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{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 : Fluid Flow in Pipes and Nozzles"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1 Page No : 147"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Given\n",
"R = 848.0;#gas consmath.tant in m Kgf/Kgmole K\n",
"M = 29.0;#molecular weight of air\n",
"g = 9.81;\n",
"T1 = 90+273.0;#initial temperature in K\n",
"y = 1.4;#gamma = Cp/Cv\n",
"W = 800/3600.0;#Mass rate of air in Kg/sec\n",
"P1 = 3.5;#initial pressure in atm\n",
"d = 2.5;#diameter of the pipe in cm\n",
"\n",
"#To find out the pressure at the final point\n",
"v1 = (R*T1)/(M*P1*1.033*10**4);#specific volume in cubic meter/Kg\n",
"u1 = (W*v1)/(math.pi*(d**2*(10**-4))/4);#inital velocity in m/sec\n",
"#Assume final temperature as\n",
"T2 = [300,310];\n",
"#Assume specific heat capacity in J/KgK corresponding to the above temperature as\n",
"Cp = [2987.56,2983.56];\n",
"us = []\n",
"u2 = []\n",
"for i in range(0,2):\n",
" us.append((g*y*R*T2[i]/M)**(1/2));#sonic velocity attained in m/sec\n",
" u2.append(((u1**2)-((2*g*Cp[i]/M)*(T2[i]-T1)))**(1/2));#From equation 9.18 & 9.19 (page no 170)\n",
"if us[i]-u2[i] <= 1: \n",
" u2 = u2[i];\n",
" Tnew2 = T2[i];\n",
"v2 = u2*(math.pi/4)*(d**2/10**4)*(1/W);\n",
"P2 = (P1*v1*Tnew2)/(T1*v2);\n",
"print \"The pressure at the final point is %f atm\"%(P2);\n",
"#end\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The pressure at the final point is 397.261807 atm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2 Page No : 151"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Given\n",
"A1 = 0.002 #inlet area in sq meter\n",
"A2 = 0.0005 #throat area in sq meter\n",
"P1 = 1.3*10**4 #inlet pressure in Kgf/sq m\n",
"P2 = 0.7*10**4 #throat pressure in Kgf/sq m\n",
"g = 9.81\n",
"v = 12*10**(-4) #specific volume in cubic m /Kg\n",
"\n",
"#To find out the mass rate of alcohol\n",
"u2 = ((v*2*g*(P1-P2))/(1-((A2/A1)**2)))**(0.5) #throat velocity in m/sec\n",
"W = (u2*A2)/v\n",
"print \"The mass rate of alcohol is \",\n",
"print \"%.4f\" %W,\n",
"print \" Kg/sec\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mass rate of alcohol is 5.1147 Kg/sec\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3 Page No : 153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import math\n",
"import matplotlib.pyplot as plt\n",
"import numpy\n",
"\n",
"#Given\n",
"P1 = 50.0;#initial pressure in Kgf/sq m\n",
"T1 = 45+273.0;#initial temperature in K\n",
"g = 9.81;\n",
"y = 1.35;#gamma\n",
"R = 848.0;#gas consmath.tant in m Kgf/Kgmole K\n",
"M = 29.0;#molecular weight of air\n",
"d = 1.0;#pipe diameter in cm\n",
"\n",
"#(i)To plot velocity,specific volume,mass velocity against P2/P1\n",
"#(ii)To calculate the critical pressure,critical mass velocity and mass rate of flow\n",
"#(i)Plotting of graph\n",
"V1 = (R*T1)/(M*P1*1.033*10**4);#initial volume of the gas in cubic m/Kg\n",
"#P3 = P2/P1 (say)\n",
"#Assume P3 values as\n",
"P3 = [1.0,0.8,0.6,0.4,0.2,0.1,0.05];\n",
"G = [0,0,0,0,0,0,0];\n",
"u2 = []\n",
"v2 = []\n",
"G = []\n",
"for i in range(0,7):\n",
" u2.append((((2*g*y*R*T1)/((y-1)*M))*(1-(P3[i]**((y-1)/y))))**(1/2.0));#final velocity in m/sec\n",
"for i in range(0,7):\n",
" v2.append(V1/(P3[i]**(1/y)));#final specific volume in cubic meter/Kg\n",
"for i in range(0,7):\n",
" G.append(u2[i]/v2[i]);#Mass velocity in Kg/sq m sec\n",
"\n",
"plt.plot(P3,u2,\"o-\")\n",
"plt.title(\"Velocity vs P2/P1\")\n",
"plt.xlabel(\"P2/P1\")\n",
"plt.ylabel(\"Velocity\")\n",
"plt.show()\n",
"\n",
"plt.plot(P3,G,\"+-\")\n",
"plt.title(\"Mass velocity vs P2/P1\")\n",
"plt.xlabel(\"P2/P1\")\n",
"plt.ylabel(\"Mass Velocity\")\n",
"plt.show()\n",
"\n",
"P_3 = [1.0,0.8,0.6,0.4,0.2,0.1,0];\n",
"plt.plot(P_3,v2,\"*-\")\n",
"plt.title(\"Sp. volume vs P2/P1\")\n",
"plt.xlabel(\"P2/P1\")\n",
"plt.ylabel(\"Specific Volume\")\n",
"plt.show()\n",
"\n",
"#(ii)Calculation of critical pressure,critical mass velocity and mass rate of flow\n",
"#From equation 9.37(page no 181)\n",
"P2 = P1*(2/(y+1))**(y/(y-1));\n",
"print \"The critical pressure is %f atm\"%(P2);\n",
"#From equation a (page no 183)\n",
"u2 = (((2*g*y*R*T1)/((y-1)*M))*(1-((P2/P1)**((y-1)/y))))**(1/2.0);\n",
"print \" The critical velocity is %f m/sec\"%(u2);\n",
"#From equation b (page no 183)\n",
"v2 = ((R*T1)/(M*P1*1.033*10**4))/((P2/P1)**(1.0/y));\n",
"print \" The critical specific volume is %f cubic meter/Kg\"%(v2);\n",
"#From relation c (page no 183)\n",
"Gnew = float(u2)/v2;\n",
"print \" The critical mass velocity is %f Kg/sq meter sec\"%(Gnew);\n",
"W = Gnew*(math.pi/4.0)*(d/(100.0))**2;\n",
"print \" Mass rate of flow through nozzle is %f Kg/sec\"%(W);\n",
"#end\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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CQsbrtZLFN99Ysrj6aiULkVinJCEhl59vyeKrr2DcOLjmGq1lIRKrlCQkbN55x5LF+vWW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\n",
"text": [
"<matplotlib.figure.Figure at 0x104438150>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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FF/odiYgko4EDYfLk9CsyGUtSOejuL8OKP76OLVqUYjz2mLVSVDBSRKJp2tQW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\n",
"text": [
"<matplotlib.figure.Figure at 0x104489650>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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vfwkbN/qdOhGpDQUM8Uzv3taqavlyK5o67TS4/HL47381/IhIOlKRlCRNcTE8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\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1045fb150>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical pressure is 26.842561 atm\n",
" The critical velocity is 323.738941 m/sec\n",
" The critical specific volume is 0.028541 cubic meter/Kg\n",
" The critical mass velocity is 11343.108938 Kg/sq meter sec\n",
" Mass rate of flow through nozzle is 0.890886 Kg/sec\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4 Page No : 156"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Given\n",
"A1 = 0.1;#Inlet area in sq meter\n",
"u1 = 60.0;#inlet velocity in m/sec\n",
"v1 = 0.185;#inlet specific volume in cubic meter/Kg\n",
"H1 = 715.0;#inlet enthalpy in Kcal/Kg\n",
"H2 = 660.0;#exit enthalpy in Kcal/Kg\n",
"v2 = 0.495;#exit specific volume in cubic meter/Kg\n",
"g = 9.81\n",
"\n",
"#To calculate the area at exit of nozzle and hence decide the type of the nozzle\n",
"#From the first law\n",
"u2 = ((u1**2)-(2*g*(H2-H1)*427))**(1/2);\n",
"W = (u1*A1)/v1;#Mass rate of gas in Kg/sec\n",
"A2 = (W*v2)/u2;#Area at exit of nozzle\n",
"if(A2 < A1):\n",
" print \"The nozzle is convergent\";\n",
"else:\n",
" print \"The nozzle is divergent\";\n",
"#end\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The nozzle is divergent\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|