{
"metadata": {
"name": "",
"signature": "sha256:fb647d6d0a9fd1fab503f1e20b9cd4c1b8f196f963f97a28e2375980e25dde26"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7 : Steady, One-Dimensional, Irreversible Flow"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1 Page No : 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#initialisation of variables\n",
"r= 1.5\n",
"f= 0.025 # friction factor\n",
"\t\n",
"#CALCULATIONS\n",
"r1= (2/f)*(r**2-1)\n",
"\t\n",
"#RESULTS\n",
"print 'ratio L/D2 = %.f'%(r1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"ratio L/D2 = 100\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2 Page No : 214"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\t\n",
"#initialisation of variables\n",
"a= 6. \t#degrees angle\n",
"r= 1.5\n",
"l= 100. \t#ft\n",
"f= 0.025\n",
"K= 0.15\n",
"\t\n",
"#CALCULATIONS\n",
"R= r**4-1\n",
"R1= 1/math.tan(math.radians(a/2))*(1-(1./r))\n",
"p1= f*l\n",
"p2= 2.5*(l-p1)/l\n",
"p3= (1-r**2)**2\n",
"p4= K*p3\n",
"pt= p4+p2\n",
"\t\n",
"#RESULTS\n",
"print ' lowest ratio = %.2f'%(R)\n",
"print ' contribtuion of friction in pipe = %.3f lbf/ft**2'%(p1)\n",
"print ' contribtuion of diffuser in pipe = %.3f lbf/ft**2'%(p2)\n",
"print ' stagnant pressure drop = %.3f lbf/ft**2'%(p3)\n",
"print ' contribtuion of friction in pipe after reduction = %.3f lbf/ft**2'%(pt)\n",
"\n",
"# note : rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" lowest ratio = 4.06\n",
" contribtuion of friction in pipe = 2.500 lbf/ft**2\n",
" contribtuion of diffuser in pipe = 2.438 lbf/ft**2\n",
" stagnant pressure drop = 1.562 lbf/ft**2\n",
" contribtuion of friction in pipe after reduction = 2.672 lbf/ft**2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3 Page No : 219"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"d= 4. \t #in galvanised iron pipe diameter\n",
"q= 0.5 \t #ft**3/sec flow rate\n",
"w= 62.4 \t#lb/ft**3 density\n",
"u= 2.7*10**-5 \t#lbf sec/ft**2 viscosity\n",
"e= 0.0005 \t#ft\n",
"g= 32.1 \t#ft/sec**2 acceleration\n",
"f= 0.0235\n",
"lt= 400. \t#ft long\n",
"\t\n",
"#CALCULATIONS\n",
"V= 4*q/(math.pi*(d/12)**2)\n",
"Re= w*V*(d/12)/(u*g)\n",
"r= e/(d/12)\n",
"dz= (V**2/(2*g))*(1.7+f*lt/(d/12))\n",
"\t\n",
"#RESULTS\n",
"print ' mean flow velocity = %.2f ft/sec'%(V)\n",
"print ' Reynolds number = %.2e'%(Re)\n",
"print ' Relative roughness = %.4f'%(r)\n",
"print ' difference in the levels of water = %.1f ft'%(dz)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" mean flow velocity = 5.73 ft/sec\n",
" Reynolds number = 1.38e+05\n",
" Relative roughness = 0.0015\n",
" difference in the levels of water = 15.3 ft\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4 Page No : 220"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"d= 4. \t#in\n",
"v= 6.64 \t#ft/sec\n",
"\t\n",
"#CALCULATIONS\n",
"Q= math.pi*0.25*(d/12)**2*v\n",
"\t\n",
"#RESULTS\n",
"print 'Flow rate= %.3f ft**3/sec'%(Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow rate= 0.579 ft**3/sec\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5 Page No : 221"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#initialisation of variables\n",
"d= 0.366 \t#ft\n",
"i= 12\n",
"\t\n",
"#CALCULATIONS\n",
"pd= d*i\n",
"\t\n",
"#RESULTS\n",
"print 'Required pipe diameter = %.2f in'%(pd)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Required pipe diameter = 4.39 in\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6 Page No : 222"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#initialisation of variables\n",
"Ps1= 1050. \t#lbf/ft**2\n",
"fr= 10.7\n",
"p= 36.6 \t#lbf/ft**2\n",
"p1= 195. \t#lbf/ft**2\n",
"fr1= 16.\n",
"fr2= 1.8\n",
"\t\n",
"#CALCULATIONS\n",
"deltap = (p+957+p1+Ps1)\n",
"p2= round(fr*p)\n",
"dp= Ps1-p2\n",
"lc= round(dp/p)\n",
"sp= Ps1+p1-p*(fr1+fr2)\n",
"lc1= sp/p\n",
"\n",
"#RESULTS\n",
"print ' Pressure = %.f lbf/ft**2'%(round(deltap,-1))\n",
"print ' pressure difference = %.f lbf/ft**2'%(dp)\n",
"print ' Loss coefficient = %.f '%(lc)\n",
"print ' Loss coefficient = %.1f '%(lc1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Pressure = 2240 lbf/ft**2\n",
" pressure difference = 658 lbf/ft**2\n",
" Loss coefficient = 18 \n",
" Loss coefficient = 16.2 \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7 Page No : 232"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"p1= 50. \t#lbf/in**2 pressure\n",
"R= 96.3 \t#ft lbf/lbm R\n",
"T= 80. \t #F temperature\n",
"p2= 20. \t#lbf/in**2 pressure\n",
"r= 1.31\n",
"u= 2.34*10**-7 \t#lbf sec/ft**2\n",
"e= 0.00005 \t #ft\n",
"m= 5.*10**4 \t#lbm/sec\n",
"d= 1.5 \t #ft\n",
"g= 32.2 \t #ft/sec**2\n",
"f= 0.113\n",
"\t\n",
"#CALCULATIONS\n",
"w1= p1*144/(R*(460+T))\n",
"V1= 4*(m/3600)/(math.pi*w1*d**2)\n",
"Ma1= V1/(r*R*g*(460+T))**0.5\n",
"Re= w1*V1*d/(u*g)\n",
"dx= (((1/(r*Ma1**2))*10*(1-(p2/p1)**2))+math.log(p2/p1))*d/f\n",
"\t\n",
"#RESULTS\n",
"print ' density = %.3f lbm/ft**3'%(w1)\n",
"print ' mean flow velocity = %.1f ft/sec'%(V1)\n",
"print ' Match number = %.4f '%(Ma1)\n",
"print ' Reynolds number = %.2e '%(Re)\n",
"print ' Length of pipe = %.2e ft'%(dx)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" density = 0.138 lbm/ft**3\n",
" mean flow velocity = 56.8 ft/sec\n",
" Match number = 0.0383 \n",
" Reynolds number = 1.56e+06 \n",
" Length of pipe = 5.79e+04 ft\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9 Page No : 238"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"r= 1.4\n",
"R= 53.3 \t#ft lbf/lbm R\n",
"g= 32.2 \t#ft/sec**2\n",
"T1= 410. \t#R temperature\n",
"v= 2500. \t#ft/sec steadility\n",
"P1= 628. \t#lbf/in**2 pressure\n",
"\t\n",
"#CALCULATIONS\n",
"v1= int(math.sqrt(r*g*R*T1))\n",
"Ma1= round(v/v1,2)\n",
"Ts1= int(T1*(1+0.5*(r-1)*Ma1**2))\n",
"Ps1= P1*(1+0.5*(r-1)*Ma1**2)**(r/(r-1))\n",
"Ps2= Ps1*((r+1)/(2*r*Ma1**2-r+1))**(1/(r-1))*(0.5*(r+1)*Ma1**2/(1+0.5*(r-1)*Ma1**2))**(r/(r-1))\n",
"\n",
"#RESULTS\n",
"print ' acoustic velocity = %.f ft/sec'%(v1)\n",
"print ' Match number = %.2f '%(Ma1)\n",
"print ' Stagnition temperature = %.f R'%(Ts1)\n",
"print ' Stagnition pressure = %.f lbf/ft**2'%(Ps1)\n",
"print ' Stagnition pressure = %.f lbf/ft**2'%(Ps2)\n",
"\n",
"# note : answer in book is wrong. Please check manually.\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" acoustic velocity = 992 ft/sec\n",
" Match number = 2.52 \n",
" Stagnition temperature = 930 R\n",
" Stagnition pressure = 11069 lbf/ft**2\n",
" Stagnition pressure = 5435 lbf/ft**2\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10 Page No : 245"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#initialisation of variables\n",
"p2= 67.2 \t#lbf/in**2 pressure\n",
"p1= 63. \t#lbf/in62 pressure\n",
"r= 1.4\n",
"n= 0.6 # efficiency\n",
"T1= 870. \t#R temperature\n",
"ma1= 0.8 \t#ft/sec mach number\n",
"\n",
"#CALCULATIONS\n",
"dt= (p2/p1)**((r-1)/r)-1\n",
"dt1= dt/n\n",
"T2= T1*(1+dt1)\n",
"Ts1= T1*(1+0.5*(r-1)*ma1**2)\n",
"ps1= p1*(1+0.5*(r-1)*ma1**2)**(r/(r-1))\n",
"ps2= p2*(Ts1/T2)**(r/(r-1))\n",
"dp= ps1-ps2\n",
"\n",
"#RESULTS\n",
"print ' dT = %.5f '%(dt)\n",
"print ' dT1 = %.5f '%(dt1)\n",
"print ' Temperature = %.f R'%(T2)\n",
"print ' Temperature = %.1f R'%(Ts1)\n",
"print ' Pressure = %.1f lbf/in**2'%(ps1)\n",
"print ' Pressure = %.1f lbf/in**2'%(ps2)\n",
"print ' pressure difference = %.1f lbf/in**2'%(dp)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" dT = 0.01861 \n",
" dT1 = 0.03102 \n",
" Temperature = 897 R\n",
" Temperature = 981.4 R\n",
" Pressure = 96.0 lbf/in**2\n",
" Pressure = 92.0 lbf/in**2\n",
" pressure difference = 4.0 lbf/in**2\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11 Page No : 246"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#initialisation of variables\n",
"r= 1.4\n",
"ma3= 3. \t#ft/sec mach number\n",
"ps= 80. \t#lbf/ft**2 pressure\n",
"Ts= 840. \t#R temperature\n",
"r1= 53.3 \t#ft lbm/ft**3\n",
"A3= 2. \t#in**2 flow area\n",
"g= 32.2 \t#ft/sec**2\n",
"ma1= 1.6\n",
"\n",
"#CALCULATIONS\n",
"R= (1+(r-1)*0.5*ma3**2)**(r/(r-1))\n",
"p3= ps/R\n",
"R1= 1+0.5*(r-1)*ma3**2\n",
"T3= Ts/R1\n",
"w3= p3*144/(r1*T3)\n",
"V3= ma3*math.sqrt(r*r1*g*T3)\n",
"m= w3*V3*A3/144\n",
"ra= ((r+1)/(2*r*ma1**2-(r-1)))**(1/(r-1))*(0.5*(r+1)*ma1**2/(1+0.5*(r-1)*ma1**2))**(r/(r-1))\n",
"ps2= ps*ra\n",
"dp= ps-ps2\n",
"\n",
"#RESULTS\n",
"print ' outlet pressure = %.2f lbf/in**2'%(p3)\n",
"print ' outlet temperature = %.f R'%(T3)\n",
"print ' mass flow rate = %.3f lbm/sec'%(m)\n",
"print ' ps2 = %.1f lbf/in**2'%(ps2)\n",
"print ' Stagnation pressure loss = %.1f lbf/in**2'%(dp)\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" outlet pressure = 2.18 lbf/in**2\n",
" outlet temperature = 300 R\n",
" mass flow rate = 0.694 lbm/sec\n",
" ps2 = 71.6 lbf/in**2\n",
" Stagnation pressure loss = 8.4 lbf/in**2\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}