [kN/m^2]\n",
+"Pm3 = 88;// actual pressure of LP cylinder, [kN/m^2]\n",
+"\n",
+"// solution\n",
+"// (a)\n",
+"// for HP cylinder\n",
+"PmH = Pm1*(dh/dl)^2;// PmH referred to LP cylinder, [kN/m^2]\n",
+"// for IP cylinder\n",
+"PmI = Pm2*(di/dl)^2;// PmI referred to LP cylinder, [kN/m^2]\n",
+"PmA = PmH+PmI+Pm3;// actual mean effective pressure referred to LP cylinder, [kN/m^2]\n",
+"\n",
+"R = dl^2/(dh^2*Chp);// expansion ratio\n",
+"Pm = P/R*(1+log(R))-Pb;// hypothetical mean effective pressure referred to LP cylinder, [kN/m^2]\n",
+"\n",
+"mprintf('\n (a) The actual mean effective pressure referred to LP cylinder is = %f kN/m^2\n',PmA);\n",
+"mprintf('\n The hypothetical mean effective pressure referred to LP cylinder is = %f kN/m^2\n',Pm);\n",
+"\n",
+"// (b)\n",
+"ko = PmA/Pm;// overall diagram factor\n",
+"mprintf('\n (b) The overall diagram factor is = %f\n',ko);\n",
+"\n",
+"// (c)\n",
+"HP = PmH/PmA*100;// %age of indicated power developed in HP\n",
+"IP = PmI/PmA*100; // %age of indicated power developed in IP\n",
+"LP = Pm3/PmA*100; // %age of indicated power developed in LP\n",
+"mprintf('\n (c) The pecentage of the total indicated power developed in HP cylinder is = %f percent\n',HP);\n",
+"mprintf('\n The pecentage of the total indicated power developed in IP cylinder is = %f percent\n',IP);\n",
+"mprintf('\n The pecentage of the total indicated power developed in LP cylinder is = %f percent\n',LP);\n",
+"\n",
+"// End"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
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generated by cgit (git 2.34.1) at 2024-12-20 10:13:14 +0000