{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 12: Steam Engine"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, page no. 536"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"p1 = 0.2 #Pressure at which steam is supplied(in MPa):\n",
"T = 250 #Temperature of steam(in C):\n",
"p2 = 0.3 #Pressure upto which steam is expanded(in bar):\n",
"p3 = 0.05 #Pressure at which it is finally released(in bar):\n",
"\n",
"#From steam tables:\n",
"h1 = 2971 #kJ/kg\n",
"s1 = 7.7086 #kJ/kg.K\n",
"s2 = s1\n",
"h2 = 2601.97 #kJ/kg\n",
"v2 = 5.1767 #m**3/kg\n",
"hf = 137.82 #kJ/kg\n",
"Tmax = 393.23 #K\n",
"Tmin = 305.88 #K\n",
"\n",
"#Calculations:\n",
"W = h1-h2+v2*(p2-p3)*10**2 #Work output from engine cycle per kg of steam(in kJ/kg):\n",
"Q = h1-hf #Heat input per kg of steam(in kJ/kg):\n",
"n = W/Q*100 #Efficiency of modified Rankine cycle:\n",
"nc = (1-Tmin/Tmax)*100 #Carnot efficiency:\n",
"\n",
"#Results:\n",
"print \"Modified Rankine cycle efficiency: \",round(n,2),\"%\"\n",
"print \"Carnot efficiency: \",round(nc,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Modified Rankine cycle efficiency: 17.59 %\n",
"Carnot efficiency: 22.21 %\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, page no. 537"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration: \n",
"p1 = 10 #Pressure at which steam is supplied(in bar):\n",
"d = 0.3 #Diameter of the cylinder(in m):\n",
"L = 0.6 #Length of stroke(in m):\n",
"p2 = 0.75 #Pressure to which steam is expanded(in bar):\n",
"p3 = 0.25 #Pressure at which steam is released in the condensor(in bar):\n",
"#From steam tables:\n",
"h1 = 2676.2 #kJ/kg\n",
"s1 = 7.3614 #kJ/kg.K\n",
"v2 = 2.1833 #m**3/kg\n",
"h2 = 2628.35 #kJ/kg\n",
"h4 = 271.93 #kJ/kg\n",
"h6 = 2459.38 #kJ/kg\n",
"s6 = 7.3614 #kJ/kg.K\n",
"v6 = 5.784 #m**3/kg\n",
"\n",
"#Calculations:\n",
"s2 = s1\n",
"s6 = s2\n",
"W = h1-h2+v2*(p2-p3)*10**2 #Work output from engine cycle per kg of steam(in kJ/kg):\n",
"Q = h1-h4 #Heat input per kg of steam(in kJ/kg):\n",
"n = W/Q*100 #Efficiency of modified Rankine cycle:\n",
"V = pi*d**2*L/4 #Volume of the cylinder(in m**3):\n",
"m = V/v2 #Mass of steam in a stroke(in kg):\n",
"V1 = m*v6 #Volume requiremnet at 6(in m**3):\n",
"L1 = V1*4/(pi*d**2) #New stroke length(in m):\n",
"\n",
"#Results:\n",
"print \"Modified Rankine cycle efficiency: \",round(n,2),\"%\"\n",
"print \"New stroke length:\",round(L1*100,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Modified Rankine cycle efficiency: 6.53 %\n",
"New stroke length: 158.95 cm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, page no. 538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import log,pi\n",
"\n",
"#Variable Declaration: \n",
"d = 0.3 #Diameter of the bore(in m):\n",
"L = 0.6 #Length of the stroke(in m):\n",
"r1 = 0.4 #Occerance od cut-off:\n",
"p1 = 7.5 #Pressure at which steam enters(in bar):\n",
"p3 = 0.1 #Pressure at exhaust(in bar):\n",
"n = 180 #Rpm of the engine:\n",
"d1 = 0.6 #Diagram factor:\n",
"\n",
"#Calculations:\n",
"r = 1/r1 #Expansion ratio:\n",
"mep = p1/r*(1+log(r))-p3 #Hypothetical mean effective pressure(in bar):\n",
"mepa = mep*d1 #Actual mean effective pressure(in bar):\n",
"IP = mepa*L*pi*d**2*2*n*10**2/(4*60)#Indicated power(in kW):\n",
"\n",
"#Results:\n",
"print \"Indicated power: \",round(IP,2),\"kW\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Indicated power: 86.25 kW\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, page no. 539"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import log,pi\n",
"\n",
"#Variable Declaration: \n",
"p1 = 15 #Steam is admitted at pressure(in bar):\n",
"p3 = 0.75 #Pressure at which steam exhausts(in bar):\n",
"r1 = 0.25 #Cut-off occuring at:\n",
"P = 150 #Power produced by the engine(in hp):\n",
"n = 240 #Rpm of engine:\n",
"nm = 0.85#Mechanical efficiency:\n",
"d1 = 0.7 #Diagram factor:\n",
"nb = 0.2 #Brake thermal efficiency:\n",
"r2 = 1.5 #Stroke to bore ratio:\n",
"h15 = 2803.3 #From steam tables:\n",
"hf = 384.39\n",
"\n",
"#Calculations:\n",
"r = 1/r1 #Expansion ratio:\n",
"mep = p1/r*(1+log(r))-p3 #Hypothetical mean effective pressure(in bar):\n",
"mepa = mep*d1 #Actual mean effective pressure(in bar):\n",
"IP = P/nm #Indicated horse power(in kW):\n",
"d = ((IP*4*60*0.7457)/(mepa*10**2*r2*pi*n))**(1/3) #Diameter of bore(in m):\n",
"L = d*r2 #Stroke length(in m):\n",
"Q = h15-hf #Heat added per kg of steam(in kJ/kg):\n",
"m = 0.7457*3600/(nb*Q) #Specific steam consumption(in kg/hp.hr):\n",
"\n",
"#Results:\n",
"print \"Bore: \",round(d*100,2),\"cm\"\n",
"print \"Stroke: \",round(L*100,2),\"cm\"\n",
"print \"Specific steam consumption: \",round(m,2),\"kg/hp.hr\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bore: 36.51 cm\n",
"Stroke: 54.76 cm\n",
"Specific steam consumption: 5.55 kg/hp.hr\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, page no. 541"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import log,pi\n",
"\n",
"#Variable Declaration: \n",
"m = 18/60 #Steam consumption rate(in kg/a):\n",
"IP = 100 #Indicated power(in kW):\n",
"n = 240 #Rpm of engine:\n",
"d = 0.3 #Bore diameter(in m):\n",
"L = 0.4 #Stroke length(in m):\n",
"p1 = 10 #Pressure at which steam is admitted(in bar):\n",
"p3 = 0.75 #Exhaust pressure(in bar):\n",
"r1 = 0.25 #Occurance of cut-off:\n",
"h1 = 2875.3 #Enthalpy of steam(in kJ/kg):\n",
"hf = 384.39 \n",
"\n",
"#Calculations:\n",
"Q = h1-hf #Heat added per kg of steam(in kJ/kg):\n",
"r = 1/r1 #Expansion ratio:\n",
"mep = p1/r*(1+log(r))-p3 #Hypothetical mean effective pressure(in bar):\n",
"IPt = mep*L*pi*d**2*n*10**2/(60)#Theoretical indicated power(in kW):\n",
"d1 = IP/IPt #Diagarm factor:\n",
"n = IPt/(m*Q)*100 #Indicated thermal efficiency:\n",
"\n",
"#Results:\n",
"print \"Diagram factor: \",round(d1,4)\n",
"print \"Indicated thermal efficiency: \",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diagram factor: 0.4238\n",
"Indicated thermal efficiency: 31.58 %\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6, page no. 542"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import log\n",
"\n",
"#Variable Declaration: \n",
"p1 = 10 #Pressure at which steam is aupplied(in bar):\n",
"x = 0.9 #Dryness fraction:\n",
"p3 = 1 #Pressure at exhaust(in bar):\n",
"r1 = 0.6 #Occurence of cut-off:\n",
"#From steam tables:\n",
"h1 = 2576.58 #kJ/kg \n",
"v1 = 0.1751 #m**3/kg\n",
"hf = 417.46 #kJ/kg\n",
"\n",
"#Calculations:\n",
"Q = h1-hf #Heat added per kg of steam(in kJ/kg):\n",
"v2 = v1/r1 #Specific volume at state 2(inm**3/kg):\n",
"r = 1/r1 #Expansion ratio:\n",
"Wne = v1*(p1-p3)*10**2 #Net expansive work per kg of steam(in kJ/kg):\n",
"We = p1*v1*10**2*log(r)-p3*10**2*(v2-v1)#Expansive work per kg of steam(in kJ/kg):\n",
"Wt = Wne+We #Total work per kg of steam(in kJ/kg):\n",
"r2 = We/Wt*100 #Fraction of work obtained by expansive working:\n",
"n = Wt/Q*100 #Thermal efficiency of cycle:\n",
"\n",
"#Results:\n",
"print \"Fraction of expansive work: \",round(r2,2),\"% of total output\"\n",
"print \"Thermal efficiency: \",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Fraction of expansive work: 33.04 % of total output\n",
"Thermal efficiency: 10.9 %\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7, page no. 543"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import log,sqrt,pi\n",
"\n",
"#Variable Declaration: \n",
"P = 60 #Power produced(in bhp):\n",
"p1 = 12 #Pressure at which steam is admitted(in bar):\n",
"p3 = 1 #Pressure at exhaust(in bar):\n",
"n = 240 #Rpm of engine:\n",
"v = 2 #Piston speed(in m/s):\n",
"d = 0.04 #Diameter of piston(in m):\n",
"n = 0.60 #Occurence of cut-off:\n",
"r1 = 0.05 #Clearance volume to stroke volume ratio:\n",
"d1 = 0.8 #Diagram factor:\n",
"nm = 0.90 #Mechanical efficiency:\n",
"\n",
"#Calculations:\n",
"r = (1+r1)/n #Expansion ratio:\n",
"mep = (p1*12*(1+log(r))-1*21-(12-1))/(21-1) #Mean effective pressure(in bar):\n",
"mepa = mep*d1 #Actual mean effective pressure(in bar):\n",
"A = P*0.7457/(nm*mepa*10**2*v) #Effective area(in m**2):\n",
"D = sqrt((A-pi*d**2/4)*4/(2*pi)) #Bore diameter(in m):\n",
"\n",
"#Results:\n",
"print \"Bore: \",round(D*100,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bore: 14.05 cm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8, page no. 545"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import pi,log\n",
"\n",
"#Variable Declaration: \n",
"D = 0.2 #Diameter of cylinder(in m):\n",
"L = 0.3 #Length of stroke(in m):\n",
"Vc = 2*10**3 #Clearance volume(in cm**3):\n",
"ms = 0.05 #Mass of steam used per stroke(in kg):\n",
"c = 0.80 #Point at which compression starts:\n",
"p4 = 1 #Pressure of steam when compression starts(in bar):\n",
"r1 = 0.10 #Cut-off point:\n",
"r2 = 0.90 #Release:\n",
"p1 = 15 #Pressure at states 1 & 2(in bar):\n",
"#From steam tables:\n",
"v4 = 1.6940 #m**3/kg\n",
"vg15 = 0.13177 #m**3/kg\n",
"vg3 = 0.6058 #m**3/kg\n",
"u1 = 1590.79 #kJ/kg\n",
"u2 = 1216.73 #kJ/kg\n",
"\n",
"#Calculations:\n",
"p2 = 3\n",
"V6 = Vc*10**(-6) #Clearance volume(in m**3):\n",
"V5 = V6\n",
"Vs = pi*D**2/4*L #Stroke volume(in m**3):\n",
"V3 = V6+Vs #Volume at state 3(in m**3):\n",
"V4 = V3-c*(V3-V6) #Volume at state 4(in m**3):\n",
"m4 = V4/v4 #Mass of steam at state 4(in kg):\n",
"m = m4+ms #Total mass of steam during expansion(in kg):\n",
"V1 = V6+r1*(V3-V6) #Volume at cut-off point(in m**3):\n",
"x1 = V1/(m*vg15) #Dryness fraction at cut-off point:\n",
"V2 = V6+r2*(V3-V6) #Volume at point of release(in m**3):\n",
"x2 = V2/(m*vg3) #Dryness fraction at point of release:\n",
"n = log(p1/p2)/log(V2/V1) #Index of expansion:\n",
"W = (p1*V1-p2*V2)/(n-1)*100 #Work done in a stroke(in kJ):\n",
"Ws = W/m #Work done per kg of steam(in kJ/kg):\n",
"du = u2-u1 #Change in internal energy(in kJ/kg):\n",
"dQ = du-Ws #Heat transfer(in kJ/kg):\n",
"\n",
"#Results:\n",
"print \"Total mass of steam during expansion: \",round(m,6),\"kg\"\n",
"print \"Dryness fraction at cut-off and release: \",round(x1,4),round(x2,4)\n",
"print \"Heat leakage: \",round(-dQ,2),\"kJ/kg steam\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total mass of steam during expansion: 0.052293 kg\n",
"Dryness fraction at cut-off and release: 0.427 0.3309\n",
"Heat leakage: 465.0 kJ/kg steam\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9, page no. 547"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import pi\n",
"#Variable Declaration: \n",
"r1 = 0.3 #Point of sut-off:\n",
"p4 = 4 #Pressure at state 4(in bar):\n",
"V4 = 0.15 #Volume at state 4(in m**3):\n",
"p1 = 12 #Pressure at state 1(in m**3):\n",
"p2 = 5 #Pressure at release(in bar):\n",
"V2 = 0.5 #Indicated volume at release(in m**3):\n",
"d = 0.6 #Bore diameter(in m):\n",
"L = 1.20 #Stroke length(in m):\n",
"c = 0.10 #Clearance volume ratio:\n",
"ms = 1.5 #Mass of steam admitted(in kg/stroke):\n",
"nw = 180*60 #Number of working strokes(per second):\n",
"#From steam tables:\n",
"vg4 = 0.4625 #m**3/kg\n",
"vg12 = 0.16333 #m**3/kg\n",
"vg5 = 0.3749 #m**3/kg\n",
"\n",
"#Calculations:\n",
"Vs = pi*d**2/4*L #Stroke volume(in m**3):\n",
"V5 = c*Vs #Clearance volume(in m**3):\n",
"V3 = V5+Vs #Total volume of cylinder(in m**3):\n",
"V1 = V5+r1*Vs #Volume at cut-off point(in m**3):\n",
"m4 = V4/vg4 #Mass of steam at state 4(in kg):\n",
"m = m4+ms #Total mass during steam expansion(in kg):\n",
"x1 = V1/(m*vg12) #Dryness fraction at cut-off point:\n",
"mq1 = (m-m*x1)*nw #Missing quantity per hour(in kg):\n",
"x2 = V2/(m*vg5) #Dryness fraction at point of release:\n",
"mq2 = (m-m*x2)*nw #Missing quantity per hour(in kg):\n",
"P = (mq1-mq2)/mq1*100 #Percentage re-evaporation during expansion:\n",
"\n",
"#Results:\n",
"print \"Dryness fraction at cut-off: \",round(x1,3)\n",
"print \"Dryness fraction at release: \",round(x2,3)\n",
"print \"Missing quanity at cut off: \",round(mq1,2),\"kg/hr\"\n",
"print \"Missing quanity at release: \",round(mq2,2),\"kg/hr\"\n",
"print \"Percentage re-evaporation: \",round(P,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dryness fraction at cut-off: 0.455\n",
"Dryness fraction at release: 0.731\n",
"Missing quanity at cut off: 10728.59 kg/hr\n",
"Missing quanity at release: 5298.86 kg/hr\n",
"Percentage re-evaporation: 50.61 %\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10, page no. 549"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi,log\n",
"#Variable Declaration: \n",
"p1 = 1.5*10**3 #Pressure at which steam is supplied(in kPa):\n",
"x1 = 0.9 #Dryness fraction:\n",
"p4 = 40 #Pressure at exhaust(in kPa):\n",
"d1LP = 0.8 #Diagram factor reffered to LP cylinder:\n",
"L = 0.38 #Stroke length(in m):\n",
"dHP = 0.20 #Bore of HP cylinder(in m):\n",
"dLP = 0.30 #Bore of LP cylinder(in m):\n",
"N = 240 #Rpm of engine:\n",
"\n",
"#Calculations:\n",
"AHP = pi*(dHP**2)/4 #Area of HP cylinder(in m**2):\n",
"ALP = pi*(dLP**2)/4 #Area of LP cylinder(in m**2):\n",
"p2 = 192 #Intermediate pressure(in kPa):\n",
"V2 = AHP*L #Volume at state 2(in m**3):\n",
"V1 = V2*p2/p1 #Volume at state 1(in m**3):\n",
"VLP = ALP*L #Volume of LP cylinder(in m**3):\n",
"r = VLP/V1 #Expansion ratio throughout the engine:\n",
"mep = p1/r*(1+log(r))-p4 #Mean effective pressure(in kPa):\n",
"mepa = mep*d1LP #Actual mep(in kPa):\n",
"IP = mepa*L*ALP*N/60*2 #Indicated power(in kW):\n",
"Vs = V1*N*2*60 #Volume of steam admitted per hour(in m**3):\n",
"v1 = 0.1187 #Specific volume of steam being admitted(in m**3/kg):\n",
"m = Vs/v1 #Steam consumption(in kg/hr):\n",
"\n",
"#Results:\n",
"print \"Intermidiate pressure: \",round(p2),\"kPa\"\n",
"print \"Indicated power: \",round(IP,2),\"kW\"\n",
"print \"Steam consumption: \",round(m,2),\"kg/hr\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Intermidiate pressure: 192.0 kPa\n",
"Indicated power: 49.85 kW\n",
"Steam consumption: 370.75 kg/hr\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11, page no. 550"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import pi,sqrt,log\n",
"\n",
"#Variable Declaration: \n",
"p1 = 1.4*10**3 #Pressure at which steam is supplied(in kPa):\n",
"p4 = 25 #Pressure at exhaust(in kPa):\n",
"r = 8 #Expansion ratio:\n",
"N = 240 #Rpm of engine:\n",
"d = 0.60 #Bore diameter(in m):\n",
"L = 0.60 #Stroke length(in m):\n",
"d1 = 0.8 #Diagram factor:\n",
"\n",
"#Calculations:\n",
"A = pi*d**2/4 #Area of cylinder(in m**2):\n",
"mep = p1/r*(1+log(r))-p4 #Hypothetical mep(in kPa):\n",
"mepa = mep*d1 #Actual mep(in kPa):\n",
"IP = mepa*L*A*N/60*2 #Indicated power(in kW):\n",
"W = mepa*A*L/2 #Work done in HP cylinder(in kJ):\n",
"V1 = pi*d**2*L/(4*8) #Volume at state 1(in m**3):\n",
"V2 = 2.71**(W/(p1*V1))*V1 #Volume at state 2(in m**3):\n",
"D = sqrt(V2*4/(L*pi)) #Diameter of HP cylinder(in m):\n",
"p2 = p1*V1/V2 #Intermediate pressure(in kPa):\n",
"\n",
"#Results:\n",
"print \"Indicated power: \",round(IP,2),\"kW\"\n",
"print \"Diameter of HP cylinder: \",round(D*100,2),\"cm\"\n",
"print \"Intermediate pressure: \",round(p2,2),\"kPa\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Indicated power: 557.96 kW\n",
"Diameter of HP cylinder: 38.1 cm\n",
"Intermediate pressure: 434.06 kPa\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12, page no. 552"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi, log,sqrt\n",
"\n",
"#Variable Declaration: \n",
"p1 = 1.5*10**3 #Pressure at which steam is supplied(in kPa):\n",
"p4 = 25 #Pressure at exhaust(in kPa):\n",
"P = 250 #Power output(in kW):\n",
"r = 12 #Expansion ratio:\n",
"d = 0.40 #Diameter of LP cylinder(in m):\n",
"L = 0.60 #Stroke length(in m):\n",
"d1 = 0.75 #Diagram factor:\n",
"r1 = 2.5 #Expansion ratio in HP cylinder:\n",
"\n",
"#Calculations:\n",
"A = pi*d**2/4 #Area of cylinder(in m**2):\n",
"mep = p1/r*(1+log(r))-p4 #Hypothetical mep(in kPa):\n",
"mepa = mep*d1 #Actual mep(in kPa):\n",
"N = P/(mepa*L*A*2)*60 #Rpm of engine:\n",
"V3 = A*L #Volume of LP cylinder(in m**3):\n",
"V4 = V3\n",
"Vc = V4/r #Cut-off volume in HP cylinder(in m**3):\n",
"Vt = Vc*r1 #Total volume in HP cylinder(in m**3):\n",
"D = sqrt(Vt*4/(L*pi)) #Diameter of HP cylinder(in m):\n",
"\n",
"print \"Speed of engine: \",round(N),\"rpm\"\n",
"print \"Diameter of HP cylinder: \",round(D*100,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed of engine: 323.0 rpm\n",
"Diameter of HP cylinder: 18.26 cm\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13, page no. 553"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi, log\n",
"\n",
"#Variable Declaration: \n",
"dhp = 0.25 #Diameter of HP, LP and IP cylinder(in m):\n",
"dip = 0.40\n",
"dlp = 0.85\n",
"mephp = 0.5*10**3 #MEPs of the cylinders(in kPa):\n",
"mepip = 0.3*10**3\n",
"meplp = 0.1*10**3\n",
"p1 = 1.5*10**3 #Pressure at which steam is supplied(in kPa):\n",
"p4 = 25 #Pressure at exhaust(in kPa):\n",
"r1 = 0.60 #Cut-off occurs at:\n",
"\n",
"#Calculations:\n",
"AHP = pi*dhp**2/4 #Area of HP cylinder(in m**2):\n",
"AIP = pi*dip**2/4 #Area of IP cylinder(in m**2):\n",
"ALP = pi*dlp**2/4 #Area of LP cylinder(in m**2):\n",
"mep1 = mephp*AHP/ALP #Mep of HP referred to LP cylinder(in kPa):\n",
"mep2 = mepip*AIP/ALP #Mep of IP referred to LP cylinder(in kPa):\n",
"mept = mep1+mep2+meplp #Overall mep referred to LP cylinder(in kPa):\n",
"r = ALP/(r1*AHP) #Overall expansion ratio:\n",
"mep = p1/r*(1+log(r))-p4 #Hypothetical mep(in kPa):\n",
"d1 = mept/mep #Overall diagram factor: \n",
"P1 = mep1/mept*100 #% of HP cylinder output:\n",
"P2 = mep2/mept*100 #% of HP cylinder output:\n",
"P3 = meplp/mept*100 #% of HP cylinder output:\n",
"\n",
"#Results:\n",
"print \"Actual mep referred to LP: \",round(mept,2),\"kPa\"\n",
"print \"Hypothetical mep referred to LP: \",round(mep,2),\"kPa\"\n",
"print \"Overall diagram factor: \",round(d1,3)\n",
"print \"Percentage of HP, IP and LP cylinder outputs: \",round(P1,2),\"%\",round(P2,2),\"%\",round(P3,2),\"% respectively\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Actual mep referred to LP: 209.69 kPa\n",
"Hypothetical mep referred to LP: 283.18 kPa\n",
"Overall diagram factor: 0.74\n",
"Percentage of HP, IP and LP cylinder outputs: 20.63 % 31.68 % 47.69 % respectively\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14, page no. 555"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi, log\n",
"#Variable Declaration: \n",
"p1 = 7 #Pressure at which steam is supplied(in bars):\n",
"p5 = 0.25 #Pressure at exhaust(in bars):\n",
"dhp = 0.25 #Diameter of HP and LP cylinder(in m):\n",
"dlp = 0.50\n",
"r1 = 0.30 #Cut-off point of HP and LP cylinders:\n",
"r2 = 0.45\n",
"c1 = 0.10 #Clearance volume of HP and LP cylinders:\n",
"c2 = 0.05\n",
"d1hp = 0.8 #Diagram factors of HP and LP cylinders:\n",
"d1lp = 0.7\n",
"N = 100 #Rpm pf engine:\n",
"L = 1 #Let the length of stroke(in m):\n",
"\n",
"#Calculations:\n",
"VHP = pi*dhp**2/4*L #Volume of HP cylinder(in m**2):\n",
"VLP = pi*dlp**2/4*L #Volume of LP cylinder(in m**2):\n",
"V9 = c1*VHP #Clearance volume(in m**2):\n",
"V7 = c2*VLP\n",
"V2 = VHP+V9 #Total volume of cylinders(in m**3):\n",
"V5 = VLP+V7\n",
"V1 = V9+r1*VHP #Volume at cut-off in HP cylinder(in m**3):\n",
"V3 = V7+r2*VLP\n",
"rhp = V2/V1 #Expansion ratio:\n",
"rlp = V5/V3\n",
"p3 = p1*10**2*V1/V3 #Pressure at state 3(in kPa):\n",
"mepahp = d1hp*(p1*10**2*V1*(1+log(rhp))-p3*V2-(p1*10**2-p3)*V9)/VHP #Actual mep for HP cylinder(in kPa):\n",
"mepalp = 62.96 #Actual mep for LP cylinder(in kPa):\n",
"mepa = mepahp*VHP/VLP #Actual mep of HP reffered to LP cylinder:\n",
"mept = mepalp+mepa #Total mep(in kPa):\n",
"W = mept*VLP*100/60 #Total output(in kW):\n",
"\n",
"#Results:\n",
"print \"mep of Hp referred to LP: \",round(mepa,2),\"kPa\"\n",
"print \"mep of LP: \",round(mepalp,2),\"kPa\"\n",
"print \"Total output: \",round(W,2),\" x L kW where L is stroke length\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"mep of Hp referred to LP: 70.65 kPa\n",
"mep of LP: 62.96 kPa\n",
"Total output: 43.72 x L kW where L is stroke length\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15, page no. 557"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi\n",
"#Variable Declaration: \n",
"t = 15 #Duration of trial(in min):\n",
"d = 0.25 #Bore diameter(in m):\n",
"L = 0.30 #Stroke length(in m):\n",
"bd = 1.5 #Brake diameter(in m):\n",
"bl = 300 #Net brake load(in N):\n",
"N = 240 #Speed of engine:\n",
"p1 = 10 #Steam pressure(in bar):\n",
"x = 0.9 #Dryness fraction:\n",
"mep = 0.9#Mep at cover end(in bar):\n",
"m1 = 15 #Steam utilised(in kg):\n",
"\n",
"#Calculations:\n",
"m = m1/t*60 #Steam consumption per hour(in kg/hr):\n",
"IP = mep*10**2*L*pi*d**2*240*2/(4*0.7457*60)#Indicated horse power(in kW):\n",
"m2 = 60/IP #Steam used per(hp.hr):\n",
"\n",
"#Results:\n",
"print \"Steam used per ihp.hr: \",round(m2,2),\"kg/ihp.hr\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Steam used per ihp.hr: 4.22 kg/ihp.hr\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16, page no. 558"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import pi\n",
"\n",
"#Variable Declaration: \n",
"d = 0.38 #Bore diameter(in m):\n",
"L = 0.50 #Stroke length(in m):\n",
"pd = 0.05#Piston rod diameter(in m):\n",
"N = 150 #Speed of engine(in rpm):\n",
"m = 36 #Steam consumption(in kg/min):\n",
"F = 7 #Brake load(in kN):\n",
"bd = 2 #Brake diameter(in m):\n",
"aco = 28 #Area of indicator diagram at cover end(in cm**2):\n",
"acr = 26 #Area of indicator diagram at crank end(in cm**2):\n",
"l = 0.07 #Length of indicator diagram(in m):\n",
"s = 15 #Spring scale(in kPa/mm):\n",
"\n",
"#Calculations:\n",
"mepcr = acr*100*s/(l*10**3) #Mep at crank end(in kPa):\n",
"mepco = aco*100*s/(l*10**3) #Mep at cover end(in kPa):\n",
"IPcr = mepcr*L*pi*(d**2-pd**2)/4*N/60 #IP at crank end(in kW):\n",
"IPco = mepco*L*pi*(d**2)/4*N/60\t #IP at cover end(in kW):\n",
"IP = IPcr+IPco #IP(in kW):\n",
"BP = 2*pi*N/60*F*1 #Brake power(in kW):\n",
"n = BP/IP #Mechanical efficiency:\n",
"ISFC = m*60/IP #ISFC(in kg/kW.h):\n",
"BSFC = m*60/BP #BSFC(in kg/kW.h):\n",
"\n",
"#Results:\n",
"print \"Indicated power: \",round(IP,2),\"kW\"\n",
"print \"Brake power: \",round(BP,2),\"kW\"\n",
"print \"Indicated specific steam consumption: \",round(ISFC,2),\"kg/kW.h\"\n",
"print \"Brake specific steam consumption: \",round(BSFC,2),\"kg/kW.h\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Indicated power: 162.67 kW\n",
"Brake power: 109.96 kW\n",
"Indicated specific steam consumption: 13.28 kg/kW.h\n",
"Brake specific steam consumption: 19.64 kg/kW.h\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17, page no. 559"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration: \n",
"#From steam tables:\n",
"hf = 844.89 #kJ/kg\n",
"hfg = 1947.3 #kJ/kg\n",
"hcond = 209.33 #kJ/kg\n",
"\n",
"#Calculations:\n",
"BP = 2*pi*150*(120*9.81-100)*(100/2)*10**(-2)/(1000*60)#Brake power(in kW):\n",
"IPco = 1.8*10**2*0.34*pi/4*(0.24)**2*150/60#IP at cover end(in kW):\n",
"IPcr = 1.6*10**2*0.34*pi/4*(0.24**2-0.05**2)*150/60\t#IP at crank end(in kW):\n",
"IP = IPco+IPcr #Total IP(in kW):\n",
"n = BP/IP #Mechanical efficiency:\n",
"hs = hf+0.98*hfg #Enthalpy of steam at inlet(in kJ/kg):\n",
"E = hs-hcond #Energy supplied by the steam(in kJ/kg):\n",
"m = 4*60 #Steam consumption rate(in kg/hr):\n",
"nbth = 3600/((m/BP)*E)*100 #Brake thermal efficiency:\n",
"ISFC = m/IP #Indicated steam consumption(in kg/kW.h):\n",
"\n",
"#Results:\n",
"print \"Brake thermal efficiency: \",round(nbth,2),\"%\" \n",
"print \"Indicated specific steam consumption: \",round(ISFC,2),\"kg/kW.h\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Brake thermal efficiency: 4.99 %\n",
"Indicated specific steam consumption: 18.74 kg/kW.h\n"
]
}
],
"prompt_number": 17
}
],
"metadata": {}
}
]
}