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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 14 - Air and gas compressors"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1: pg 400"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.1\n",
+ " (a) The free air delivered is (m^3/min) = 3.814\n",
+ " (b) The volumetric efficiency is (percent) = 80.9\n",
+ " (c) The air delivery temperature is (C) = 164.3\n",
+ " (d) The cycle power is (kW) = 14.0\n",
+ " (e) The isothermal efficiency neglecting clearence is (percent) = 81.3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 400\n",
+ "print(' Example 14.1');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# (a) the free air delivered\n",
+ "# (b) the volumetric efficiency\n",
+ "# (c) the air delivery temperature\n",
+ "# (d) the cycle power\n",
+ "# (e) the isothermal efficiency\n",
+ "from math import pi,log\n",
+ "# given values\n",
+ "d = 200.*10**-3;# bore, [m]\n",
+ "L = 300.*10**-3;# stroke, [m]\n",
+ "N = 500.;# speed, [rev/min]\n",
+ "n = 1.3;# polytropic index\n",
+ "P1 = 97.;# intake pressure, [kN/m**2]\n",
+ "T1 = 273.+20;# intake temperature, [K]\n",
+ "P3 = 550.;# compression pressure, [kN/m**2]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "P4 = P1;\n",
+ "P2 = P3;\n",
+ "Pf = 101.325;# free air pressure, [kN/m**2]\n",
+ "Tf = 273+15;# free air temperature, [K]\n",
+ "SV = pi/4*d**2*L;# swept volume, [m**3]\n",
+ "V3 = .05*SV;# [m**3]\n",
+ "V1 = SV+V3;# [m**3]\n",
+ "V4 = V3*(P3/P4)**(1/n);# [m**3]\n",
+ "ESV = (V1-V4)*N;# effective swept volume/min, [m**3]\n",
+ "# using PV/T=constant\n",
+ "Vf = P1*ESV*Tf/(Pf*T1);# free air delivered, [m**3/min]\n",
+ "print ' (a) The free air delivered is (m^3/min) = ',round(Vf,3)\n",
+ "\n",
+ "# (b)\n",
+ "VE = Vf/(N*(V1-V3));# volumetric efficiency\n",
+ "print ' (b) The volumetric efficiency is (percent) = ',round(VE*100,1)\n",
+ "\n",
+ "# (c)\n",
+ "T2 = T1*(P2/P1)**((n-1)/n);# free air temperature, [K]\n",
+ "print ' (c) The air delivery temperature is (C) = ',round(T2-273,1)\n",
+ "\n",
+ "# (d)\n",
+ "CP = n/(n-1)*P1*(V1-V4)*((P2/P1)**((n-1)/n)-1)*N/60;# cycle power, [kW]\n",
+ "print ' (d) The cycle power is (kW) = ',round(CP)\n",
+ "\n",
+ "# (e)\n",
+ "# neglecting clearence\n",
+ "W = n/(n-1)*P1*V1*((P2/P1)**((n-1)/n)-1)\n",
+ "Wi = P1*V1*log(P2/P1);# isothermal efficiency\n",
+ "IE = Wi/W;# isothermal efficiency\n",
+ "print ' (e) The isothermal efficiency neglecting clearence is (percent) = ',round(IE*100,1)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2: pg 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.2\n",
+ " (a) The intermediate pressure is (MN/m^2) = 0.265\n",
+ " (b) The total volume of the HP cylinder is (litres) = 7.6\n",
+ " (c) The cycle power is (MW) = 43.0\n",
+ " there is rounding mistake in the book so answer is not matching\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 408\n",
+ "print(' Example 14.2');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# (a) the intermediate pressure\n",
+ "# (b) the total volume of each cylinder\n",
+ "# (c) the cycle power\n",
+ "from math import sqrt\n",
+ "# given values\n",
+ "v1 = .2;# air intake, [m^3/s]\n",
+ "P1 = .1;# intake pressure, [MN/m^2]\n",
+ "T1 = 273.+16;# intake temperature, [K]\n",
+ "P3 = .7;# final pressure, [MN/m^2]\n",
+ "n = 1.25;# compression index\n",
+ "N = 10;# speed, [rev/s]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "P2 = sqrt(P1*P3);# intermediate pressure, [MN/m^2]\n",
+ "print ' (a) The intermediate pressure is (MN/m^2) = ',round(P2,3)\n",
+ "\n",
+ "# (b)\n",
+ "V1 = v1/N;# total volume,[m^3]\n",
+ "# since intercooling is perfect so 2 lie on the isothermal through1, P1*V1=P2*V2\n",
+ "V2 = P1*V1/P2;# volume, [m^3]\n",
+ "print ' (b) The total volume of the HP cylinder is (litres) = ',round(V2*10**3,1)\n",
+ "\n",
+ "# (c)\n",
+ "CP = 2*n/(n-1)*P1*v1*((P2/P1)**((n-1)/n)-1);# cycle power, [MW]\n",
+ "print ' (c) The cycle power is (MW) = ',round(CP*10**3)\n",
+ "\n",
+ "print ' there is rounding mistake in the book so answer is not matching'\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3: pg 409"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.3\n",
+ " (a) The intermediate pressure is P2 (bar) = 2.466\n",
+ " The intermediate pressure is P3 (bar) = 6.082\n",
+ " (b) The effective swept volume of the LP cylinder is (litres) = 45.32\n",
+ " (c) The delivery temperature is (C) = 85.4\n",
+ " The delivery volume is (litres) = 3.72\n",
+ " (d) The work done per kilogram of air is (kJ) = 254.1\n",
+ "The answer is a bit different due to rounding off error in textbook\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 409\n",
+ "print(' Example 14.3');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# (a) the intermediate pressures\n",
+ "# (b) the effective swept volume of the LP cylinder\n",
+ "# (c) the temperature and the volume of air delivered per stroke at 15 bar\n",
+ "# (d) the work done per kilogram of air\n",
+ "import math\n",
+ "# given values\n",
+ "d = 450.*10**-3;# bore , [m]\n",
+ "L = 300.*10**-3;# stroke, [m]\n",
+ "cl = .05;# clearence\n",
+ "P1 = 1.; # intake pressure, [bar]\n",
+ "T1 = 273.+18;# intake temperature, [K]\n",
+ "P4 = 15.;# final delivery pressure, [bar]\n",
+ "n = 1.3;# compression and expansion index\n",
+ "R = .29;# gas constant, [kJ/kg K]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "k=(P4/P1)**(1./3); \n",
+ "# hence\n",
+ "P2 = k*P1;# intermediare pressure, [bar]\n",
+ "P3 = k*P2;# intermediate pressure, [bar]\n",
+ "\n",
+ "print ' (a) The intermediate pressure is P2 (bar) = ',round(P2,3)\n",
+ "print ' The intermediate pressure is P3 (bar) = ',round(P3,3)\n",
+ "\n",
+ "# (b)\n",
+ "SV = math.pi*d**2/4*L;# swept volume of LP cylinder, [m**3]\n",
+ "# hence\n",
+ "V7 = cl*SV;# volume, [m**3]\n",
+ "V1 = SV+V7;# volume, [m**3]\n",
+ "# also\n",
+ "P7 = P2;\n",
+ "P8 = P1;\n",
+ "V8 = V7*(P7/P8)**(1/n);# volume, [m**3]\n",
+ "ESV = V1-V8;# effective swept volume of LP cylinder, [m**3]\n",
+ "\n",
+ "print ' (b) The effective swept volume of the LP cylinder is (litres) = ',round(ESV*10**3,2)\n",
+ "\n",
+ "# (c)\n",
+ "T9 = T1;\n",
+ "P9 = P3;\n",
+ "T4 = T9*(P4/P9)**((n-1)/n);# delivery temperature, [K]\n",
+ "# now using P4*(V4-V5)/T4=P1*(V1-V8)/T1\n",
+ "V4_minus_V5 = P1*T4*(V1-V8)/(P4*T1);# delivery volume, [m**3]\n",
+ " \n",
+ "print ' (c) The delivery temperature is (C) = ',round(T4-273,1)\n",
+ "print ' The delivery volume is (litres) = ',round(V4_minus_V5*10**3,2)\n",
+ "\n",
+ "# (d)\n",
+ "\n",
+ "W = 3*n*R*T1*((P2/P1)**((n-1)/n)-1)/(n-1);# work done/kg ,[kJ]\n",
+ "print ' (d) The work done per kilogram of air is (kJ) = ',round(W,1)\n",
+ " \n",
+ "print 'The answer is a bit different due to rounding off error in textbook'\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4: pg 416"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.4\n",
+ " (a) The final temperature is (C) = 221.0\n",
+ " (b) The final pressure is (kN/m^2) = 500.0\n",
+ " (b) The energy required to drive the compressor is (kW) = -2023.0\n",
+ "The negative sign indicates energy input\n",
+ "The answer is a bit different due to rounding off error in textbook\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 416\n",
+ "print(' Example 14.4');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# (a) the final pressure and temperature\n",
+ "# (b) the energy required to drive the compressor\n",
+ "\n",
+ "# given values\n",
+ "rv = 5.;# pressure compression ratio\n",
+ "m_dot = 10.;# air flow rate, [kg/s]\n",
+ "P1 = 100.;# initial pressure, [kN/m**2]\n",
+ "T1 = 273.+20;# initial temperature, [K]\n",
+ "n_com = .85;# isentropic efficiency of compressor\n",
+ "Gama = 1.4;# heat capacity ratio\n",
+ "cp = 1.005;# specific heat capacity, [kJ/kg K]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "T2_prim = T1*(rv)**((Gama-1)/Gama);# temperature after compression, [K]\n",
+ "# using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
+ "T2 = T1+(T2_prim-T1)/n_com;# final temperature, [K]\n",
+ "P2 = rv*P1;# final pressure, [kN/m**2]\n",
+ "print ' (a) The final temperature is (C) = ',round(T2-273)\n",
+ "print ' (b) The final pressure is (kN/m^2) = ',P2\n",
+ "\n",
+ "# (b)\n",
+ "E = m_dot*cp*(T1-T2);# energy required, [kW]\n",
+ "print ' (b) The energy required to drive the compressor is (kW) = ',round(E)\n",
+ "if(E<0):\n",
+ " print('The negative sign indicates energy input');\n",
+ "else:\n",
+ " print('The positive sign indicates energy output');\n",
+ "\n",
+ "print 'The answer is a bit different due to rounding off error in textbook'\n",
+ " # End\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5: pg 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.5\n",
+ " The power absorbed by compressor is (kW) = 12.64\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 417\n",
+ "print(' Example 14.5');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# the power absorbed in driving the compressor\n",
+ "\n",
+ "# given values\n",
+ "FC = .68;# fuel consumption rate, [kg/min]\n",
+ "P1 = 93.;# initial pressure, [kN/m^2]\n",
+ "P2 = 200.;# final pressure, [kN/m^2]\n",
+ "T1 = 273.+15;# initial temperature, [K]\n",
+ "d = 1.3;# density of mixture, [kg/m^3]\n",
+ "n_com = .82;# isentropic efficiency of compressor\n",
+ "Gama = 1.38;# heat capacity ratio\n",
+ "\n",
+ "# solution\n",
+ "R = P1/(d*T1);# gas constant, [kJ/kg K]\n",
+ "# for mixture\n",
+ "cp = Gama*R/(Gama-1);# heat capacity, [kJ/kg K]\n",
+ "T2_prim = T1*(P2/P1)**((Gama-1)/Gama);# temperature after compression, [K]\n",
+ "# using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
+ "T2 = T1+(T2_prim-T1)/n_com;# final temperature, [K]\n",
+ "m_dot = FC*15/60.;# given condition, [kg/s]\n",
+ "P = m_dot*cp*(T2-T1);# power absorbed by compressor, [kW]\n",
+ "#results\n",
+ "print ' The power absorbed by compressor is (kW) = ',round(P,2)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6: pg 418"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.6\n",
+ " The power required to drive the blower is (kW) = 99.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 418\n",
+ "print(' Example 14.6');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# the power required to drive the blower\n",
+ "\n",
+ "# given values\n",
+ "m_dot = 1;# air capacity, [kg/s]\n",
+ "rp = 2;# pressure ratio\n",
+ "P1 = 1*10**5;# intake pressure, [N/m^2]\n",
+ "T1 = 273+70.;# intake temperature, [K]\n",
+ "R = .29;# gas constant, [kJ/kg k]\n",
+ "\n",
+ "# solution\n",
+ "V1_dot = m_dot*R*T1/P1*10**3;# [m^3/s]\n",
+ "P2 = rp*P1;# final pressure, [n/m^2]\n",
+ "P = V1_dot*(P2-P1);# power required, [W]\n",
+ "#results\n",
+ "print ' The power required to drive the blower is (kW) = ',round(P*10**-3,1)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7: pg 418"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.7\n",
+ " The power required to drive the vane pump is (kW) = 78.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 418\n",
+ "print(' Example 14.7');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# the power required to drive the vane pump\n",
+ "\n",
+ "# given values\n",
+ "m_dot = 1;# air capacity, [kg/s]\n",
+ "rp = 2;# pressure ratio\n",
+ "P1 = 1*10**5;# intake pressure, [N/m^2]\n",
+ "T1 = 273.+70;# intake temperature, [K]\n",
+ "Gama = 1.4;# heat capacity ratio\n",
+ "rv = .7;# volume ratio\n",
+ "\n",
+ "# solution\n",
+ "V1 = .995;# intake pressure(as given previous question),[m^3/s] \n",
+ "# using P1*V1^Gama=P2*V2^Gama, so\n",
+ "P2 = P1*(1/rv)**Gama;# pressure, [N/m^2]\n",
+ "V2 = rv*V1;# volume,[m^3/s]\n",
+ "P3 = rp*P1;# final pressure, [N/m^2]\n",
+ "P = Gama/(Gama-1)*P1*V1*((P2/P1)**((Gama-1)/Gama)-1)+V2*(P3-P2);# power required,[W]\n",
+ "#results\n",
+ "print ' The power required to drive the vane pump is (kW) = ',round(P*10**-3)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8: pg 420"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Example 14.8\n",
+ " The power required to drive compressor is (kW) = 54.6\n",
+ " The temperature in the engine is (C) = 109.19\n",
+ " The pressure in the engine cylinder is (kN/m^2) = 160.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 420\n",
+ "print(' Example 14.8');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# the total temperature and pressure of the mixture\n",
+ "\n",
+ "# given values\n",
+ "rp = 2.5;# static pressure ratio\n",
+ "FC = .04;# fuel consumption rate, [kg/min]\n",
+ "P1 = 60.;# inilet pressure, [kN/m^2]\n",
+ "T1 = 273.+5;# inilet temperature, [K]\n",
+ "n_com = .84;# isentropic efficiency of compressor\n",
+ "Gama = 1.39;# heat capacity ratio\n",
+ "C2 = 120.;#exit velocity from compressor, [m/s]\n",
+ "rm = 13.;# air-fuel ratio\n",
+ "cp = 1.005;# heat capacity ratio\n",
+ "\n",
+ "# solution\n",
+ "P2 = rp*P1;# given condition, [kN/m^2]\n",
+ "T2_prim = T1*(P2/P1)**((Gama-1)/Gama);# temperature after compression, [K]\n",
+ "# using isentropic efficiency=(T2_prim-T1)/(T2-T1)\n",
+ "T2 = T1+(T2_prim-T1)/n_com;# final temperature, [K]\n",
+ "m_dot = FC*(rm+1);# mass of air-fuel mixture, [kg/s]\n",
+ "P = m_dot*cp*(T2-T1);# power to drive compressor, [kW]\n",
+ "print ' The power required to drive compressor is (kW) = ',round(P,1)\n",
+ "\n",
+ "Tt2 = T2+C2**2/(2*cp*10**3);# total temperature,[K]\n",
+ "Pt2 = P2*(Tt2/T2)**(Gama/(Gama-1));# total pressure, [kN/m^2]\n",
+ "print ' The temperature in the engine is (C) = ',round(Tt2-273,2)\n",
+ "print ' The pressure in the engine cylinder is (kN/m^2) = ',round(Pt2,1)\n",
+ "\n",
+ "print ' There is rounding mistake in the book'\n",
+ "\n",
+ "\n",
+ "# End\n"
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