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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 17 - Engine and plant trails"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1: pg 589 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.1\n",
+ " The Indicated power is (kW) = 26.2\n",
+ " The Brake power is (kW) = 22.0\n",
+ " The mechanical efficiency is (percent) = 837.0\n",
+ "Energy can be tabulated as :-\n",
+ "----------------------------------------------------------------------------------------------------\n",
+ " kJ/s Percentage \n",
+ "----------------------------------------------------------------------------------------------------\n",
+ " Energy from fuel 88.0 100.0 \n",
+ " Energy to brake power 22.0 25.0 \n",
+ " Energy to coolant 20.7 23.5 \n",
+ " Energy to exhaust 33.6 38.2 \n",
+ " Energy to suroundings,etc. 11.8 13.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 589\n",
+ "print('Example 17.1');\n",
+ "\n",
+ "# aim : To determine\n",
+ "# the indicated and brake output and the mechanicl efficiency\n",
+ "# draw up an overall energy balance and as % age\n",
+ "import math\n",
+ "# given values\n",
+ "h = 21;# height of indicator diagram, [mm]\n",
+ "ic = 27;# indicator calibration, [kN/m**2 per mm]\n",
+ "sv = 14*10**-3;# swept volume of the cylinder;,[m**3]\n",
+ "N = 6.6;# speed of engine, [rev/s]\n",
+ "ebl = 77;# effective brake load, [kg]\n",
+ "ebr = .7;# effective brake radious, [m]\n",
+ "fc = .002;# fuel consumption, [kg/s]\n",
+ "CV = 44000;# calorific value of fuel, [kJ/kg]\n",
+ "cwc = .15;# cooling water circulation, [kg/s]\n",
+ "Ti = 38;# cooling water inlet temperature, [C]\n",
+ "To = 71;# cooling water outlet temperature, [C]\n",
+ "c = 4.18;# specific heat capacity of water, [kJ/kg]\n",
+ "eeg = 33.6;# energy to exhaust gases, [kJ/s]\n",
+ "g = 9.81;# gravitational acceleration, [m/s**2]\n",
+ "\n",
+ "# solution\n",
+ "PM = ic*h;# mean effective pressure, [kN/m**2]\n",
+ "LA = sv;# swept volume of the cylinder, [m**3]\n",
+ "ip = PM*LA*N/2;# indicated power,[kW]\n",
+ "T = ebl*g*ebr;# torque, [N*m]\n",
+ "bp = 2*math.pi*N*T;# brake power, [W]\n",
+ "n_mech = bp/ip;# mechanical efficiency\n",
+ "print ' The Indicated power is (kW) = ',round(ip,2)\n",
+ "print ' The Brake power is (kW) = ',round(bp*10**-3)\n",
+ "print ' The mechanical efficiency is (percent) = ',round(n_mech)\n",
+ "\n",
+ "ef = CV*fc;# energy from fuel, [kJ/s]\n",
+ "eb = bp*10**-3;# energy to brake power,[kJ/s]\n",
+ "ec = cwc*c*(To-Ti);# energy to coolant,[kJ/s]\n",
+ "es = ef-(eb+ec+eeg);# energy to surrounding,[kJ/s]\n",
+ "\n",
+ "print('Energy can be tabulated as :-');\n",
+ "print('----------------------------------------------------------------------------------------------------');\n",
+ "print(' kJ/s Percentage ')\n",
+ "print('----------------------------------------------------------------------------------------------------');\n",
+ "print ' Energy from fuel ',ef,' ',ef/ef*100,'\\n Energy to brake power ',round(eb),' ',round(eb/ef*100),'\\n Energy to coolant ',round(ec,1),' ',round(ec/ef*100,1),' \\n Energy to exhaust ',eeg,' ',round(eeg/ef*100,1),'\\n Energy to suroundings,etc. ',round(es,1),' ',round(es/ef*100,1)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2: pg 591"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.2\n",
+ " (a) The brake power is (kW) = 14.657\n",
+ " (b) The indicated power is (kW) = 18.2\n",
+ " (c) The mechanical efficiency is (percent) = 80.4\n",
+ " (d) The indicated thermal efficiency is (percent) = 12.94\n",
+ " (e) The brake steam consumption is (kg/kWh) = 13.75\n",
+ " (f) Energy supplied/min is (kJ) = 9092.0\n",
+ " Energy to bp/min is (kJ) = 879.0\n",
+ " Energy to condenser cooling water/min is (kJ) = 5196.0\n",
+ " Energy to condensate/min is (kJ) = 534.0\n",
+ " Energy to surrounding, etc/min is (kJ) = 2483.0\n",
+ "answer in the book is misprinted for Es\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 591\n",
+ "print('Example 17.2');\n",
+ "import math\n",
+ "# aim : To determine\n",
+ "# (a) bp\n",
+ "# (b) ip\n",
+ "# (c) mechanical efficiency\n",
+ "# (d) indicated thermal efficiency\n",
+ "# (e) brake specific steam consumption\n",
+ "# (f) draw up complete energy account for the test one-minute basis taking 0 C as datum\n",
+ "\n",
+ "# given values\n",
+ "d = 200.*10**-3;# cylinder diameter, [mm]\n",
+ "L = 250.*10**-3;# stroke, [mm]\n",
+ "N = 5.;# speed, [rev/s]\n",
+ "r = .75/2;# effective radious of brake wheel, [m]\n",
+ "Ps = 800.;# stop valve pressure, [kN/m**2]\n",
+ "x = .97;# dryness fraction of steam\n",
+ "BL = 136.;# brake load, [kg]\n",
+ "SL = 90.;# spring balance load, [N]\n",
+ "PM = 232.;# mean effective pressure, [kN/m**2]\n",
+ "Pc = 10.;# condenser pressure, [kN/m**2]\n",
+ "m_dot = 3.36;# steam consumption, [kg/min]\n",
+ "CC = 113.;# condenser cooling water, [kg/min]\n",
+ "Tr = 11.;# temperature rise of condenser cooling water, [K]\n",
+ "Tc = 38.;# condensate temperature, [C]\n",
+ "C = 4.18;# heat capacity of water, [kJ/kg K]\n",
+ "g = 9.81;# gravitational acceleration, [m/s**2]\n",
+ "\n",
+ "# solution\n",
+ "# from steam table\n",
+ "# at 800 kN/m**2\n",
+ "tf1 = 170.4;# saturation temperature, [C]\n",
+ "hf1 = 720.9;# [kJ/kg]\n",
+ "hfg1 = 2046.5;# [kJ/kg]\n",
+ "hg1 = 2767.5;# [kJ/kg]\n",
+ "vg1 = .2403;# [m**3/kg]\n",
+ "\n",
+ "# at 10 kN/m**2\n",
+ "tf2 = 45.8;# saturation temperature, [C]\n",
+ "hf2 = 191.8;# [kJ/kg]\n",
+ "hfg2 = 2392.9;# [kJ/kg]\n",
+ "hg2 = 2584.8;# [kJ/kg]\n",
+ "vg2 = 14.67;# [m**3/kg]\n",
+ "\n",
+ "# (a)\n",
+ "T = (BL*g-SL)*r;# torque, [Nm]\n",
+ "bp = 2*math.pi*N*T*10**-3;# brake power,[W]\n",
+ "print ' (a) The brake power is (kW) = ',round(bp,3)\n",
+ "\n",
+ "# (b)\n",
+ "A = math.pi*d**2/4;# area, [m**2]\n",
+ "ip = PM*L*A*N*2;# double-acting so*2, [kW]\n",
+ "print ' (b) The indicated power is (kW) = ',round(ip,1)\n",
+ "\n",
+ "# (c)\n",
+ "n_mec = bp/ip;# mechanical efficiency\n",
+ "print ' (c) The mechanical efficiency is (percent) = ',round(n_mec*100,1)\n",
+ "\n",
+ "# (d)\n",
+ "h = hf1+x*hfg1;# [kJ/kg]\n",
+ "hf = hf2;\n",
+ "ITE = ip/((m_dot/60)*(h-hf));# indicated thermal efficiency\n",
+ "print ' (d) The indicated thermal efficiency is (percent) = ',round(ITE*100,2)\n",
+ "# (e)\n",
+ "Bsc=m_dot*60/bp;# brake specific steam consumption, [kg/kWh]\n",
+ "print ' (e) The brake steam consumption is (kg/kWh) = ',round(Bsc,2)\n",
+ "\n",
+ "# (f)\n",
+ "# energy balanvce reckoned from 0 C\n",
+ "Es = m_dot*h;# energy supplied, [kJ]\n",
+ "Eb = bp*60;# energy to bp, [kJ]\n",
+ "Ecc = CC*C*Tr;# energy to condensate cooling water, [kJ]\n",
+ "Ec = m_dot*C*Tc;# energy to condensate, [kJ]\n",
+ "Ese = Es-Eb-Ecc-Ec;# energy to surrounding,etc, [kJ]\n",
+ "\n",
+ "print ' (f) Energy supplied/min is (kJ) = ',round(Es)\n",
+ "\n",
+ "print ' Energy to bp/min is (kJ) = ',round(Eb)\n",
+ "print ' Energy to condenser cooling water/min is (kJ) = ',round(Ecc)\n",
+ "print ' Energy to condensate/min is (kJ) = ',round(Ec)\n",
+ "print ' Energy to surrounding, etc/min is (kJ) = ',round(Ese)\n",
+ "\n",
+ "print 'answer in the book is misprinted for Es'\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3: pg 593"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.3\n",
+ " (a) The Brake power is (kW) = 60.5\n",
+ " (b) The brake specific fuel consumption is (kg/kWh) = 0.309\n",
+ " (c) The indicated thermal efficiency is (percent) = 33.2\n",
+ " (d) Energy from fuel is (kJ) = 13184.0\n",
+ " Energy to brake power is (kJ) = 3629.0\n",
+ " Energy to cooling water is (kJ) = 4038.0\n",
+ " Energy to exhaust is (kJ) = 3739.0\n",
+ " Energy to surrounding, etc is (kJ) = 1778.0\n",
+ "The answer is a bit different due to rounding off error in textbook\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 593\n",
+ "print('Example 17.3');\n",
+ "\n",
+ "# aim : To determine\n",
+ "# (a) the brake power\n",
+ "# (b) the brake specific fuel consumption\n",
+ "# (c) the indicated thermal efficiency\n",
+ "# (d) the energy balance, expressing the various items\n",
+ "import math\n",
+ "# given values\n",
+ "t = 30.;# duration of trial, [min]\n",
+ "N = 1750.;# speed of engine, [rev/min]\n",
+ "T = 330.;# brake torque, [Nm]\n",
+ "mf = 9.35;# fuel consumption, [kg]\n",
+ "CV = 42300.;# calorific value of fuel, [kJ/kg]\n",
+ "cwc = 483.;# jacket cooling water circulation, [kg]\n",
+ "Ti = 17.;# inlet temperature, [C]\n",
+ "To = 77.;# outlet temperature, [C]\n",
+ "ma = 182.;# air consumption, [kg]\n",
+ "Te = 486.;# exhaust temperature, [C]\n",
+ "Ta = 17.;# atmospheric temperature, [C]\n",
+ "n_mec = .83;# mechanical efficiency\n",
+ "c = 1.25;# mean specific heat capacity of exhaust gas, [kJ/kg K]\n",
+ "C = 4.18;# specific heat capacity, [kJ/kg K]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "bp = 2*math.pi*N*T/60*10**-3;# brake power, [kW]\n",
+ "print ' (a) The Brake power is (kW) = ',round(bp,1)\n",
+ "\n",
+ "# (b)\n",
+ "bsf = mf*2/bp;#brake specific fuel consumption, [kg/kWh]\n",
+ "print ' (b) The brake specific fuel consumption is (kg/kWh) = ',round(bsf,3)\n",
+ "\n",
+ "# (c)\n",
+ "ip = bp/n_mec;# indicated power, [kW]\n",
+ "ITE = ip/(2*mf*CV/3600);# indicated thermal efficiency\n",
+ "print ' (c) The indicated thermal efficiency is (percent) = ',round(ITE*100,1)\n",
+ "\n",
+ "# (d)\n",
+ "# taking basis one minute \n",
+ "ef = CV*mf/30;# energy from fuel, [kJ]\n",
+ "eb = bp*60;# energy to brake power,[kJ]\n",
+ "ec = cwc/30*C*(To-Ti);# energy to cooling water,[kJ]\n",
+ "ee = (ma+mf)/30*c*(Te-Ta);# energy to exhaust, [kJ]\n",
+ "es = ef-(eb+ec+ee);# energy to surrounding,etc,[kJ]\n",
+ "\n",
+ "print ' (d) Energy from fuel is (kJ) = ',round(ef)\n",
+ "print ' Energy to brake power is (kJ) = ',round(eb)\n",
+ "print ' Energy to cooling water is (kJ) = ',round(ec)\n",
+ "print ' Energy to exhaust is (kJ) = ',round(ee)\n",
+ "print ' Energy to surrounding, etc is (kJ) = ',round(es)\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 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.4\n",
+ " (a) The indicated power of the engine is (kW) = 69.9\n",
+ " (b) The mechanical efficiency of the engine is (percent) = 74.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 594\n",
+ "print('Example 17.4');\n",
+ "\n",
+ "# aim : To determine\n",
+ "# (a) the indicated power of the engine\n",
+ "# (b) the mechanical efficiency of the engine\n",
+ "\n",
+ "# given values\n",
+ "bp = 52;# brake power output, [kW]\n",
+ "bp1 = 40.5;# brake power of cylinder cut1, [kW]\n",
+ "bp2 = 40.2;# brake power of cylinder cut2, [kW]\n",
+ "bp3 = 40.1;# brake power of cylinder cut3, [kW]\n",
+ "bp4 = 40.6;# brake power of cylinder cut4, [kW]\n",
+ "bp5 = 40.7;# brake power of cylinder cut5, [kW]\n",
+ "bp6 = 40.0;# brake power of cylinder cut6, [kW]\n",
+ "\n",
+ "# sollution\n",
+ "ip1 = bp-bp1;# indicated power of cylinder cut1, [kW]\n",
+ "ip2 = bp-bp2;# indicated power of cylinder cut2, [kW]\n",
+ "ip3 = bp-bp3;# indicated power of cylinder cut3, [kW]\n",
+ "ip4 = bp-bp4;# indicated power of cylinder cut4, [kW]\n",
+ "ip5 = bp-bp5;# indicated power of cylinder cut5, [kW]\n",
+ "ip6 = bp-bp6;# indicated power of cylinder cut6, [kW]\n",
+ "\n",
+ "ip = ip1+ip2+ip3+ip4+ip5+ip6;# indicated power of engine,[kW]\n",
+ "print ' (a) The indicated power of the engine is (kW) = ',ip\n",
+ "\n",
+ "# (b)\n",
+ "n_mec = bp/ip;# mechanical efficiency\n",
+ "print ' (b) The mechanical efficiency of the engine is (percent) = ',round(n_mec*100,1)\n",
+ "\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5: pg 595"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.5\n",
+ " The Brake power is (kW) = 29.3\n",
+ " The Indicated power is (kW) = 37.3\n",
+ " The mechanical efficiency is (percent) = 78.8\n",
+ "Energy can be tabulated as :-\n",
+ "----------------------------------------------------------------------------------------------------\n",
+ " kJ/s Percentage \n",
+ "----------------------------------------------------------------------------------------------------\n",
+ " Energy from fuel 135.3 100.0 \n",
+ " Energy to brake power 29.3 21.7 \n",
+ " Energy to exhaust 35.4 26.0 \n",
+ " Energy to coolant 44.5 32.9 \n",
+ " Energy to suroundings,etc. 26.1 19.3\n",
+ "there is minor variation in the result reported in the book due to rounding off error\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 595\n",
+ "print('Example 17.5');\n",
+ "\n",
+ "# aim : To determine\n",
+ "# the brake power,indicated power and mechanicl efficiency\n",
+ "# draw up an energy balance and as % age of the energy supplied\n",
+ "\n",
+ "# given values\n",
+ "N = 50.;# speed, [rev/s]\n",
+ "BL = 267.;# break load.,[N]\n",
+ "BL1 = 178.;# break load of cylinder cut1, [N]\n",
+ "BL2 = 187.;# break load of cylinder cut2, [N]\n",
+ "BL3 = 182.;# break load of cylinder cut3, [N]\n",
+ "BL4 = 182.;# break load of cylinder cut4, [N]\n",
+ "\n",
+ "FC = .568/130;# fuel consumption, [L/s]\n",
+ "s = .72;# specific gravity of fuel\n",
+ "CV = 43000;# calorific value of fuel, [kJ/kg]\n",
+ "\n",
+ "Te = 760;# exhaust temperature, [C]\n",
+ "c = 1.015;# specific heat capacity of exhaust gas, [kJ/kg K]\n",
+ "Ti = 18;# cooling water inlet temperature, [C]\n",
+ "To = 56;# cooling water outlet temperature, [C]\n",
+ "mw = .28;# cooling water flow rate, [kg/s]\n",
+ "Ta = 21;# ambient tempearture, [C]\n",
+ "C = 4.18;# specific heat capacity of cooling water, [kJ/kg K]\n",
+ "\n",
+ "# solution\n",
+ "bp = BL*N/455;# brake power of engine, [kW]\n",
+ "bp1 = BL1*N/455;# brake power of cylinder cut1, [kW]\n",
+ "i1 = bp-bp1;# indicated power of cylinder cut1, [kW]\n",
+ "bp2 = BL2*N/455;# brake power of cylinder cut2, [kW]\n",
+ "i2 = bp-bp2;# indicated power of cylinder cut2, [kW]\n",
+ "bp3 = BL3*N/455;# brake power of cylinder cut3, [kW]\n",
+ "i3 = bp-bp3;# indicated power of cylinder cut3, [kW]\n",
+ "bp4 = BL4*N/455;# brake power of cylinder cut4, [kW]\n",
+ "i4 = bp-bp4;# indicated power of cylinder cut4, [kW]\n",
+ "\n",
+ "ip = i1+i2+i3+i4;# indicated power of engine, [kW]\n",
+ "n_mec = bp/ip;# mechanical efficiency\n",
+ "\n",
+ "print ' The Brake power is (kW) = ',round(bp,1)\n",
+ "print ' The Indicated power is (kW) = ',round(ip,1)\n",
+ "print ' The mechanical efficiency is (percent) = ',round(n_mec*100,1)\n",
+ "\n",
+ "mf = FC*s;# mass of fuel/s, [kg]\n",
+ "ef = CV*mf;# energy from fuel/s, [kJ]\n",
+ "me = 15*mf;# mass of exhaust/s,[kg],(given in condition)\n",
+ "ee = me*c*(Te-Ta);# energy to exhaust/s,[kJ]\n",
+ "ec = mw*C*(To-Ti);# energy to cooling water/s,[kJ]\n",
+ "es = ef-(ee+ec+bp);# energy to surrounding,etc/s,[kJ]\n",
+ "\n",
+ "print('Energy can be tabulated as :-');\n",
+ "print('----------------------------------------------------------------------------------------------------');\n",
+ "print(' kJ/s Percentage ')\n",
+ "print('----------------------------------------------------------------------------------------------------');\n",
+ "print ' Energy from fuel ',round(ef,1),' ',ef/ef*100,'\\n Energy to brake power ',round(bp,1),' ',round(bp/ef*100.,1),'\\n Energy to exhaust ',round(ee,1),' ',round(ee/ef*100),'\\n Energy to coolant ',round(ec,1),' ',round(ec/ef*100,1),'\\n Energy to suroundings,etc. ',round(es,1),' ',round(es/ef*100,1)\n",
+ "\n",
+ "print 'there is minor variation in the result reported in the book due to rounding off error'\n",
+ "# End\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6: pg 596"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Example 17.6\n",
+ " (a) The brake power is (MW) = 23.719\n",
+ " (b) The fuel consumption is (tonne/h) = 4.74\n",
+ " (c) The brake thermal efficiency is (percent) = 42.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#pg 596\n",
+ "print('Example 17.6');\n",
+ "\n",
+ "# aim : To determine \n",
+ "# (a) the break power of engine\n",
+ "# (b) the fuel consumption of the engine\n",
+ "# (c) the brake thermal efficiency of the engine\n",
+ "import math\n",
+ "# given values\n",
+ "d = 850*10**-3;# bore , [m]\n",
+ "L = 2200*10**-3;# stroke, [m]\n",
+ "PMb = 15;# BMEP of cylinder, [bar]\n",
+ "N = 95./60;# speed of engine, [rev/s]\n",
+ "sfc = .2;# specific fuel oil consumption, [kg/kWh]\n",
+ "CV = 43000;# calorific value of the fuel oil, [kJ/kg]\n",
+ "\n",
+ "# solution\n",
+ "# (a)\n",
+ "A = math.pi*d**2/4;# area, [m**2]\n",
+ "bp = PMb*L*A*N*8/10;# brake power,[MW]\n",
+ "print ' (a) The brake power is (MW) = ',round(bp,3)\n",
+ "\n",
+ "# (b)\n",
+ "FC = bp*sfc;# fuel consumption, [kg/h]\n",
+ "print ' (b) The fuel consumption is (tonne/h) = ',round(FC,2)\n",
+ "\n",
+ "# (c)\n",
+ "mf = FC/3600;# fuel used, [kg/s]\n",
+ "n_the = bp/(mf*CV);# brake thermal efficiency\n",
+ "print ' (c) The brake thermal efficiency is (percent) = ',round(n_the*100)\n",
+ "\n",
+ "# End\n"
+ ]
+ }
+ ],
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