{
"metadata": {
"name": "",
"signature": "sha256:f7a19d25377671432cfde9f9d56148d23c8e97851f20fd5f765a471e71e2f5a2"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 15: Steam Condenser"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, page no. 695"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"\n",
"#Variable Declaration: \n",
"h = 71 #Height of mercury column in condenser(in mm of Hg):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"mw = 800 #Rate at which cooling water is circulated(in kg/min):\n",
"ms = 25 #Condensate available at(in kg/min):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"#From steam tables:\n",
"ps = 5.62 #kPa\n",
"hf = 146.68 #kJ/kg\n",
"hfg = 2418.6 #kJ/kg\n",
"\n",
"#Calculations:\n",
"pt = (76-h)*10**(-2)*d*10**6*9.81*10**(-3)#Absolute pressure in the condenser(in kPa):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"ma = pa/((273+35)*R) #Mass of air per m**3 of condenser volume:\n",
"hs = mw/ms*Cpw*(25-15)+Cpw*30#Enthalpy of steam(in kJ/kg):\n",
"x = (hs-hf)/hfg#Dryness fraction of the steam entering:\n",
"n = h*d*10**4*g/(76*d*10**4*g-ps*10**3)*100#Vacuum efficiency:\n",
"\n",
"#Results: \n",
"print \"Mass of air of condenser volume: \",round(ma,3),\"kg/m**3\"\n",
"print \"Dryness fraction of steam entering: \",round(x,4)\n",
"print \"Vacuum efficiency: \",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass of air of condenser volume: 0.012 kg/m**3\n",
"Dryness fraction of steam entering: 0.5442\n",
"Vacuum efficiency: 98.9 %\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, page no. 695"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"\n",
"#Variable Declaration: \n",
"h = 70 #Height of mercury column in condenser(in mm of Hg):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"r = 2500 #Leakage of air in condenser:\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"#From steam tables:\n",
"ps = 4.246 #kPa \n",
"vg = 32.89 #m**3/kg\n",
"\n",
"#Calculations:\n",
"pt = (76-h)*10**(-2)*d*10**6*9.81*10**(-3)#Absolute pressure in the condenser(in kPa):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"m = 1/r #Mass of air accoumpanying per kg of steam due to leakage(in kg):\n",
"v = m*R*(273+30)/pa #Volume of air per kg of steam(in m**3/kg):\n",
"m1 = v/vg #Mass of water vapour accompanying air:\n",
"\n",
"#Results: \n",
"print \"Capacity of air pump: \",round(v*10**3,2),\" x 10^-3 m**3 per kg steam\"\n",
"print \"Mass of water vapour accompanying air: \",round(m1*10**4,2),\" x 10^-4 kg/kg of steam\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacity of air pump: 9.26 x 10^-3 m**3 per kg steam\n",
"Mass of water vapour accompanying air: 2.82 x 10^-4 kg/kg of steam\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, page no. 696"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"h = 67 #Height in mercury column in condenser(in cm):\n",
"pt = 10.67 #Absolute pressure in the condenser(in kPa):\n",
"ps = 7.384 #Partial pressure of steam(in kPa):\n",
"ms = 50 #Mass flow rate of steam(in kg/min):\n",
"mw = 1000 #Mass flow rate of water(in kg/min):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"#From steam tables:\n",
"hf = 167.57 #kJ/kg \n",
"hfg = 2406.7 #kJ/kg\n",
"vg = 19.52 #m**3/kg\n",
"\n",
"#Calculations:\n",
"cv = 76-(75-h) #Corrected vacuum(in cm):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"n = h*d*10**4*g/(75*d*10**4*g-ps*10**3)*100\t#VAcuum efficiency:\n",
"u = 40-35 #Undercooling of condensate(in C):\n",
"n1 = (25-10)/(46.9-10)*100 #Condenser efficiency:\n",
"h = mw/ms*Cpw*(25-10)+Cpw*40 #Enthalpy of steam(in kJ/kg):\n",
"x = (h-hf)/hfg #Dryness fraction:\n",
"m = pa/(R*(273+40)) #Mass of air per m**3 of condenser volume(in kg/m**3):\n",
"m1 = pa*vg/(R*(273+40)) #Mass of air in 1kg of uncondensate steam(in kg):\n",
"\n",
"#Results:\n",
"print \"Corrected vacuum: \",round(cv,2),\"cm of Hg\"\n",
"print \"Vacuum efficiency: \",round(n,2),\"%\"\n",
"print \"Undercooling: \",round(u,2),\"\u00b0C\"\n",
"print \"Dryness fraction of steam entering: \",round(x,4)\n",
"print \"Mass of air/m**3 of condenser volume: \",round(m,4),\"kg/m**3\"\n",
"print \"Mass of air in per kg of uncondensate steam: \",round(m1,3),\"kg\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Corrected vacuum: 68.0 cm of Hg\n",
"Vacuum efficiency: 96.45 %\n",
"Undercooling: 5.0 \u00b0C\n",
"Dryness fraction of steam entering: 0.5209\n",
"Mass of air/m**3 of condenser volume: 0.0366 kg/m**3\n",
"Mass of air in per kg of uncondensate steam: 0.714 kg\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, page no. 697"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"from math import pi\n",
"\n",
"#Variable Declaration: \n",
"h = 69 #Height in mercury column in condenser(in cm):\n",
"T1 = 30 #Inlet temperature(in \u00b0C):\n",
"L = 60 #Leakage(in kg/hr):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"n = 240 #Rpm of engine:\n",
"r = 1.5 #L/D ratio:\n",
"#From steam tables:\n",
"ps = 4.246 #kPa \n",
"vg = 32.89 #m**3/kg\n",
"pt = (76-h)*d*10**4*g #Absolute pressure at inlet to air pump(in kPa):\n",
"pa = 5.09 #Partial pressure of air(in kPa):\n",
"V = L*R*(273+T1)/pa #Volume of 60 kg air(in m**3/hr):\n",
"D = ((V*4)/(pi*r*n*60))**(1/3)*100 #Bore diameter(in cm):\n",
"l = D*r #Stroke length(in cm):\n",
"m = V/vg #Mass of water vapour extracted with air(in kg/hr):\n",
"\n",
"#Results: \n",
"print \"Capacity of air pump: \",round(V,1),\"m**3/hr\"\n",
"print \"Bore: \",round(D,2),\"cm\"\n",
"print \"Stroke: \",round(l,2),\"cm\"\n",
"print \"Mass of water vapour extracted with air: \",round(m,2),\"kg/hr\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacity of air pump: 1025.1 m**3/hr\n",
"Bore: 39.24 cm\n",
"Stroke: 58.86 cm\n",
"Mass of water vapour extracted with air: 31.17 kg/hr\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, page no. 698"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"\n",
"#Variable Declaration: \n",
"h = 70 #Height in mercury column in condenser(in cm):\n",
"T = 30+273 #Inlet temperature(in K):\n",
"m = 5*10**(-4) #Leakage(in kg/kg of steam):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"dT = 15 #Increase in temperature of cooling water(in K):\n",
"x = 0.90 #Dryness fraction:\n",
"#From steam tables:\n",
"hf = 125.79 #kJ/kg\n",
"hfg = 2430.5 #kJ/kg\n",
"vg = 32.89 #m**3/kg\n",
"ps = 4.246 #kPa\n",
"\n",
"#Calculations:\n",
"pt = (77-h)*d*10**4*g #Absolute pressure in condenser(in kPa):\n",
"pa = 5.094 #Partial pressure of air(in kPa):\n",
"V = m*10**3*R*T/pa #Volume of air extracted per minute(in m**3/min):\n",
"ms = V/vg #Mass of steam extracted in maixture(in kg/min):\n",
"mt = m*10**3+ms #Mass handled by air extraction pump(in kg/min):\n",
"h = hf+x*hfg #Enthalpy of steam entering(in kJ/kg):\n",
"mw = 1000*(h-Cpw*T)/(Cpw*dT) #Water circulation rate(in kg/min):\n",
"\n",
"#Results: \n",
"print \"Mass handled by air pump: \",round(mt,4),\"kg/min\"\n",
"print \"Water circulation rate: \",round(mw,2),\"kg/min\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass handled by air pump: 0.7595 kg/min\n",
"Water circulation rate: 16693.78 kg/min\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6, page no. 699"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"#Variable Declaration: \n",
"h = 70 #Height in mercury column in condenser(in cm):\n",
"T = 30+273 #Inlet temperature(in K):\n",
"x = 0.85 #Dryness fraction:\n",
"m = 300 #Rate at which steam enters(in kg/min):\n",
"v = 50 #Velocity of water flow:\n",
"ph = 5 #Pressure head(in m):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"#From steam tables:\n",
"ps = 4.246 #kPa \n",
"mw = 7415 #kg/min\n",
"A = 24.79 #Cooling surface area required(in m**2):\n",
"\n",
"#Calculations:\n",
"pt = (76-h)*d*10**4*g #Absolute pressure in condenser(in kPa):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"V = mw/1000 #Volume flow of water(in m**3/min):\n",
"a = V/v #Flow surface area required(in m**2):\n",
"vh = 1/2*(v/60)**2/g #Velocity head present(in m):\n",
"th = ph+vh #Total head required(in m):\n",
"\n",
"#Results:\n",
"print \"Flow surface area required: \",round(a,4),\"m**2\" \n",
"print \"Cooling surface area required: \",round(A,2),\"m**2\"\n",
"print \"Head required: \",round(th,4),\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow surface area required: 0.1483 m**2\n",
"Cooling surface area required: 24.79 m**2\n",
"Head required: 5.0354 m\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7, page no. 700"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"#Variable Declaration: \n",
"m1 = 350 #Mass of steam entering(in kg/min):\n",
"v = 0.02 #Volume of water required(in m**3 per kg steam):\n",
"r = 0.05/100 #Amount of air mass going into condenser:\n",
"r1 = 5/100 #Volume of air dissolved in the water injected:\n",
"h = 68 #Height in mercury column in condenser(in cm):\n",
"T = 20+273 #Inlet temperature(in K):\n",
"p = 101.3 #Atmospheric pressure(in kPa):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"n = 0.90 #Volumetric efficiency:\n",
"#From steam tables:\n",
"ps = 4.246 #kPa \n",
"vf = 0.001004 #m**3/kg\n",
"\n",
"#Calculations:\n",
"pt = (76-h)*d*10**4*g*10**(-3)#Absolute pressure in condenser(in kPa):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"V1 = m1*v #Volume of cooling water required per minute(in m**3/min):\n",
"m2 = m1*r #Mass of air going into condenser(in kg/min):\n",
"V = V1*r1 #Volume of air entering per minute with cooling water(in m**3/min):\n",
"m = p*V/(R*T) #Mass of air with cooling water(in kg):\n",
"mt = m+m2 #Total mass of air inside condenser(in kg):\n",
"V2 = mt*R*(273+30)/pa #Volume of air corresponding:\n",
"V3 = m1*vf #Volume of steam condensed(in m**3/min):\n",
"Vt = V3+V2+V1 #Total volume(in m**3/min):\n",
"C = Vt/n #Actual capacity of air pump(in m**3/min):\n",
"\n",
"#Results: \n",
"print \"Capacity of air pump: \",round(C,2),\"m**3/min\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacity of air pump: 17.14 m**3/min\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8, page no. 701"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"H = 65 #Height in mercury column in condenser(in cm):\n",
"ms = 20 #Rate at which steam enters(in kg/min):\n",
"m = 12 #Mass of cooling water per kg of steam:\n",
"H1 = 66 #Height in mercury column in air pump(in cm):\n",
"p = 101.3 #Atmospheric pressure(in kPa):\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"#From steam tables:\n",
"ps = 7.384 #kPa\n",
"ps1 = 5.628 #kPa\n",
"hf = 167.57 #kJ/kg\n",
"hfg = 2406.7 #kJ/kg\n",
"\n",
"#Calculations:\n",
"pt = (76-H)*d*10**4*g*10**(-3) #Absolute pressure in condenser(in kPa):\n",
"pa = pt-ps #Partial pressure of air(in kPa):\n",
"mw = m*ms #Cooling water required(in kg/min):\n",
"h = ((ms+mw)*Cpw*40-mw*Cpw*20)/ms #Enthalpy of steam entering:\n",
"x = (h-hf)/hfg #Dryness fraction of steam entering:\n",
"pt1 = (76-H1)*d*10**4*g*10**(-3) #Absolute partial pressure at suction in air pump(in kPa): \n",
"pa1 = pt1-ps1 #Partial pressure of air(in kPa):\n",
"V = 2 #Volume of mixture(in m**3):\n",
"m1 = pa1*V/(R*(273+35)) #Mass of air entering(in kg/min):\n",
"H2 = (p-pt)/(g*d*10**3) #Head(in m):\n",
"\n",
"#Results: \n",
"print \"Dryness fraction of steam entering: \",round(x,3)\n",
"print \"Mass of air entering: \",round(m1,4),\"kg/min\"\n",
"print \"Head: \",round(H2,4),\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dryness fraction of steam entering: 0.417\n",
"Mass of air entering: 0.1744 kg/min\n",
"Head: 0.6496 m\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9, page no. 702"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"m = 3 #Leakage(in kg/min):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"#From steam tables:\n",
"ps = 5.628 #kPa\n",
"ps1 = 5.075 #kPa\n",
"ps2 = 5.352 #kPa\n",
"pt = ps #Absolute pressure in condenser(in kPa):\n",
"\n",
"#Calculations:\n",
"pa1 = pt-ps1 #Partial pressure of air(in kPa):\n",
"V1 = m*R*(273+33)/pa1 #Volume of air handled by air pump(in m**3/hr):\n",
"pa2 = pt-ps2 #Partial pressure of air(in kPa):\n",
"V2 = m*R*(273+34)/pa2 #Volume of mixture handled(in m**3/hr):\n",
"\n",
"#Results: \n",
"print \"Volume of air handled: \",round(V1,2),\"m**3/hr\"\n",
"print \"Volume of mixture handled: \",round(V2,2),\"m**3/hr\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volume of air handled: 476.43 m**3/hr\n",
"Volume of mixture handled: 957.71 m**3/hr\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10, page no. 703"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"H1 = 72 #Height in mercury column at inlet in condenser(in cm):\n",
"H2 = 73 #Height in mercury column at outlet in condenser(in cm):\n",
"x = 0.92 #Dryness fraction:\n",
"d = 0.0135951 #Density of mercury(in kg/cm**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"R = 0.287 #Gas constant(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"#From steam tables:\n",
"hf = 141.97 #kJ/kg\n",
"hfg = 2421.33 #kJ/kg\n",
"Tsat1 = 33.87 #\u00b0C\n",
"Tsat2 = 28.96 #\u00b0C\n",
"\n",
"#Calculations:\n",
"p1 = (76-H1)*d*10**4*g*10**(-3) #Inlet pressure in condenser(in kPa):\n",
"p2 = (76-H2)*d*10**4*g*10**(-3) #Outlet pressure in the condenser(in kPa):\n",
"u = Tsat1-Tsat2 #Undercooling(in C):\n",
"h = hf+x*hfg #Enthalpy of steam entering(in kJ/kg):\n",
"m = (h-Cpw*Tsat2)/(Cpw*13.87) #Cooling water requirement(in kg/kg steam):\n",
"\n",
"#Results: \n",
"print \"Undercooling: \",round(u,2),\"\u00b0C\"\n",
"print \"Cooling water requirement: \",round(m,2),\"kg/kg steam\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Undercooling: 4.91 \u00b0C\n",
"Cooling water requirement: 38.78 kg/kg steam\n"
]
}
],
"prompt_number": 21
}
],
"metadata": {}
}
]
}