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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2 : pipe flow of gasses and gas liquid mixtures\n"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.1 page no : 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"from scipy.optimize import fsolve\n",
"from math import *\n",
"\n",
"# Initialization of Variable\n",
"pi = 3.1428\n",
"mmm = 16.04/1000 #molar mass of methane\n",
"mV = 22.414/1000 #molar volume\n",
"R = 8.314\n",
"mu = 1.08/10**5\n",
"r = 4.2/100 #radius\n",
"rr = 0.026/2/r #relative roughness\n",
"Pfinal = 560.*1000.\n",
"tfinal = 273+24\n",
"l = 68.5\n",
"m = 2.35 #mass flow rate\n",
"\n",
"#calculation\n",
"A = pi*r**2\n",
"A = round(A*10.**5)/10.**5\n",
"rho = mmm/mV\n",
"rho24 = mmm*Pfinal*273/mV/101.3/tfinal #density at 24'C\n",
"u = m/rho24/A\n",
"Re = u*rho24*2*r/mu\n",
"\n",
"#from graph\n",
"phi = 0.0032\n",
"#for solving using fsolve we copy numerical value of constant terms\n",
"#using back calculation\n",
"#as pressure maintained should be more than Pfinal so guessed value is Pfinal\n",
"\n",
"def eqn(x):\n",
" y = m**2/A**2*log(x/Pfinal)+(Pfinal**2-x**2)/2/R/tfinal*mmm+4*phi*l/2/r*m**2/A**2\n",
" return y\n",
"x = fsolve(eqn,560*10**3)\n",
"print \"pressure maintained at compressor in (kN/m**2):\",x[0]/1000\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"pressure maintained at compressor in (kN/m**2): 960.06917347\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.2 pageno : 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"from math import *\n",
"from numpy import *\n",
"from scipy.optimize import fsolve\n",
"\n",
"# Initialization of Variable\n",
"M = 28.8/1000\n",
"mu = 1.73/10**5\n",
"gamm = 1.402\n",
"P1 = 107.6*10**3\n",
"V = 22.414/1000\n",
"R = 8.314\n",
"temp = 285.\n",
"d = 4./1000\n",
"rr = 0.0008\n",
"phi = 0.00285\n",
"l = 68.5 \n",
"\n",
"#calculation\n",
"#constant term of equation\n",
"#part1\n",
"\n",
"a = 1.-8*phi*l/d #constant term in deff\n",
"def f(x):\n",
" return log(x**2)-x**2+2.938\n",
" \n",
"x = fsolve(f,1)\n",
"print x\n",
"z = 1./x[0]\n",
"z = round(z*1000.)/1000\n",
"print \"ratio of Pw/P1 : %.4f\"%z\n",
"\n",
"#part2\n",
"Pw = z*P1\n",
"nuw = V*P1*temp/Pw/M/273.\n",
"Uw = sqrt(nuw*Pw)\n",
"print \"maximum velocity in (m/s): %.4f\"%Uw\n",
"\n",
"#part3\n",
"Gw = pi*d**2/4*Pw/Uw\n",
"print \"maximum mass flow rate in(kg/s): %.4f\"%Gw\n",
"\n",
"#part4\n",
"G = 2.173/1000\n",
"J = G*Uw**2/2\n",
"print \"heat taken up to maintain isothermal codition(J/s): %.4f\"%J\n",
"\n",
"#part5\n",
"nu2 = 2.79 #found from graph\n",
"nu1 = R*temp/M/P1\n",
"P2 = P1*(nu1/nu2)**gamm\n",
"print \"crtical pressure ratio in adiabatic condition: %.4f\"%(P2/P1)\n",
"\n",
"#part6\n",
"Uw = sqrt(gamm*P2*nu2)\n",
"print \"velocity at adiabatic condition in (m/s): %.4f\"%Uw\n",
"\n",
"#part7\n",
"Gw = pi*d**2/4*Uw/nu2\n",
"print \"mass flow rate at adiabatic condition in (kg/s): %.4f\"%Gw\n",
"\n",
"\n",
"#part8\n",
"#polynomial in T of the form ax**2+bx+c = 0\n",
"c = gamm/(gamm-1)*P1*nu1+.5*Gw**2/pi**2/d**4*16*nu1**2\n",
"b = gamm/(gamm-1)*R/M\n",
"a = .5*Gw**2/pi**2/d**4*16*(R/M/P2)**2\n",
"y = poly1d([a,b,-c],False)\n",
"T2 = roots(y)\n",
"print \"temperature of discharging gas in (Celcius) : %.4f\"%(T2[1]-273)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 1.0268468]\n",
"ratio of Pw/P1 : 0.9740\n",
"maximum velocity in (m/s): 295.6723\n",
"maximum mass flow rate in(kg/s): 0.0045\n",
"heat taken up to maintain isothermal codition(J/s): 94.9841\n",
"crtical pressure ratio in adiabatic condition: 0.1629\n",
"velocity at adiabatic condition in (m/s): 261.8257\n",
"mass flow rate at adiabatic condition in (kg/s): 0.0012\n",
"temperature of discharging gas in (Celcius) : -46.3847"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:227: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
" improvement from the last ten iterations.\n",
" warnings.warn(msg, RuntimeWarning)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.3 pageno : 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"from scipy.optimize import fsolve \n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"\n",
"#1 refer to initial condition\n",
"R=8.314\n",
"P1=550.*10**3\n",
"T1=273.+350\n",
"M=18./1000\n",
"d=2.4/100\n",
"pi=3.1428\n",
"A=pi*d**2./4\n",
"gamm=1.33\n",
"roughness=0.096/1000/d\n",
"l=0.85\n",
"phi=0.0035 #assumed value of friction factor\n",
"\n",
"#calculation\n",
"nu1=R*T1/M/P1\n",
"Pw=0.4*P1 #estimation\n",
"nuw=(P1/Pw)**0.75*nu1\n",
"enthalpy=3167*1000.\n",
"Gw=math.sqrt(enthalpy*A**2/(gamm*nuw**2/(gamm-1)-nu1**2/2-nuw**2/2))\n",
"def eqn(x):\n",
" return math.log(x/nu1)+(gamm-1)/gamm*(enthalpy/2*(A/Gw)**2*(1/x**2-1/nu1**2)+0.25*(nu1**2/x**2-1)-.5*math.log(x/nu1))+4*phi*l/d\n",
"\n",
"x=fsolve(eqn,0.2)\n",
"\n",
"if x[0] != nuw:\n",
" print \"we again have to estimate Pw/P1\"\n",
" print \"new estimate assumed as 0.45\"\n",
" Pw=0.45*P1 #new estimation\n",
" nuw=(P1/Pw)**0.75*nu1\n",
" # & we equalise nu2 to nuw\n",
" nu2=nuw \n",
" Gw=math.sqrt(enthalpy*A**2/(gamm*nuw**2/(gamm-1)-nu1**2./2-nuw**2./2))\n",
" print \"mass flow rate of steam through pipe kg/s): %.2f\"%(Gw) \n",
" #part 2\n",
" print \"pressure of pipe at downstream end in (kPa):\",Pw/1000\n",
"else:\n",
" print \"our estimation is correct\"\n",
"\n",
"#part3\n",
"enthalpyw=2888.7*1000. #estimated from steam table\n",
"Tw=math.sqrt((enthalpy-enthalpyw+.5*Gw**2/A**2*nu1**2)*2*A**2/Gw**2/R**2*M**2*Pw**2)\n",
"print \"temperature of steam emerging from pipe in (Celcius): %.4f\"%(Tw-273)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"we again have to estimate Pw/P1\n",
"new estimate assumed as 0.45\n",
"mass flow rate of steam through pipe kg/s): 0.46\n",
"pressure of pipe at downstream end in (kPa): 247.5\n",
"temperature of steam emerging from pipe in (Celcius): 209.9420\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.4 pageno : 39"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"M=28.05/1000\n",
"gamm=1.23\n",
"R=8.314\n",
"atm=101.3*1000\n",
"P1=3.*atm\n",
"\n",
"#calculation\n",
"P2=P1*(2./(gamm+1))**(gamm/(gamm-1))\n",
"print \"pressure at nozzle throat (kPa): %.4f\"%(P2/1000.)\n",
"\n",
"#part2\n",
"temp=273.+50\n",
"nu1=R*temp/P1/M\n",
"G=18. #mass flow rate\n",
"nu2=nu1*(P2/P1)**(-1/gamm)\n",
"A=G**2*nu2**2*(gamm-1)/(2*gamm*P1*nu1*(1-(P2/P1)**((gamm-1)/gamm)))\n",
"d=math.sqrt(4*math.sqrt(A)/math.pi)\n",
"print \"diameter required at nozzle throat in (cm) : %.4f\"%(d*100)\n",
"#part3\n",
"vel=math.sqrt(2*gamm*P1*nu1/(gamm-1)*(1-(P2/P1)**((gamm-1)/gamm)))\n",
"print \"sonic velocity at throat in(m/s): %.4f\"%vel\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"pressure at nozzle throat (kPa): 169.7903\n",
"diameter required at nozzle throat in (cm) : 18.8847\n",
"sonic velocity at throat in(m/s): 324.9787\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.5 page no : 41"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"T=273.+15\n",
"rho=999.\n",
"rhom=13559. #density of mercury\n",
"g=9.81\n",
"P2=764.3/1000*rhom*g\n",
"R=8.314\n",
"M=16.04/1000\n",
"d=4.5/1000.\n",
"A=math.pi*d**2/4.\n",
"G=0.75/1000 #mass flow rate\n",
"delP=(1-math.exp(R*T*G**2./2/P2**2/M/A**2))*P2\n",
"h=-delP/rho/g\n",
"print \"height of manometer in (cm) %.4f\"%(h*100)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"height of manometer in (cm) 16.7941\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 2.6 page no : 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"rhol=931.\n",
"mu=1.55/10000 #viscosity of water\n",
"Vsp=0.6057 #specific volume\n",
"T=273+133.\n",
"mug=1.38/100000 #viscosity of steam\n",
"P=300*1000.\n",
"d=0.075\n",
"Gg=0.05 #mass flow gas phase\n",
"Gl=1.5 #mass flow liquid phase\n",
"A=math.pi*d**2./4\n",
"rho = 999.\n",
"#calculation\n",
"rhog=1./Vsp\n",
"rhog=round(rhog*1000)/1000.\n",
"velg=Gg/A/rhog\n",
"velg=round(velg*100)/100.\n",
"Reg=rhog*velg*d/mug\n",
"\n",
"#using chart\n",
"phig=0.00245 #friction factor gas phase\n",
"l=1\n",
"delPg=4*phig*velg**2*rhog/d\n",
"\n",
"#consider liquid phase\n",
"vell=Gl/A/rho\n",
"Rel=rho*vell*d/mu\n",
"if Rel>4000 and Reg>4000:\n",
" print \"both liquid phase and solid phase in turbulent motion\"\n",
" #from chart\n",
"\n",
"PHIg=5.\n",
"delP=PHIg**2.*delPg\n",
"print \"required pressure drop per unit length in (Pa) : %.4f\"%delP\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"both liquid phase and solid phase in turbulent motion\n",
"required pressure drop per unit length in (Pa) : 253.8050\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}