{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 6 : Boiling and condensation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.1 Page No : 177"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"So a bubble nucleus that has been detached from a cavity will not collapse in the liquid if it is larger than 1.89 micrometer \n",
"The superheat of the liquid is 9 C\n"
]
}
],
"source": [
"from scipy.optimize import fsolve \n",
"import math \n",
"import warnings\n",
"warnings.filterwarnings('ignore', 'The iteration is not making good progress')\n",
"# Variables\n",
"#(a)\n",
"Tsat = 350 \t\t\t#K, saturated temp.\n",
"Tl = Tsat+5 \t\t\t#K, liquid temp.\n",
"#By antoine eqn.\n",
"T = Tl-273 \t\t\t#C, \n",
"\n",
"# Calculations and Results\n",
"pl = math.exp(4.22658-(1244.95/(T+217.88)))\n",
"ST = 26.29-0.1161*T \t\t\t#dyne/cm, Surface tension of liquid\n",
"ST_ = ST*10**-3 \t\t\t#N/m Surface tension of liquid\n",
"Lv = 33605 \t\t\t#kj/kgmol, molar heat of vaporization\n",
"R = 0.08314 \t\t\t#m**3 bar/kgmol K, gas math.cosmath.tant\n",
"r = (2*ST_*R*Tsat**2)/((Tl-Tsat)*pl*(Lv*10**3))\n",
"print \"So a bubble nucleus that has been detached from a cavity will not collapse in \\\n",
"the liquid if it is larger than %.2f micrometer \"%(r*10**6)\n",
"\n",
"#(b)\n",
"r1 = 10**-6 \t\t\t#m\n",
"#pl1 = exp(4.22658-(1244.95/(Tl_-273+217.88))) \t\t\t#vapour pressure\n",
"#ST1 = 0.02629-1.161*10**-4(Tl_-273) \t\t\t#surface tension\n",
"\n",
"def f(Tl): \n",
" return (Tl-Tsat)-2*(0.02629-1.161*10**-4*(Tl-273))*R*Tsat**2/(r1*Lv*10**3)\n",
"Tl = fsolve(f,0.1)\n",
"T_ = (Tl-273.5)-(Tsat-273)\n",
"print \"The superheat of the liquid is %d C\"%(T_)\n",
"\n",
"# note : answers are slightly different because of rounding off error."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.2 Page No : 180"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"total rate of boiling of water is 69 kg/h \n",
"Qs2 compares reasonably well with the Qs1\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"d = 0.35 \t\t\t#m, diameter of pan\n",
"p = 1.013 \t\t\t#bar, pressure\n",
"T1 = 115. \t\t\t#C, bottom temp.\n",
"T2 = 100. \t\t\t#C, boiling temp.\n",
"Te = T1-T2 \t\t\t#C, excess temp.\n",
"#For Water\n",
"mu1 = 2.70*10**-4 \t\t\t#Ns/m**2, vismath.cosity\n",
"cp1 = 4.22 \t\t\t#kj/kg C, specific heat\n",
"rho1 = 958. \t\t\t#kg/m63. density\n",
"Lv1 = 2257. \t\t\t#kj/kg, enthalpy of vaporization \n",
"s1 = 0.059 \t\t\t#N/m , surface tension\n",
"Pr1 = 1.76 \t\t\t#Prandtl no.\n",
"#For saturated steam\n",
"rho2 = 0.5955\n",
"#For the pan\n",
"Csf = 0.013 \t\t\t#consmath.tant\n",
"n = 1. \t\t\t#exponent\n",
"g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n",
"\n",
"# Calculations and Results\n",
"#from eq. 6.6 \t\t\t#heat flux\n",
"Qs1 = mu1*Lv1*(g*(rho1-rho2)/s1)**(1./2)*(cp1*Te/(Csf*Lv1*(Pr1)**n))**3\n",
"Rate = Qs1/Lv1 \t\t\t#kg/m**2 s. rate of boiling\n",
"Ap = math.pi/4*d**2 \t\t\t#m**2, pan area\n",
"Trate = Rate*Ap \t\t\t#kg/s, Total rate of boiling\n",
"Trate_ = Trate*3600.5 \t\t\t#kg/h. Total rate of boiling\n",
"print \"total rate of boiling of water is %.0f kg/h \"%(Trate_)\n",
"\n",
"#umath.sing Lienhard's eq., \t\t\t#critical heat flux\n",
"Qmax = 0.149*Lv1*rho2*(s1*g*(rho1-rho2)/(rho2)**2)**(1/4)\n",
"#by Mostinski eq.\n",
"Pc = 221.2 \t\t\t#critical pressure\n",
"Pr = p/Pc \t\t\t#reduced pressure\n",
"hb = 0.00341*(Pc)**(2.3)*Te**(2.33)*Pr**(0.566) \t\t\t#boiling heat transfer coefficient\n",
"hb_ = hb/1000 \t\t\t#kW/m**2 C boiling heat transfer coefficient\n",
"Qs2 = hb_*(Te)\n",
"print \"Qs2 compares reasonably well with the Qs1\"\n",
"\n",
"# note: rounding off error."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.3 Page No : 181"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The boilins rate is 63 kg/m**2 h\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"A = 12.5673\n",
"B = 4234.6\n",
"pv = 1.813\n",
"T1 = 200. \t\t\t#C, tube wall temp.\n",
"#For methanol\n",
"Tc = 512.6 \t\t\t#K, critical temp.\n",
"w = 0.556 \t\t\t#acentric factor\n",
"Zra = 0.29056-0.08775*w\n",
"R = 0.08314 \t\t\t#m**3bar/gmol K, universal gas consmath.tant\n",
"Pc = 80.9 \t\t\t#bar, critical temp.\n",
"Mw = 32. \t\t\t#g, molecular wt\n",
"\n",
"#Calculation\n",
"#Estimation of liquid and vapour properties \n",
"#from antoine eq.\n",
"T = B/(A-math.log(pv)) \t\t\t#K, boiling point\n",
"Te = (T1+273)-T \t\t\t#K, excess temp.\n",
"Tm = ((T1+273)+T)/2 \t\t\t#K, mean temp.\n",
"#Liquid properties\n",
"#(a)\n",
"Tr = T/Tc \t\t\t#K, reduced temp.\n",
"#from Rackett technique\n",
"Vm = R*Tc*(Zra)**(1+(1-Tr)**(2/7))/Pc \t\t\t#m**3/kg mol, molar volume\n",
"rhol = Mw/Vm \t\t\t#kg/m**3, density of satorated liquid density\n",
"#(b)\n",
"#from Missenard technique\n",
"T2 = 348. \t\t\t#K,given data temp.\n",
"T3 = 373. \t\t\t#K,given data temp.\n",
"Cp2 = 107.5 \t\t\t#j/g mol K specific heat at T2\n",
"Cp3 = 119.4 \t\t\t#j/g mol K specific heat at T3\n",
"#By linear interpolation at T = 353.7 K\n",
"Cp = Cp2+(Cp3-Cp2)*((T-T2)/(T3-T2)) \t\t\t#kj/kg mol C, specific heat at T = 353.7 K\n",
"Cp_ = Cp*0.03125 \t\t\t#kj/kg C\n",
"#(c)Surface tension at given temp.(K)\n",
"T4 = 313.\n",
"St4 = 20.96\n",
"T5 = 333.\n",
"St5 = 19.4\n",
"#By linear interpolation at T = 353.7 K\n",
"S = 17.8 \t\t\t#dyne/cm, surface temp.\n",
"#(d) liquid vismath.cosity\n",
"T6 = 298. \n",
"MUt6 = 0.55 \t\t\t#cP, liquid vismath.cosity at temp = 298\n",
"MU = ((MUt6)**-0.2661+((T-T6)/233))**(-1/0.2661) \t\t\t#cP\n",
"#(e)Prandtl no. a,b,c are consmath.tant\n",
"a = 0.3225\n",
"b = -4.785*10**-4\n",
"c = 1.168*10**-7\n",
"kl = a+b*T+c*T**2 \t\t\t#W/m C, thermal conductivity\n",
"Prl = Cp_*1000*MU*10**-3/kl \t\t\t#Prandtl no.\n",
"#(f)heat of vaporization at 337.5 K\n",
"Lv = 1100. \t\t\t#kj/kg, enthalpy of vaporization\n",
"\n",
"#Properties of methanol vapour at Tm\n",
"#(a)\n",
"Vm1 = R*Tm/pv \t\t\t#m**3/kg mol, molar volume\n",
"rhov = Mw/Vm1 \t\t\t#kg/m**3, density of vapour\n",
"#(b) a1,b1,c1,d1 are math.cosmath.tants\n",
"a1 = -7.797*10**-3\n",
"b1 = 4.167*10**-5\n",
"c1 = 1.214*10**-7\n",
"d1 = -5.184*10**-11\n",
"#thermal conductivity of vapour\n",
"kv = a1+b1*Tm+c1*Tm**2+d1*Tm**3 \t\t\t#W/m C\n",
"#(c)heat capacity of vapour, a2,b2,c2,d2 are math.cosmath.tants\n",
"a2 = 21.15\n",
"b2 = 7.092*10**-2\n",
"c2 = 2.589*10**-5\n",
"d2 = -2.852*10**-8\n",
"#heat capacity of vapour, in kj/kh mol K\n",
"Cpv = a2+b2*Tm+c2*Tm**2+d2*Tm**3\n",
"\n",
"#(d)vismath.cosity of vapour\n",
"T7 = 67.\n",
"MUt7 = 112.\n",
"T8 = 127.\n",
"MUt8 = 132.\n",
"#from linear inter polation at Tm\n",
"MUv = 1.364*10**-5 \t\t\t#kg/m s\n",
"\n",
"#from Rohsenow's eq.\n",
"Csf = 0.027 \t\t\t#consmath.tant\n",
"n = 1.7 \t\t\t#exponent value\n",
"#from eq. 6.6\n",
"g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n",
"#heat flux \t\t\t#kW/m**2\n",
"Q = MU*10**-3*Lv*(g*(rhol-rhov)/S*10**-3)**(1./2)*(Cp_*Te/(Csf*Lv*(Prl)**n))**3\n",
"#from eq. 6.11\n",
"#from eq 6.11, critical heat flux\n",
"Qmax = 0.131*Lv*(rhov)**(1./2)*(S*10**-3*g*(rhol-rhov))**(1./4)\n",
"#dimensionless radius r_\n",
"r = 0.016\n",
"r_ = r*(g*(rhol-rhov)/(S*10**-3))**(1./2)\n",
"#peak heat flux\n",
"Qmax1 = Qmax*(0.89+2.27*math.exp(-3.44*math.sqrt(r_)))\n",
"#from eq. 6.12\n",
"#heat transfer coefficient hb\n",
"d = 0.032 \t\t\t#m, tube diameter\n",
"hb = 0.62*((kv**3)*rhov*(694-rhov)*g*(Lv*10**3+0.4*Cpv*Te)/(d*MUv*Te))**(1./4)\n",
"Qb = hb*Te \t\t\t#kw/m**2, heat flux\n",
"BR = Qb*10**-3/Lv \t\t\t#kg/m**2s, boilng rate \n",
"\n",
"# Results\n",
"print \"The boilins rate is %.0f kg/m**2 h\"%(BR*3600)\n",
"\n",
"# note : rounding off error."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.4 Page No : 188"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The total tube length is 0.393 m\n"
]
}
],
"source": [
"import math \n",
"\n",
"# Variables\n",
"W1 = 200. \t\t\t#kg/h, rate of entering toluene\n",
"muv = 10.**-5 \t\t\t#kg/m s, vismath.cosity of toluene vapour\n",
"mul = 2.31*10**-4 \t\t\t#kg/m s, vismath.cosity of benzene\n",
"rhol = 753. \t\t\t#kg/m**3, density of benzene\n",
"rhov = 3.7 \t\t\t#kg/m**3, density of toluene vapour\n",
"Cpl = 1968. \t\t\t#j/kg C, specific heat of benzene\n",
"kl = 0.112 \t\t\t#W/m C, thermal conductivity of benzene\n",
"T1 = 160. \t\t\t#C tube wall temp.\n",
"T2 = 120. \t\t\t#C , saturated temp.\n",
"Te = T1-T2 \t\t\t#C, excess temp.\n",
"Lv = 3.63*10**5 \t\t\t#j/kg, enthalpy of vaporization\n",
"s = 1.66*10**-2 \t\t\t#N/m, surface tension\n",
"\n",
"#Calculation of hc & hb\n",
"w = 0.125 \t\t\t#m, mean step size\n",
"d = 0.0211 \t\t\t#, internal diameter of tube\n",
"G = W1/(3600*math.pi/4*(d**2)) \t\t\t#kg/m**2 s, mass flow rate\n",
"Re1 = G*(1-w)*d/mul \t\t\t#Reynold no. \n",
"Prl = Cpl*mul/kl \t\t\t#Prandtl no.\n",
"#from eq. 6.23\n",
"x = (w/(1-w))**(0.9)*(rhol/rhov)**(0.5)*(muv/mul)**0.1 \t\t\t#let x = 1/succepsibility\n",
"#from eq. 6.22 \n",
"F = 2.35*(x+0.231)**0.736 \t\t\t#factor signifies 'liquid only reynold no.' to a two phase reynold no.\n",
"#from eq. 7.21\n",
"Re2 = 10**-4*Re1*F**1.25 \t\t\t#Reynold no.\n",
"#from eq. 6.18\n",
"S = (1+0.12*Re2**1.14)**-1 \t\t\t#boiling supression factor\n",
"#from eq. 6.15\n",
"hc = 0.023*Re1**(0.8)*Prl**(0.4)*(kl/d)*F \t\t\t#W/m**2 C, forced convection boiling part\n",
"#from eq. 6.16\n",
"mulv = (1/rhov)-(1/rhol) \t\t\t#m**3/kg, kinetic vismath.cosity of liquid vpaour\n",
"dpsat = Te*Lv/((T2+273)*mulv) \t\t\t#N/m**2, change in saturated presssure \n",
"#nucleate boiling part hb\n",
"hb = 1.218*10**-3*(kl**0.79*Cpl**0.45*rhol**0.49*Te**0.24*dpsat**0.75*S/(s**0.5*mul**0.29*Lv**0.24*rhov**0.24))\n",
"h = hc+hb \t\t\t#W/m**2 C, total heat transfer coefficient\n",
"\n",
"#calculation of required heat transfer area\n",
"a = 5. \t\t\t#%, persentage change in rate of vaporization\n",
"W2 = W1*a/100 \t\t\t#kg/h, rate of vaporization\n",
"W2_ = W2/3600 \t\t\t#kg/s\n",
"Q = W2_*Lv \t\t\t#W,heat load\n",
"A = Q/(h*Te) \t\t\t#m**2, area of heat transfer\n",
"l = A/(math.pi*d) \t\t\t#m, required length of tube\n",
"#from table 6.2\n",
"Tl = 0.393\n",
"\n",
"# Results\n",
"print \"The total tube length is %.3f m\"%(Tl)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.5 Page No : 195"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total rate of condensation is 33.08 kg/h\n"
]
}
],
"source": [
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"# Variables\n",
"rhol = 483. \t\t\t#kg/m**3, density of liquid propane\n",
"mul = 9.1*10**-5 \t\t\t#P ,vismath.cosity of liquid propane\n",
"kl = 0.09 \t\t\t#W/m K, thermal conductivity of liquid propane\n",
"Lv = 326. \t\t\t#kj/kg. enthalpy of vaporization\n",
"Cpl = 2.61 \t\t\t#kj/kg K, specific heat of liquid propane\n",
"T1 = 32.\n",
"T2 = 25. \t\t\t#C, surface temp.\n",
"p1 = 11.2\n",
"rhov = 24.7 \t\t\t#kg/m**3, density of vapour\n",
"g = 9.8\n",
"h = 0.3\n",
"\n",
"#Calculation\n",
"Lv1 = Lv+0.68*Cpl*(T1-T2)\n",
"#h = 0.943*(g*Lv1*10**3*rhol*(rhol-rhov)*kl**3/(mul*L*(T1-T2)))**(1/4)\n",
"#Q = h*(L*1)*(T1-T2)\n",
"#m = Q/(Lv1*10**3) = 1.867*10**-2*L**(3/4)\n",
"Ref = 30.\n",
"#from the relation 4*m/mu = Re\n",
"L = (Ref*mul/(4*1.867*10**-2))**(4./3)\n",
"m = 1.867*10**-2*L**(3./4) \t\t\t#rate of condensation for laminar flow\n",
"#from eq. 6.32\n",
"#Nu1 = h_/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1/3) = Ref/(1.08*(Ref)**(1.22)-5.2)\n",
"Lp = h-L \t\t\t#length of plate over which flow is wavy\n",
"A = Lp*1 \t\t\t#m**2 area of condensation\n",
"\n",
"\n",
"def f(h1): \n",
" return h1/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1./3)-(29.76+0.262*h1)/(1.08*(29.76+0.262*h1)**(1.22)-5.2)\n",
"h1 = fsolve(f,1000)\n",
"m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n",
"Ref1 = 4*m2/mul\n",
"m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n",
"\n",
"# Results\n",
"print \"Total rate of condensation is %.2f kg/h\"%(m2*3600)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.6 Page No : 199"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Rate of condensation is 45.7 kg/h \n",
"Rate of condensation is 1052 kg/h \n",
"thus there will be increase in the calculated rate of heat transfer and in rate of condensation as 1.188 percent\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"#data fot TCE\n",
"T1 = 87.4 \t\t\t#C, normal boiling point\n",
"T2 = 25. \t\t\t#C, surface temp.\n",
"Lv = 320.8 \t\t\t#kj/kg, heat of vaporization\n",
"cp = 1.105 \t\t\t#kj/kg C, specific heat\n",
"mu = 0.45*10**-3 \t\t\t#P. liquid vismath.cosity\n",
"k = 0.1064 \t\t\t#W/m C, thermal conductivity\n",
"rhol = 1375. \t\t\t#kg/m**3, liquid density\n",
"rhov = 4.44 \t\t\t#kg/m**3, density of vapour\n",
"Tm = (T1+T2)/2. \t\t\t#C, mean film temp.\n",
"d = 0.0254 \t\t\t#m, outside diameter of tube\n",
"l = 0.7 \t\t\t#m, length\n",
"g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n",
"\n",
"# Calculations and Results\n",
"#(a) from eq. 6.34\n",
"Lv1 = Lv+0.68*cp*(T1-T2)\n",
"h = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(mu*d*(T1-T2)))**(1./4)\n",
"A = math.pi*d*l \t\t\t#m**2, area of tube\n",
"Q = h*A*(T1-T2) \t\t\t#W, rate of heat transfer\n",
"m = (Q/Lv1)/1000 \t\t\t#kg/s rate of condensation\n",
"print \"Rate of condensation is %.1f kg/h \"%(m*3600)\n",
"\n",
"#(b) from eq. 6.35\n",
"N = 6. \t\t\t#No. of tubes in vertical tire\n",
"h1 = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(N*mu*d*(T1-T2)))**(1./4)\n",
"TN = 36. \t\t\t#total no. of tubes\n",
"TA = TN*math.pi*d*l \t\t\t#m**2, total area\n",
"Q1 = h1*TA*(T1-T2) \t\t\t#W, rate of heat transfer\n",
"m1 = (Q1/Lv1)/1000. \t\t\t#kg/s rate of condensation\n",
"print \"Rate of condensation is %.0f kg/h \"%(m1*3600)\n",
"#from chail's corelation\n",
"h2 = (1+0.2*cp*(T1-T2)*(N-1)/(Lv1))\n",
"print \"thus there will be increase in the calculated rate of\\\n",
" heat transfer and in rate of condensation as %.3f percent\"%(h2)\n",
"\n",
"# note : rounding off error."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6.7 Page No : 201"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"fraction of input vapour condensed is 52.7\n"
]
}
],
"source": [
"import math\n",
"\n",
"# Variables\n",
"Gv = 20. \t\t\t#kg/m**2 s, mass flow rate of benzene\n",
"di = 0.016 \t\t\t#m, tube diameter\n",
"muv = 8.9*(10**-6) \t\t\t#P, vismath.cosity\n",
"Lv = 391. \t\t\t#kj/kg., enthalpy of vaporization\n",
"cpl = 1.94 \t\t\t#kj/kg C, specific heat\n",
"Tv = 80. \t\t\t#C, normal boiling point of benzene\n",
"Tw = 55. \t\t\t#C, wall temp.\n",
"g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n",
"rhol = 815. \t\t\t#kg/m**3, density of benzene\n",
"rhov = 2.7 \t\t\t#kg/m**3, density of benzene vapour\n",
"kl = 0.13 \t\t\t#W/m C, thermal conductivity\n",
"mu = 3.81*10**-4 \t\t\t#P, vismath.cosity of benzene\n",
"l = 0.5 \t\t\t#m, length of tube\n",
"\n",
"#calculation\n",
"Rev = di*Gv/muv \t\t\t#Reynold no. of vapour\n",
"#from eq. 6.38\n",
"Lv1 = Lv+(3./8)*cpl*(Tv-Tw)\n",
"#heat transfer corfficient , h\n",
"h = 0.555*(g*rhol*(rhol-rhov)*kl**3*Lv1*10**3/(di*mu*(Tv-Tw)))**(1./4)\n",
"Aavl = math.pi*di*l \t\t\t#m**2, available area\n",
"Q = Aavl*h*(Tv-Tw) \t\t\t#W, rate of heat transfer\n",
"m = Q/(Lv1*10**3) \t\t\t#kg/s, rate of condensation of benzene\n",
"Ratei = Gv*(math.pi/4)*di**2 \t\t\t#kg/s rate of input of benzene vapour\n",
"n = m/Ratei \n",
"\n",
"# Results\n",
"print \"fraction of input vapour condensed is %.1f\"%(n*100)\n",
"\n",
"# note : rouding off error."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}