{
"metadata": {
"name": "",
"signature": "sha256:d460554b2abe6f6d6700d68291fcbf83cdf7b3bd9d716f5a9395eef88b744934"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 11 : Turbomachines:Elementary Analysis"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.1 Page No : 426"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from sympy.functions.elementary.trigonometric import acot\n",
"\n",
"#initialisation of variables\n",
"rt= 1.3 \t#ft\n",
"rr= 0.6 \t#ft\n",
"Q= 75. \t#ft**3 flow rate\n",
"rm= 0.95\n",
"w1= 40. \t#rev/sec \n",
"bim= 153. \t#degrees blade inlet angle\n",
"bom= 147. \t#degrees blade outlet angle\n",
"w= 62.4 \t#lb/ft**3\n",
"g= 32.2 \t#ft/sec**2\n",
"\t\n",
"#CALCULATIONS\n",
"A= round(math.pi*(rt**2-rr**2),2)\n",
"Va= round(Q/A,2)\n",
"Vbm= rm*w1\n",
"#a= -1/math.degrees(math.atan(-Vbm/Va))\n",
"a = math.degrees(acot(-Vbm/Va))\n",
"im= a-bim\n",
"vwm= Vbm+Va*1/math.tan(math.radians(bom))\n",
"dvwm= rm*vwm\n",
"C= w*Q*dvwm/g\n",
"Cw= C*w1\n",
"dp= Cw/Q\n",
"\n",
"#RESULTS\n",
"print ' Incidence = %.1f degrees'%(im) \n",
"print ' Oulet velocity = %.2f ft/sec'%(vwm)\n",
"print ' Change of whirl at the mean radius = %.2f ft**2/sec'%(dvwm)\n",
"\n",
"print ' Torque = %.f lbf/ft'%(C)\n",
"print ' Rate of working = %.f ft lbf/sec'%(Cw)\n",
"print ' Workdone by the rotor = %.f lbf/ft**2'%(dp)\n",
"\n",
"# note : answer in book is wrong. please check manually."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Incidence = -178.3 degrees\n",
" Oulet velocity = 10.37 ft/sec\n",
" Change of whirl at the mean radius = 9.86 ft**2/sec\n",
" Torque = 1432 lbf/ft\n",
" Rate of working = 57300 ft lbf/sec\n",
" Workdone by the rotor = 764 lbf/ft**2\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.2 Page No : 428"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#initialisation of variables\n",
"vbm= 38. \t#ft/sec\n",
"va= 17.94 \t#ft/sec\n",
"a= 147.5 \t#degrees\n",
"vwm= 10.37 \t#ft/sec\n",
"C= 1430. \t#lbf/ft\n",
"P= 763. \t#lbf/ft**2\n",
"\t\n",
"#CALCULATIONS\n",
"vwm1= vbm+va*1/math.tan(math.radians(a))\n",
"p= (vwm-vwm1)/vwm\n",
"C1= C*(1-p)\n",
"P1= P*(1-p)\n",
"\t\n",
"#RESULTS\n",
"print ' Oulet Velocity = %.2f ft/sec'%(vwm1) \n",
"print ' Torque = %.f lbf/ft'%(round(C1,-1))\n",
"print ' Workdone by the rotor = %.f lbf/ft**2'%(P1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Oulet Velocity = 9.84 ft/sec\n",
" Torque = 1360 lbf/ft\n",
" Workdone by the rotor = 724 lbf/ft**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.3 Page No : 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from sympy.functions.elementary.trigonometric import acot\n",
"\t\n",
"#initialisation of variables\n",
"a= 154 \t #degrees\n",
"vbm= 38 \t#ft/sec\n",
"bom= 147 \t#degrees outlet angle\n",
"vwm= -7.78 \t#ft/sec outlet whirl velocity\n",
"w= 62.4 \t#lbf/ft**3\n",
"g= 32.2 \t#ft/sec**2\n",
"vb= 38 \t#ft/sec velocity\n",
"A= 4.18 \t#ft**2 flow area\n",
"e= 0.95\n",
"\t\n",
"#CALCULATIONS\n",
"vat= (vwm-vb)*math.tan(math.radians(bom))\n",
"Q= vat*A\n",
"#a1= 1/math.tan(math.radians(-vbm/vat))\n",
"a1 = math.degrees(acot(-vbm/vat))\n",
"imt= a1-a\n",
"C= w*Q*vwm*e/g\n",
"\n",
"#RESULTS\n",
"print ' Flow rate = %.1f ft**3'%(Q)\n",
"print ' Incidence angle= %.f degrees'%(imt)\n",
"print ' Torque= %.f lbf ft'%(C)\n",
"#Incorrect value for a1 in textbook. Hence the difference in answers"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Flow rate = 124.3 ft**3\n",
" Incidence angle= -192 degrees\n",
" Torque= -1780 lbf ft\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.4 Page No : 435"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import *\n",
"\t\n",
"#initialisation of variables\n",
"rt= 0.5 \t#ft radius\n",
"rr= 0.16 \t#ft root radius\n",
"dv1= 88.3 \t#ft/sec\n",
"b= 150. \t#degrees\n",
"r= array([0.16, 0.3, 0.5])\n",
"vw= array([2.5, 5, 7.5])\n",
"vb= array([46.6, 88.3, 132.5])\n",
"vrb= array([44.16, 88.3, 132.5])\n",
"v1= array([-1.154, -0.385])\n",
"\t\n",
"#CALCULATIONS\n",
"A= math.pi*(rt**2-rr**2)\n",
"Va= -dv1*math.tan(math.radians(b))\n",
"Q= Va*A\n",
"ari = degrees((arctan(Va/(vw - vb)))) + 180\n",
"ari = array([ari[0],ari[2]])\n",
"#a= tan(radians(v1))+180\n",
"b = degrees(math.tan(0.577))\n",
"i = ari - 150\n",
"\n",
"#RESULTS\n",
"print ' Velocity = %.2f ft/sec'%(Va)\n",
"print ' Flow rate = %.1f ft**3'%(Q)\n",
"\n",
"print (v1)\n",
"print (ari)\n",
"print (i)\n",
"\n",
"# rounding off error. and for 'i' answer is wrong. please check. "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Velocity = 50.98 ft/sec\n",
" Flow rate = 35.9 ft**3\n",
"[-1.154 -0.385]\n",
"[ 130.86126801 157.81238868]\n",
"[-19.13873199 7.81238868]\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.5 Page No : 436"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import *\n",
"\t\n",
"#initialisation of variables\n",
"rt= 0.5 \t#ft\n",
"rr= 0.16 \t#ft\n",
"dv1= 88.3 \t#ft/sec\n",
"b= 150. \t#degrees\n",
"a= 5. \t#degrees mean radius\n",
"v1= array([-0.933 ,-0.311])\n",
"i= array([1.0, 5.0 ,6.7])\n",
"\t\n",
"#CALCULATIONS\n",
"b1= b+a\n",
"A= math.pi*(rt**2-rr**2)\n",
"Va= -dv1*math.radians(math.tan(b1))\n",
"Q= Va*A\n",
"a1= degrees(tan(v1))+180\n",
"\n",
"\t\n",
"#RESULTS\n",
"print ' Velocity = %.2f ft/sec'%(Va)\n",
"print ' Flow rate = %.1f ft**3/sec'%(Q)\n",
"\n",
"print (v1)\n",
"print (a1)\n",
"print (i)\n",
"#Incorrect calculations in textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity = -2.76 ft/sec\n",
" Flow rate = -1.9 ft**3/sec\n",
"[-0.933 -0.311]\n",
"[ 102.69071396 161.58339075]\n",
"[ 1. 5. 6.7]\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.6 Page No : 439"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"r= 1. \t#in\n",
"b= 0.75 \t#in rotor inlet width\n",
"w= 180. \t#rev/sec\n",
"B= 120. \t#degrees blade inlet angle\n",
"Bo= 150. \t#degrees blade outlet angle\n",
"ro= 3. \t#ft\n",
"bo= 0.5 \t#ft\n",
"Vbo= 180. \t#ft/sec\n",
"w1= 62.4 \t#lbf/ft**3 density\n",
"g= 32.2 \t#ft/sec**2\n",
"\t\n",
"#CALCULATIONS\n",
"Q= -2*math.pi*(r/12)**2*(b/12)*w*math.tan(math.radians(B))\n",
"Vfo= Q/(2*math.pi*(ro/12)*(bo/12))\n",
"Vwo= Vbo*(ro/12)+Vfo*1/math.tan(math.radians(Bo))\n",
"C= w1*Q*Vwo*(ro/12)/g\n",
"dp= w1*Vwo*w*(ro/12)/g\n",
"ari= degrees(math.atan((-Q*0.8/(2*math.pi*(r/12)**2*(b/12)*w))))+180\n",
"i1= ari-B\n",
"\n",
"#RESULTS\n",
"print ' Flow rate = %.2f ft**3/sec'%(Q)\n",
"print ' radial velocity= %.2f ft/sec'%(Vfo)\n",
"print ' outlet whirl velocity= %.2f ft/sec'%(Vwo)\n",
"print ' Torque= %.2f lbf ft'%(C)\n",
"print ' Stagnant pressure = %.f lbf/ft**2'%(dp)\n",
"print ' Incidence angle = %.1f degrees'%(i1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Flow rate = 0.85 ft**3/sec\n",
" radial velocity= 12.99 ft/sec\n",
" outlet whirl velocity= 22.50 ft/sec\n",
" Torque= 9.27 lbf ft\n",
" Stagnant pressure = 1962 lbf/ft**2\n",
" Incidence angle = 5.8 degrees\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.7 Page No : 447"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#initialisation of variables\n",
"r= 1.4\n",
"Mai= 0.5 \t#ft/sec mach number\n",
"T= 582. \t#R temperature\n",
"psi= 3040. \t#lbf/in**2 pressure\n",
"R= 53.3 \t #ft lbf/lbm gas\n",
"g= 32.2 \t#ft/sec**2\n",
"Vwi= 300. \t#ft/sec velocity\n",
"m= 35. \t#lb/sec\n",
"rm= 0.7 \t #ft radius\n",
"rp= 4.25\n",
"w= 1200. \t#rev/sec\n",
"cp= 0.24\n",
"J= 778. \t#lb\n",
"\t\n",
"#CALCULATIONS\n",
"tr= 1+0.5*(r-1)*Mai**2\n",
"Ti= round(T/tr)\n",
"pr= tr**(r/(r-1))\n",
"pi= psi/pr\n",
"ai= pi/(R*Ti)\n",
"Vi= Mai*(r*R*g*Ti)**0.5\n",
"Vai= math.sqrt(Vi**2-Vwi**2)\n",
"h= m/(2*math.pi*ai*rm*Vai)\n",
"pr1= rp**(1./12)\n",
"Vwo= Vwi+(pr1**((r-1)/r)-1)*(cp*J*g*T/(rm*w))\n",
"BO= 1/math.tan(math.radians((Vwo-w*rm)/Vai))\n",
"\n",
"\n",
"#RESULTS\n",
"print ' Absolute air velocity = %.f ft/sec'%(Vi)\n",
"print ' air velocity = %.f ft/sec'%(Vai)\n",
"print ' Blade height = %.3f ft'%(h)\n",
"print ' velocity = %.f ft/sec'%(Vwo)\n",
"print ' outlet balde angle = %.1f degrees'%(BO) #incorrect answer in the textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Absolute air velocity = 577 ft/sec\n",
" air velocity = 493 ft/sec\n",
" Blade height = 0.186 ft\n",
" velocity = 446 ft/sec\n",
" outlet balde angle = -71.7 degrees\n"
]
}
],
"prompt_number": 30
}
],
"metadata": {}
}
]
}