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{
"metadata": {
"name": "",
"signature": "sha256:c21785277c0a99c3eb4c310a9e20c477f6ab2a0a22da1b2d3844df1699a78d21"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 17: Compressible Flow in Pipes"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.1, Page 566"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"import sympy\n",
"from sympy import solve,symbols\n",
"\n",
" #Initializing the variables\n",
"g = 9.81;\n",
"rho = 1000;\n",
"rhoHg = 13.6*rho;\n",
"d1 = 0.075;\n",
"d2 = 0.025;\n",
"Pi = 0.250;\n",
"Pt = 0.150;\n",
"P_Hg = 0.760;\n",
"rho1 = 1.6;\n",
"gma = 1.4;\n",
"\n",
" #Calculations\n",
"P1 = (Pi+P_Hg)*rhoHg*g;\n",
"P2 = (Pt+P_Hg)*rhoHg*g;\n",
"rho2 = rho1*(P2/P1)**(1/gma);\n",
"V0=symbols('V0')\n",
"V1=symbols('V1')\n",
"Velo = solve([d2**2*V1*rho2-d1**2*V0*rho1,0.5*(V1**2 - V0**2)*((gma-1)/gma)*(rho2*rho1/(rho2*P1-rho1*P2))-1],[V0,V1])\n",
"s=(Velo[1])[0]\n",
"Flow = math.pi*d1**2/4*s;\n",
"\n",
"print \"Volume of flow (m3/s):\",round(Flow,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volume of flow (m3/s): 0.06\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.2, Page 571"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"Ma = 4;\n",
"gma = 1.4;\n",
"At = 500; # in mm\n",
"\n",
" #Calculations\n",
"N = 1 + (gma-1)*Ma**2/2;\n",
"D = (gma+1)/2 ;\n",
"#ratio of A/At ==R\n",
"R = round( (N/D)**((gma+1)/(2*(gma-1)))/Ma,2);\n",
"A=At*R\n",
"print \"Area of test section (mm^2):\",A"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Area of test section (mm^2): 5360.0\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.3, Page 575"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"Ma1 = 2;\n",
"gma = 1.4;\n",
"T1 = 15+273; # In kelvin\n",
"P1 = 105; \n",
"\n",
" #Calculations\n",
"Ma2 = (((gma-1)*Ma1**2 +2)/(2*gma*Ma1**2-gma+1))**0.5;\n",
"P2 = P1*(1+gma*Ma1**2)/(1+gma*Ma2**2);\n",
"T2 = T1*(1 +(gma-1)/2*Ma1**2)/(1 +(gma-1)/2*Ma2**2);\n",
"\n",
"\n",
"print \"Mach No downstream shock wave :\",round(Ma2,3)\n",
"print \"Pressure (bar) of downstream shock wave :\",round(P2)\n",
"print \"Temperature (Degree C) of downstream shock wave :\",T2 - 273"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mach No downstream shock wave : 0.577\n",
"Pressure (bar) of downstream shock wave : 473.0\n",
"Temperature (Degree C) of downstream shock wave : 213.0\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.4, Page 581"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"gma = 1.4;\n",
"f = 0.00375;\n",
"d = 0.05;\n",
"\n",
" #Calculations\n",
"m = d/4;\n",
"def x(Ma):\n",
" A =(1 -Ma**2 )/(gma*Ma**2);\n",
" B = (gma+1)*Ma**2/(2+(gma-1)*Ma**2); \n",
" y = m/f*(A+ (gma+1)*math.log(B)/(2*gma));\n",
" return y\n",
"\n",
"X1 = x(0.2); # At entrance Ma = 0.2;\n",
"X06_X1 =x(0.6); # Section(b) Ma = 0.6;\n",
"\n",
"X06 = X1-X06_X1;\n",
"\n",
"print \"The Distance X1 at which the Mach number is unity (m) :\",round(X1,2)\n",
"print \"Distance from the entrance (m) :\",round(X06,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Distance X1 at which the Mach number is unity (m) : 48.44\n",
"Distance from the entrance (m) : 46.81\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.5, Page 585"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"from scipy.optimize import fsolve\n",
"\n",
" #Initializing the variables\n",
"gma = 1.4;\n",
"Q = 28/60; # m3/s\n",
"d = 0.1;\n",
"p1 = 200*10**3;\n",
"f = 0.004;\n",
"x_x1 = 60;\n",
"R = 287;\n",
"T = 15+273;\n",
"\n",
" #Calculations\n",
"A = math.pi*d**2/4;\n",
"m = d/4;\n",
"v1 = Q/A;\n",
"pa = p1*(1-f*(x_x1)*v1**2/(m*R*T))**0.5;\n",
"\n",
"def g(p):\n",
" A = (v1*p1)**2/(R*T)\n",
" B = f*A*x_x1/(2*m);\n",
" y = (p**2 - p1**2)/2 -A*math.log(p/p1) +B;\n",
" return y\n",
" \n",
"pb=fsolve(g,pa) # Guessing solution around pa\n",
"pb=pb[0]\n",
"print \"Pressure at the outlet, neglecting velocity changes (kN/m2) :\",round(pa/1000,1)\n",
"print \"Pressure at the outlet, allowing for velocity changes (kN/m2) :\",round(pb/1000,1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure at the outlet, neglecting velocity changes (kN/m2) : 153.6\n",
"Pressure at the outlet, allowing for velocity changes (kN/m2) : 150.4\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
|
