{
"metadata": {
"name": "",
"signature": "sha256:3c23e07bbff73d50716bb3f0344f5f19803ca8de755edfb991f464d2a6411a44"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 13: Nozzles"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, page no. 584"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"#Variable Declaration: \n",
"p1 = 10 #Pressure of dry steam(in bar):\n",
"C1 = 100 #Velocity of steam entering(in m/s):\n",
"C2 = 300 #Velocity of steam leaving the nozzle(in m/s):\n",
"p2 = 5 #Pressure of steam at exit(in bar):\n",
"m = 16 #Mass flow rate(in kg/s):\n",
"q = 10 #Heat loss to surroundings(in kJ/kg):\n",
"#From steam tables:\n",
"h1 = 2778.1 #kJ/kg\n",
"hf = 640.23 #kJ/kg\n",
"hfg = 2108.5 #kJ/kg\n",
"\n",
"#Calculations:\n",
"dh = (q*10**3+(C1**2-C2**2)/2)/1000\t#Heat drop in the nozzle(in kJ/kg):\n",
"dQ = -dh*m #Total heat drop(in kJ/s):\n",
"h2 = h1+dh #Enthalpy at state 2(in kJ/kg):\n",
"x2 = (h2-hf)/hfg #Dryness fraction at state 2:\n",
"\n",
"#Results: \n",
"print \"Heat drop in the nozzle: \",round(-dh,2),\"kJ/kg\" \n",
"print \"Total heat drop: \",round(dQ,2),\"kJ/s\"\n",
"print \"Dryness fraction at exit: \",round(x2,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat drop in the nozzle: 30.0 kJ/kg\n",
"Total heat drop: 480.0 kJ/s\n",
"Dryness fraction at exit: 0.9997\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, page no. 585"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"p1 = 10 #Steam entering at pressure(in bar):\n",
"p2 = 6 #Pressure at which steam leaves(in bar):\n",
"A2 = 20 #Cross-section area of exit of nozzle(in cm**2):\n",
"#From steam tables:\n",
"h1 = 3478.5 #kJ/kg \n",
"s1 = 7.7622 #kJ/kg.K\n",
"T2 = 418.45 #C(by interpolation)\n",
"h2 = 3309.51 #kJ/kg\n",
"v2 = 0.5281 #m**3/kg\n",
"\n",
"#Calculations:\n",
"s2 = s1\n",
"C2 = sqrt(2*(h1-h2)*10**3) #Velocity at exit(in m/s):\n",
"m = A2*10**(-4)*C2/v2 #Mass flow rate(in kg/s):\n",
"\n",
"#Result: \n",
"print \"Mass flow rate: \",round(m,3),\"kg/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass flow rate: 2.202 kg/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, page no. 587"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import sqrt \n",
"\n",
"#Variable Declaration: \n",
"p1 = 12 #Pressure of steam entering(in bar):\n",
"p2 = 6 #Pressure at exit(in bar):\n",
"m1 = 5 #Mass flow rate(in kg/s):\n",
"m2 = m1\n",
"m3 = m1\n",
"C3a = 500 #Exit velocity(in m/s):\n",
"#From steam tables:\n",
"h1 = 3045.8 #kJ/kg \n",
"h2 = 2900.05 #kJ/kg\n",
"s2 = 7.0317 #kJ/kg.K\n",
"v2 = 0.3466 #m**3/kg\n",
"h3 = 2882.55 #kJ/kg\n",
"v3 = 0.3647 #m**3/kg\n",
"n = 1.3 #For superheated steam:\n",
"\n",
"#Calculations:\n",
"s1 = s2\n",
"s3 = s2\n",
"p2 = p1*(2/(n+1))**(n/(n-1)) #Pressue at state 2(in bar):\n",
"C2 = sqrt(2*(h1-h2)*10**3) #Velocity at throat(in m/s):\n",
"A2 = m2*v2/C2 #Cross-sectional area at throat(in m**2):\n",
"C3 = sqrt(2*(h1-h3)*10**3) #Ideal velocity at exit(in m/s):\n",
"A3 = m3*v3/C3a #Cross-sectional area at exit(in m**2): \n",
"r = C3a/C3 #Coefficient of velocity:\n",
"\n",
"#Results: \n",
"print \"Cross-sectional area at throat: \",round(A2*10**3,3),\" x 10^-3 m^2\"\n",
"print \"Cross-sectional area at exit: \",round(A3*10**3,3),\" x 10^-3 m^2\"\n",
"print \"Coefficient of velocity: \",round(r,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cross-sectional area at throat: 3.21 x 10^-3 m^2\n",
"Cross-sectional area at exit: 3.647 x 10^-3 m^2\n",
"Coefficient of velocity: 0.875\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, page no. 588"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"\n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"p1 = 16 #Pressure of steam entering(in bar):\n",
"p3 = 5 #Pressure at exit(in bar):\n",
"m1 = 1 #Mass flow rate(in kg/s):\n",
"m2 = m1\n",
"m3 = m1\n",
"#From steam tables:\n",
"#For case 1:\n",
"h1 = 3034.8 #kJ/kg\n",
"s1 = 6.8844 #kJ/kg.K\n",
"v1 = 0.15862 #m**3/kg\n",
"n = 1.3\n",
"h2 = 2891.39 #kJ/kg\n",
"h3 = 2777 #kJ/kg\n",
"v2 = 0.2559 #m**3/kg\n",
"v3 = 0.3882 #m**3/kg\n",
"#For case 2:\n",
"h2a = 2905.73 #kJ/kg\n",
"v2a = 0.2598 #m**3/kg\n",
"v3a = 0.40023 #m**3/kg\n",
"\n",
"#Calculations:\n",
"p2 = p1*(2/(n+1))**(n/(n-1)) #Pressure at the throat of nozzle(in bar):\n",
"q12 = h1-h2 #Heat drop up to throat section(in kJ/kg):\n",
"C2 = sqrt(2*(h1-h2)*10**3) #Velocity at throat(in m/s):\n",
"q23 = h2-h3 #Heat drop from exit(in kJ/kg):\n",
"C3 = sqrt(2*(h2-h3)*10**3+C2**2) #Velocity at exit(in m/s):\n",
"A2 = m2*v2/C2 #Throat area(in m**2):\n",
"A3 = m3*v3/C3 #Exit area(in m**2):\n",
"q12a = 0.9*q12 #Considering expansion to have 10% friction loss:\n",
"C2a = sqrt(2*q12a*10**3) #Actual velocity at throat(in m/s):\n",
"A2a = m2*v2a/C2a #Actual throat area(in m**2):\n",
"q23a = 0.9*q23 #Actual drop at the exit of the nozzle(in kJ/kg):\n",
"h3a = h2a-q23a #Actual enthalpy at state 3(in kJ/kg):\n",
"C3a = sqrt(2*q23a*10**3+C2a**2) #Actual velocity at exit(in m/s):\n",
"A3a = m3*v3a/C3a #Actual area at exit(in m**2):\n",
"\n",
"#Results:\n",
"print \"Throat area, without friction consideration: \",round(A2*10**4,2),\"cm**2\"\n",
"print \"Exit area, without friction consideration: \",round(A3*10**4,2),\"cm**2\"\n",
"print \"Throat area, with friction consideration: \",round(A2a*10**4,2),\"cm**2\"\n",
"print \"Exit area, with friction consideration: \",round(A3a*10**4,3),\"cm**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Throat area, without friction consideration: 4.78 cm**2\n",
"Exit area, without friction consideration: 5.41 cm**2\n",
"Throat area, with friction consideration: 5.11 cm**2\n",
"Exit area, with friction consideration: 5.875 cm**2\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, page no. 590"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
" \n",
"from math import sqrt,pi\n",
"#Variable Declaration: \n",
"P = 1 #Power of turbine(in MW):\n",
"p1 = 20 #Pressure of steam entering(in bar):\n",
"m = 8 #Steam consumption rate(in kg/kW.h):\n",
"p3 = 0.2 #Pressure at which steam leaves(in bar):\n",
"d = 0.01 #Throat diameter(in m):\n",
"#From Mollier diagram:\n",
"q12 = 142 #kJ/kg \n",
"v2 = 0.20 #m**3/kg\n",
"q13 = 807 #kJ/kg\n",
"v3 = 7.2 #m**3/kg\n",
"\n",
"#Calculations:\n",
"C2 = sqrt(2*q12*10**3) #Velocity at throat(in m/s):\n",
"m2 = pi*d**2/4*C2/v2 #Mass flow rate:\n",
"m3 = m2\n",
"n = 10**3*m/(3600*m2) #Number of nozzles:\n",
"q13a = 0.90*q13 #Useful heat drop:\n",
"C3 = sqrt(2*10**3*q13a)#Velocity at exit(in m/s):\n",
"A3 = m3*v3/C3 #Area at exit(in m**2):\n",
"\n",
"#Results: \n",
"print \"Number of nozzles required: \",round(n) \n",
"print \"Area at exit: \",round(A3*10**4,2),\"cm**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of nozzles required: 11.0\n",
"Area at exit: 12.5 cm**2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6, page no. 591"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"from math import pi, atan, sqrt\n",
"#Variable Declaration: \n",
"p1 = 0.7 #Pressure at which steam is supplied(in MPa):\n",
"l = 0.06 #Length of diverging nozzle(in m):\n",
"d = 0.005 #Throat diameter(in mm):\n",
"p3 = 0.1 #Pressure at which steam leaves the nozzle(in MPa):\n",
"#From Mollier diagram:\n",
"q12 = 138 #kJ/kg\n",
"v2 = 0.58 #m**3/kg\n",
"T = 203 #\u00b0C\n",
"q23 = 247 #kJ/kg\n",
"q23a = 209.95 #kJ/kg\n",
"v3a = 1.7 #m**3/kg\n",
"\n",
"#Calculations:\n",
"C2 = sqrt(2*q12*10**3) #Velocity at throat(in m/s):\n",
"m1 = pi*d**2/4*C2/v2 #Mass flow rate(in kg/s):\n",
"m2 = m1\n",
"m3 = m1\n",
"q = q12+q23a #Total heat drop(in kJ/kg):\n",
"C3 = sqrt(2*10**3*q) #Velocity at exit(in m/s):\n",
"A3 = m3*v3a/C3 #Area at exit(in m**2):\n",
"d1 = (sqrt(A3*4/pi))*10**3 #Diameter at exit(in mm):\n",
"a = atan((d1-d*10**3)/(2*60))*180/pi\n",
"\n",
"#Results: \n",
"print \"With no losses, temperature at throat: \",round(T,2),\"\u00b0C\"\n",
"print \"Velocity at throat: \",round(C2,2),\"m/s\"\n",
"print \"With losses, cone angle: \",round(2*a,2),\"\u00b0\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"With no losses, temperature at throat: 203.0 \u00b0C\n",
"Velocity at throat: 525.36 m/s\n",
"With losses, cone angle: 1.71 \u00b0\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7, page no. 593"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"from math import sin,pi,sqrt\n",
"\n",
"#Variable Declaration:\n",
"P = 5000 #Power of the turbine(in hp):\n",
"m = P*6/3600 #Steam required(in kg of steam/hp-hr):\n",
"n = 0.90 #Efficiency of nozzle:\n",
"a = 12 #Nozzle angle:\n",
"p = 5 #Pitch(in cm):\n",
"t = 0.3 #Thickness(in cm):\n",
"#From steam tables:\n",
"h1 = 2794 #kJ/kg\n",
"s1 = 6.4218 #kJ/kg.K\n",
"x2 = 0.9478\n",
"h2 = 2662.2 #kJ/kg\n",
"x2a = 0.9542\n",
"v2a = 0.2294 #m**3/kg\n",
"\n",
"#Calculations:\n",
"s2 = s1\n",
"h12 = h1-h2 #Change in enthalpy(in kJ/kg):\n",
"h12a = n*h12 #Actual change(in kJ/kg):\n",
"C2 = sqrt(2*h12a*10**3) #Velocity at inlet(in m/s):\n",
"A2 = m*v2a/C2*10**4 #Area at exit of nozzle(in cm**2):\n",
"l = 60*pi/3 #Approximate length of the nozzle(in cm):\n",
"n = int(l/p)+1 #Number of nozzles:\n",
"l1 = n*p #Correct length of nozzle arc:\n",
"h = A2/((p*sin(a*pi/180)-t)*n)#Radial height of nozzle(in cm):\n",
"\n",
"#Results:\n",
"print \"Length of nozzle: \",round(l1,2),\"cm\"\n",
"print \"Radial height of nozzle: \",round(h,2),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length of nozzle: 65.0 cm\n",
"Radial height of nozzle: 4.08 cm\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8, page no. 594"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"p1 = 13 #Pressure at which steam enters(in bar):\n",
"p2 = 6 #Pressure at which steam leaves(in bar):\n",
"T1 = 150+273 #Temperature of steam entering(in K):\n",
"r = 1.4 #Adibatic insex of compression:\n",
"\n",
"#Calculations:\n",
"T2 = T1*(p2/p1)**((r-1)/r) #Final temperature of steam(in K):\n",
"C2 = sqrt(2*1.005*(T1-T2)) #Exit velocity(in m/s):\n",
"\n",
"#Results: \n",
"print \"Exit velocity: \",round(C2,2),\"m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Exit velocity: 12.98 m/s\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9, page no. 595"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"F = 350 #Force on the plate(in N):\n",
"p1 = 8 #Initial pressure(in bar):\n",
"p3 = 1 #Final pressure(in bar):\n",
"A2 = 5*10**(-4) #Throat cross-sectional area(in m**2):\n",
"#From steam tables:\n",
"h1 = 2769.1 #kJ/kg\n",
"s1 = 6.6628 #kJ/kg.K\n",
"x2 = 0.9717\n",
"h2 = 2685.17 #kJ/kg\n",
"v2 = 0.3932 #m**3/kg\n",
"x3 = 0.8238\n",
"h3 = 2277.6 #kJ/kg\n",
"\n",
"#Calculations:\n",
"s2 = s1\n",
"s3 = s1\n",
"h12 = h1-h2 #Enthalpy change(in kJ/kg):\n",
"C2 = sqrt(2*h12*10**3) #Velocity at throat(in m/s):\n",
"m = A2*C2/v2 #Discharge at throat(in kg/s):\n",
"C3a = F/m #Actual exit velocity(in m/s):\n",
"h23 = h2-h3 #Theoretical enthalpy drop(in kJ/kg):\n",
"n = C3a**2/(2*h23*10**3) #Nozzle efficiency:\n",
"\n",
"#Results:\n",
"print \"Discharge at throat: \",round(m,3),\"kg/s\"\n",
"print \"Nozzle efficiency: \",round(n*100,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Discharge at throat: 0.521 kg/s\n",
"Nozzle efficiency: 55.37 %\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10, page no. 597"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"from math import sqrt,pi\n",
"\n",
"#Variable Declaration: \n",
"m = 5/60 #Mass flow rate(in kg/s):\n",
"p3 = 1 #Pressure at which steam is discharged(in bar):\n",
"p1 = 10 #Initial pressure(in bar):\n",
"T1 = 200+273 #Initial temperature(in K)\n",
"n = 1.3 #Adiabatic index of compression:\n",
"\n",
"#From steam tables:\n",
"h1 = 2827.9 #kJ/kg\n",
"s1 = 6.6940 #kJ/kg.K\n",
"v1 = 0.2060 #m**3/kg\n",
"h2a = 2711.23 #kJ/kg\n",
"s2a = 6.6749 #kJ/kg.K\n",
"h3 = 2420.08 #kJ/kg\n",
"v3 = 1.5025 #m**3/kg\n",
"psat = 3.44 #bar (at T = 138.18 \u00b0C)\n",
"Tsat = 155.12 #C (at p = 5.45 bar)\n",
"\n",
"#Calculations:\n",
"s3 = s2a\n",
"p2 = p1*(2/(n+1))**(n/(n-1)) #Pressure at throat(in bar):\n",
"C3 = sqrt(2*(h1-h3)*10**3) #Velocity at exit(in m/s):\n",
"A3 = m*v3/C3 #Exit area(in m**2):\n",
"d = sqrt(A3*4/pi) #Diameter of nozzle at exit(in m):\n",
"T2 = T1*(p2/p1)**((n-1)/n) #Temperature at throat(in K):\n",
"d1 = p2/psat #Degree of supersaturation:\n",
"u = Tsat-(T2-273) #Amount of undercooling(in \u00b0C):\n",
"\n",
"#Results: \n",
"print \"Degree of supersaturation: \",round(d1,2) \n",
"print \"Amount of undercooling: \",round(u,2),\"\u00b0C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Degree of supersaturation: 1.59\n",
"Amount of undercooling: 16.82 \u00b0C\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11, page no. 599"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"\n",
"#Variable Declaration: \n",
"p1 = 4 #Initial pressure(in bar):\n",
"T1 = 180+273 #Initial temperature(in K):\n",
"p2 = 1.5 #Final pressure(in bar):\n",
"n = 1.3 #Index of compression:\n",
"nn = 0.95 #Efficiency due to heat loss:\n",
"C = 2.174 #Specific heat(in kJ/kg.K):\n",
"#From steam tables:\n",
"v1 = 0.5088 #m**3/kg \n",
"Tsat = 111.37+273 #K (at p = 1.5 bar)\n",
"\n",
"#Calculations:\n",
"h1 = p1*v1*10**2+2614 #Enthalpy at state 1(in kJ/kg):\n",
"v2 = v1*(p1/p2)**(1/n) #Specific volume at state 2(in m**3/kg):\n",
"h2 = p2*v2*10**2+2614 #Enthalpy at state 2(in kJ/kg):\n",
"dh = nn*(h1-h2) #Actual heat drop(in kJ/kg):\n",
"T2 = T1*(p2/p1)**((n-1)/n) #Temperature at state 2(in K):\n",
"dT = (1-nn)*(h1-h2)/C #Temperature rise due to supersaturation:\n",
"T2a = T2+dT #Actual temperature at state 2(in K):\n",
"u = Tsat-T2a #Amount of undercooling(in \u00b0C):\n",
"\n",
"#Results:\n",
"print \"Actual heat drop: \",round(dh,2),\"kJ/kg\"\n",
"print \"Amount of undercooling: \",round(u,2),\"\u00b0C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Actual heat drop: 39.16 kJ/kg\n",
"Amount of undercooling: 22.18 \u00b0C\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12, page no. 600"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"p1 = 14 #Initial pressure(in bar):\n",
"T1 = 400+273 #Initial temperature(in K):\n",
"N = 16 #Number of nozzles:\n",
"p2 = 10 #Final pressure(in bar):\n",
"m = 5 #Discharge(in kg/s):\n",
"nn = 0.90 #Nozzle efficiency:\n",
"C1 = 100 #Inlet velocity(in m/s):\n",
"n = 1.3 #Insex of compression:\n",
"\n",
"#From steam tables:\n",
"h1 = 3257.5 #kJ/kg \n",
"s1 = 7.3026 #kJ/kg.K\n",
"T2 = 350.46 #\u00b0C\n",
"h2 = 3158.7 #kJ/kg\n",
"v2 = 0.2827 #m**3/kg\n",
"\n",
"#Calculations:\n",
"h12 = (h1-h2)*nn #Actual enthalpy change(inn kJ/kg):\n",
"C2 = sqrt(2*h12*10**3) #Velocity at exit(in m/s):\n",
"A2 = m*v2/(C2*N)*10**4 #Cross-sectional area at exit(in cm**2):\n",
"C2a = sqrt(2*h12*10**3+C1**2)#Modified velocity at nozzle exit(in m/s):\n",
"ma = 16*2.13*433.41*10**(-4)/0.2827#ma = A2*C2a*N/v2*10**(-4) \n",
"p = (ma-m)/m*100 #% increase in discharge:\n",
"\n",
"#Results: \n",
"print \"Cross-sectional area at exit of nozzle: \",round(A2,2),\"cm**2\"\n",
"print \"Percentage increase in discharge: \",round(p,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cross-sectional area at exit of nozzle: 2.09 cm**2\n",
"Percentage increase in discharge: 4.5 %\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13, page no. 602"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#Variable Declaration: \n",
"p1 = 20 #Initial pressure(in bar):\n",
"p3 = 5 #Final pressure(in bar):\n",
"n = 1.3\n",
"#From steam tables:\n",
"T1 = 212.42+273 #K\n",
"Tsat = 186.43+273 #K (at 11.6 bar)\n",
"psat = 5.452 #bar (at 155.14 \u00b0C)\n",
"h1 = 2799.5 #kJ/kg\n",
"v1 = 0.009963 #m**3/kg\n",
"s1 = 6.3409 #kJ/kg.K\n",
"h2aa = 2693.98 #kJ/kg\n",
"s2a = 6.5484 #kJ/kg.K\n",
"h3a = 2632.76 #kJ/kg\n",
"h3 = 2544.21 #kJ/kg\n",
"p2 = p1*0.58 #Pressure at throat(in bar):\n",
"\n",
"#Calculations:\n",
"s2aa = s1\n",
"s3a = s2a\n",
"s3 = s1\n",
"T2 = T1*(p2/p1)**((n-1)/n)\t#Temperature at state 2(in K):\n",
"d = p2/psat #Degree of supersaturation:\n",
"d1 = Tsat-T2 #Degree of undercooling:\n",
"h12 = (n/(n-1))*p1*10**2*v1*(1-(T2/T1)) #Isentropic enthalpy drop:\n",
"h2 = h1-h12 #Enthalpy at state 2(in kJ/kg):\n",
"h12aa = h1-h2aa #Heat drop with no saturation(in kJ/kg):\n",
"L = h12aa-h12 #Loss of available heat drop(in kJ/kg):\n",
"s12a = L/Tsat #Increase in entropy(in kJ/kg.K):\n",
"L1 = h3a-h3 #Loss due to undercooling(in kJ/kg):\n",
"p = L1/(h1-h3)*100 #Percentage loss:\n",
"\n",
"#Results: \n",
"print \"Degree of supersaturation: \",round(d,2)\n",
"print \"Degree of undercooling: \",round(d1,2),\"\u00b0C\"\n",
"print \"Entropy change: \",round(s12a,4),\"kJ/kg.K\"\n",
"print \"Loss due to undercooling: \",round(L1,2),\"kJ/kg\"\n",
"print \"Percentage loss: \",round(p,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Degree of supersaturation: 2.13\n",
"Degree of undercooling: 31.35 \u00b0C\n",
"Entropy change: 0.2075 kJ/kg.K\n",
"Loss due to undercooling: 88.55 kJ/kg\n",
"Percentage loss: 34.69\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14, page no. 604"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
" \n",
"from math import sqrt,pi\n",
"\n",
"#Variable Declaration: \n",
"m1 = 150/60 #Mass flow rate(in kg/s):\n",
"H = 5 #Height of water level from the axis of injector(in m):\n",
"p4 = 20 #Pressuer at which steam is injected(in bar):\n",
"Z4 = 0.8 #Water level in boiler from the injector(in m):\n",
"x1 = 0.95 #Dryness fraction at state 1:\n",
"C4 = 20 #Velocity in delivery pipe(in m/s):\n",
"p3 = 1.013 #Atmospheric pressure(in bar):\n",
"d = 10**3 #Density(in kg/m**3):\n",
"g = 9.81 #Acceleration due to gravity(in m/s**2):\n",
"Cps = 3.18 #Specific heat of steam(in kJ/kg.K):\n",
"Cpw = 4.18 #Specific heat of water(in kJ/kg.K):\n",
"#From steam tables:\n",
"T1 = 212.42 #\u00b0C\n",
"Tw = 25 #\u00b0C\n",
"p2 = 0.7*p4\n",
"h1 = 2704.95 #kJ/kg\n",
"hfg1 = 1890.7 #kJ/kg\n",
"s1 = 6.1462 #kJ/kg.K\n",
"x2 = 0.923\n",
"h2 = 2639.10 #kJ/kg\n",
"v2 = 0.13 #m**3/kg\n",
"\n",
"#Calculations:\n",
"s2 = s1\n",
"C2 = sqrt(2*(h1-h2)*10**3) #Velocity of steam at throat(in m/s):\n",
"C3 = sqrt(2*(g*Z4+p4*10**5/d+C4**2/2-p3*10**5/d))#Velocity at state 3(in m/s):\n",
"m = (C2-C3)/(sqrt(2*g*H)+C3) #Mass of water pumped per kg of steam(in kg):\n",
"m3 = m1+m1/m #Mass of mixture passing through state 3(in kg/s):\n",
"A3 = m3/(d*C3)*10**4 #Area of throat of mixing nozzle(in cm**2):\n",
"d3 = sqrt(A3*4/pi) #Diameter of throat of the mixing nozzle(in cm):\n",
"ms = m1/m #Mass of steam required for given flow rate(in kg/s):\n",
"A2 = ms*v2/C2*10**4 #Area at state 2(in cm**2):\n",
"d2 = sqrt(A2*4/pi) #Diameter of throat of steam nozzle(in cm):\n",
"T3 = (x1*hfg1+Cps*T1+m*Cpw*Tw)/(m*Cpw+Cps)#Temperature of water coming out of the injector(in C):\n",
"\n",
"#Results: \n",
"print \"Mass of water pumped per kg of steam: \",round(m,2),\"kg\"\n",
"print \"Diameter of throat of the mixing nozzle: \",round(d3,3),\"cm\"\n",
"print \"Diameter of throat of steam nozzle: \",round(d2,2),\"cm\"\n",
"print \"Temperature of water coming out of the injector: \",round(T3,2),\"\u00b0C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass of water pumped per kg of steam: 3.98 kg\n",
"Diameter of throat of the mixing nozzle: 0.783 cm\n",
"Diameter of throat of steam nozzle: 1.69 cm\n",
"Temperature of water coming out of the injector: 145.63 \u00b0C\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15, page no. 607"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"from math import sqrt\n",
"\n",
"#Variable Declaration: \n",
"p4 = 20 #Pressure at which steam is generated(in bar):\n",
"p1 = 1.5 #Pressure at inlet(in bar):\n",
"x1 = 0.9 #Dryness fraction:\n",
"M = 5000 #Mass of water taken from feed water tank(in kg/hr):\n",
"d = 10**3 #Density(in kg/m**3):\n",
"#From steam tables:\n",
"h1 = 2470.96 #kJ/kg \n",
"s1 = 6.6443 #kJ/kg.K\n",
"s2 = s1\n",
"x2 = 0.88\n",
"h2 = 2396.72 #kJ/kg\n",
"v2 = 1.7302 #m**3/kg\n",
"\n",
"#Calculations:\n",
"C2 = sqrt(2*(h1-h2)*10**3) #Steam velocity(in m/s):\n",
"C3 = sqrt(1.2*p4*2*10**5/d) #Velocity at 3(in m/s):\n",
"m = C2/C3-1 #Mass entrained per kg of steam:\n",
"ms = M/(3600*m) #Mass of steam supplied per second(in kg/s):\n",
"A2 = ms*v2/C2*10**4 #Area of steam nozzle(in cm**2):\n",
"D = M/3600+ms #Total discharge from injector(in kg/s):\n",
"A = D/(C3*d)*10**4 #Area of discharge orifice(in cm**2):\n",
"\n",
"#Results: \n",
"print \"Mass of water pumped per kg of steam: \",round(m,2),\"kg water/kg of steam\"\n",
"print \"Area of steam nozzle: \",round(A2,2),\"cm**2\"\n",
"print \"Area of discharge orifice: \",round(A,3),\"cm**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mass of water pumped per kg of steam: 4.56 kg water/kg of steam\n",
"Area of steam nozzle: 13.67 cm**2\n",
"Area of discharge orifice: 0.244 cm**2\n"
]
}
],
"prompt_number": 29
}
],
"metadata": {}
}
]
}