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diff --git a/Power_System_Engineering_by_S_Chakraborthy/40-HEATING_AND_WELDING.ipynb b/Power_System_Engineering_by_S_Chakraborthy/40-HEATING_AND_WELDING.ipynb new file mode 100644 index 0000000..7342e4c --- /dev/null +++ b/Power_System_Engineering_by_S_Chakraborthy/40-HEATING_AND_WELDING.ipynb @@ -0,0 +1,490 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 40: HEATING AND WELDING" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.1: Diameter_Length_and_Temperature_of_the_wire.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.1 :\n", +"// Page number 724-725\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"P = 15.0*10**3 // Power supplied(W)\n", +"V = 220.0 // Voltage(V)\n", +"T_w = 1000.0 // Temperature of wire(°C)\n", +"T_c = 600.0 // Temperature of charges(°C)\n", +"k = 0.6 // Radiatting efficiency\n", +"e = 0.9 // Emissivity\n", +"\n", +"// Calculations\n", +"rho = 1.016/10**6 // Specific resistance(ohm-m)\n", +"d_square = 4*rho*P/(%pi*V**2) // d^2 in terms of l\n", +"T_1 = T_w+273 // Absolute temperature(°C)\n", +"T_2 = T_c+273 // Absolute temperature(°C)\n", +"H = 5.72*10**4*k*e*((T_1/1000)**4-(T_2/1000)**4) // Heat produced(watts/sq.m)\n", +"dl = P/(%pi*H)\n", +"l = (dl**2/d_square)**(1.0/3) // Length of wire(m)\n", +"d = dl/l // Diameter of wire(m)\n", +"T_2_cold = 20.0+273 // Absolute temperature at the 20°C normal temperature(°C)\n", +"T_1_cold = (H/(5.72*10**4*k*e)+(T_2_cold/1000)**4)**(1.0/4)*1000 // Absolute temperature when charge is cold(°C)\n", +"T_1_c = T_1_cold-273 // Temperature when charge is cold(°C)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.1 : SOLUTION :-')\n", +"printf('\nDiameter of the wire, d = %.3f cm', d*100)\n", +"printf('\nLength of the wire, l = %.2f m', l)\n", +"printf('\nTemperature of the wire when charge is cold, T_1 = %.f°C absolute = %.f°C \n', T_1_cold,T_1_c)\n", +"printf('\nNOTE: Slight changes in the obtained answer from that of textbook is due to more precision here')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.2: Width_and_Length_of_nickel_chrome_strip.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.2 :\n", +"// Page number 725\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"P = 15.0*10**3 // Power supplied(W)\n", +"V = 220.0 // Voltage(V)\n", +"T_w = 1000.0 // Temperature of wire(°C)\n", +"T_c = 600.0 // Temperature of charges(°C)\n", +"k = 0.6 // Radiatting efficiency\n", +"e = 0.9 // Emissivity\n", +"thick = 0.25/1000 // Thickness of nickel-chrome strip(m)\n", +"\n", +"// Calculations\n", +"rho = 1.016/10**6 // Specific resistance(ohm-m)\n", +"R = V**2/P // Resistance(ohm)\n", +"l_w = R*thick/rho // Length of strip in terms of w\n", +"T_1 = T_w+273 // Absolute temperature(°C)\n", +"T_2 = T_c+273 // Absolute temperature(°C)\n", +"H = 5.72*10**4*k*e*((T_1/1000)**4-(T_2/1000)**4) // Heat produced(watts/sq.m)\n", +"wl = P/(2*H)\n", +"w = (wl/l_w)**0.5 // Width of nickel-chrome strip(m)\n", +"l = w*l_w // Length of nickel-chrome strip(m)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.2 : SOLUTION :-')\n", +"printf('\nWidth of nickel-chrome strip, w = %.3f cm', w*100)\n", +"printf('\nLength of nickel-chrome strip, l = %.1f m', l)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.3: Power_drawn_under_various_connections.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.3 :\n", +"// Page number 726-727\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"R = 50.0 // Resistance of each resistor in oven(ohm)\n", +"n = 6.0 // Number of resistance\n", +"V = 400.0 // Supply voltage(V)\n", +"tap = 50.0 // Auto-transformer tapping(%)\n", +"\n", +"// Calculations\n", +"// Case(a)(i)\n", +"P_a_i = n*V**2/R*10**-3 // Power consumption for 6 elements in parallel(kW)\n", +"// Case(a)(ii)\n", +"P_each_a_ii = V**2/(R+R)*10**-3 // Power consumption in each group of 2 resistances in series(kW)\n", +"P_a_ii = n/2*P_each_a_ii // Power consumption for 3 groups(kW)\n", +"// Case(b)(i)\n", +"V_b_i = V/3**0.5 // Supply voltage against each resistance(V)\n", +"P_each_b_i = 2*V_b_i**2/R*10**-3 // Power consumption in each branch(kW)\n", +"P_b_i = n/2*P_each_b_i // Power consumption for 2 elements in parallel in each phase(kW)\n", +"// Case(b)(ii)\n", +"V_b_ii = V/3**0.5 // Supply voltage to any branch(V)\n", +"P_each_b_ii = V_b_ii**2/(R+R)*10**-3 // Power consumption in each branch(kW)\n", +"P_b_ii = n/2*P_each_b_ii // Power consumption for 2 elements in series in each phase(kW)\n", +"// Case(c)(i)\n", +"P_each_c_i = V**2/(R+R)*10**-3 // Power consumption by each branch(kW)\n", +"P_c_i = n/2*P_each_c_i // Power consumption for 2 elements in series in each branch(kW)\n", +"// Case(c)(ii)\n", +"P_each_c_ii = 2*V**2/R*10**-3 // Power consumption by each branch(kW)\n", +"P_c_ii = n/2*P_each_c_ii // Power consumption for 2 elements in parallel in each branch(kW)\n", +"// Case(d)\n", +"V_d = V*tap/100 // Voltage under tapping(V)\n", +"ratio_V = V_d/V // Ratio of normal voltage to tapped voltage\n", +"loss = ratio_V**2 // Power loss in terms of normal power\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.3 : SOLUTION :-')\n", +"printf('\nCase(a): AC Single phase 400 V supply')\n", +"printf('\n Case(i) : Power consumption for 6 elements in parallel = %.1f kW', P_a_i)\n", +"printf('\n Case(ii): Power consumption for 3 groups in parallel with 2 element in series = %.1f kW', P_a_ii)\n", +"printf('\nCase(b): AC Three phase 400 V supply with star combination')\n", +"printf('\n Case(i) : Power consumption for 2 elements in parallel in each phase = %.1f kW', P_b_i)\n", +"printf('\n Case(ii): Power consumption for 2 elements in series in each phase = %.1f kW', P_b_ii)\n", +"printf('\nCase(c): AC Three phase 400 V supply with delta combination')\n", +"printf('\n Case(i) : Power consumption for 2 elements in series in each branch = %.1f kW', P_c_i)\n", +"printf('\n Case(ii): Power consumption for 2 elements in parallel in each branch = %.1f kW', P_c_ii)\n", +"printf('\nCase(d): Power loss will be %.2f of the values obtained as above with auto-transformer tapping', loss)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.4: Amount_of_energy_required_to_melt_brass.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.4 :\n", +"// Page number 728\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"w_brass = 1000.0 // Weight of brass(kg)\n", +"time = 1.0 // Time(hour)\n", +"heat_sp = 0.094 // Specific heat\n", +"fusion = 40.0 // Latent heat of fusion(kcal/kg)\n", +"T_initial = 24.0 // Initial temperature(°C)\n", +"melt_point = 920.0 // Melting point of brass(°C)\n", +"n = 0.65 // Efficiency\n", +"\n", +"// Calculations\n", +"heat_req = w_brass*heat_sp*(melt_point-T_initial) // Heat required to raise the temperature(kcal)\n", +"heat_mel = w_brass*fusion // Heat required for melting(kcal)\n", +"heat_total = heat_req+heat_mel // Total heat required(kcal)\n", +"energy = heat_total*1000*4.18/(10**3*3600*n) // Energy input(kWh)\n", +"power = energy/time // Power(kW)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.4 : SOLUTION :-')\n", +"printf('\nAmount of energy required to melt brass = %.f kWh', energy)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.5: EX40_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.5 :\n", +"// Page number 728-729\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"V_2 = 12.0 // Secondary voltage(V)\n", +"P = 30.0*10**3 // Power(W)\n", +"PF = 0.5 // Power factor\n", +"\n", +"// Calculations\n", +"I_2 = P/(V_2*PF) // Secondary current(A)\n", +"Z_2 = V_2/I_2 // Secondary impedance(ohm)\n", +"R_2 = Z_2*PF // Secondary resistance(ohm)\n", +"sin_phi = (1-PF**2)**0.5\n", +"X_2 = Z_2*sin_phi // Secondary reactance(ohm)\n", +"h = R_2/X_2\n", +"H_m = h // Height up to which the crucible should be filled to obtain maximum heating effect in terms of H_c\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.5 : SOLUTION :-')\n", +"printf('\nHeight up to which the crucible should be filled to obtain maximum heating effect, H_m = %.3f*H_c \n', H_m)\n", +"printf('\nNOTE: ERROR: Calculation mistake in textbook solution and P is 30 kW not 300 kW')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.6: Voltage_necessary_for_heating_and_Current_flowing_in_the_material.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.6 :\n", +"// Page number 732\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"l = 10.0 // Length of material(cm)\n", +"b = 10.0 // Breadth of material(cm)\n", +"t = 3.0 // Thickness of material(cm)\n", +"f = 20.0*10**6 // Frequency(Hz)\n", +"P = 400.0 // Power absorbed(W)\n", +"e_r = 5.0 // Relative permittivity\n", +"PF = 0.05 // Power factor\n", +"\n", +"// Calculations\n", +"e_0 = 8.854*10**-12 // Absolute permittivity\n", +"A = l*b*10**-4 // Area(Sq.m)\n", +"C = e_0*e_r*A/(t/100) // Capacitace of parallel plate condenser(F)\n", +"X_c = 1.0/(2*%pi*f*C) // Reactance of condenser(ohm)\n", +"phi = acosd(PF) // Φ(°)\n", +"R = X_c*tand(phi) // Resistance of condenser(ohm)\n", +"V = (P*R)**0.5 // Voltage necessary for heating(V)\n", +"I_c = V/X_c // Current flowing in the material(A)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.6 : SOLUTION :-')\n", +"printf('\nVoltage necessary for heating, V = %.f V', V)\n", +"printf('\nCurrent flowing in the material, I_c = %.2f A\n', I_c)\n", +"printf('\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here & approximation in textbook')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.7: Voltage_applied_across_electrodes_and_Current_through_the_material.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.7 :\n", +"// Page number 732-733\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"l = 4.0 // Length of material(cm)\n", +"b = 2.0 // Breadth of material(cm)\n", +"t = 1.0 // Thickness of material(cm)\n", +"l_e = 20.0 // Length of area(cm)\n", +"b_e = 2.0 // Breadth of area(cm)\n", +"dis = 1.6 // Distance of separation of electrode(cm)\n", +"f = 20.0*10**6 // Frequency(Hz)\n", +"P = 80.0 // Power absorbed(W)\n", +"e_r1 = 5.0 // Relative permittivity\n", +"e_r2 = 1.0 // Relative permittivity of air\n", +"PF = 0.05 // Power factor\n", +"\n", +"// Calculations\n", +"e_0 = 8.854*10**-12 // Absolute permittivity\n", +"A_1 = (l_e-l)*b_e*10**-4 // Area of one electrode(sq.m)\n", +"A_2 = l*b*10**-4 // Area of material under electrode(sq.m)\n", +"d = dis*10**-2 // Distance of separation of electrode(m)\n", +"d_1 = t*10**-2 // (m)\n", +"d_2 = (d-d_1) // (m)\n", +"C = e_0*((A_1*e_r2/d)+(A_2/((d_1/e_r1)+(d_2/e_r2)))) // Capacitance(F)\n", +"X_c = 1.0/(2*%pi*f*C) // Reactance(ohm)\n", +"phi = acosd(PF) // Φ(°)\n", +"R = X_c*tand(phi) // Resistance(ohm)\n", +"V = (P*R)**0.5 // Voltage applied across electrodes(V)\n", +"I_c = V/X_c // Current through the material(A)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.7 : SOLUTION :-')\n", +"printf('\nVoltage applied across electrodes, V = %.f V', V)\n", +"printf('\nCurrent through the material, I_c = %.1f A\n', I_c)\n", +"printf('\nNOTE: ERROR: Calculation mistake in the textbook solution')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40.8: Time_taken_to_melt_Power_factor_and_Electrical_efficiency_of_the_furnace.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART IV : UTILIZATION AND TRACTION\n", +"// CHAPTER 2: HEATING AND WELDING\n", +"\n", +"// EXAMPLE : 2.8 :\n", +"// Page number 736-737\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"weight = 3000.0 // Weight of steel(kg)\n", +"I = 5000.0 // Current(A)\n", +"V_arc = 60.0 // Arc voltage(V)\n", +"R_t = 0.003 // Resistance of transformer(ohm)\n", +"X_t = 0.005 // Reactance of transformer(ohm)\n", +"heat_sp = 0.12 // Specific heat of steel\n", +"heat_latent = 8.89 // Latent heat of steel(kilo-cal/kg)\n", +"t_2 = 1370.0 // Melting point of steel(°C)\n", +"t_1 = 18.0 // Initial temperature of steel(°C)\n", +"n = 0.6 // Overall efficiency\n", +"\n", +"// Calculations\n", +"R_arc_phase = V_arc/I // Arc resistance per phase(ohm)\n", +"IR_t = I*R_t // Voltage drop across resistance(V)\n", +"IX_t = I*X_t // Voltage drop across reactance(V)\n", +"V = ((V_arc+IR_t)**2+IX_t**2)**0.5 // Voltage(V)\n", +"PF = (V_arc+IR_t)/V // Power factor\n", +"heat_kg = (t_2-t_1)*heat_sp+heat_latent // Amount of heat required per kg of steel(kcal)\n", +"heat_total = weight*heat_kg // Heat for 3 tonnes(kcal)\n", +"heat_actual_kcal = heat_total/n // Actual heat required(kcal)\n", +"heat_actual = heat_actual_kcal*1.162*10**-3 // Actual heat required(kWh)\n", +"P_input = 3*V*I*PF*10**-3 // Power input(kW)\n", +"time = heat_actual/P_input*60 // Time required(min)\n", +"n_elect = 3*V_arc*I/(P_input*1000)*100 // Electrical efficiency(%)\n", +"\n", +"// Results\n", +"disp('PART IV - EXAMPLE : 2.8 : SOLUTION :-')\n", +"printf('\nTime taken to melt 3 metric tonnes of steel = %.f minutes', time)\n", +"printf('\nPower factor of the furnace = %.2f ', PF)\n", +"printf('\nElectrical efficiency of the furnace = %.f percent\n', n_elect)\n", +"printf('\nNOTE: ERROR: Calculation and substitution mistake in the textbook solution')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |