path: root/Theory_Of_Machines_by__B._K._Sarkar/Chapter7_1.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter7-Governors"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg196"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 1 PAGE NO 196\n",
      "##TITLE:GOVERNORS\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "L=.4##                     LENGTH OF UPPER ARM IN m\n",
      "THETA=30.##                 INCLINATION TO THE VERTICAL IN degrees\n",
      "K=.02##                    RISED LENGTH IN m\n",
      "##============================================================================================\n",
      "h2=L*math.cos(THETA/57.3)##         GOVERNOR HEIGHT IN m\n",
      "N2=(895./h2)**.5##           SPEED AT h2 IN rpm\n",
      "h1=h2-K##                  LENGTH WHEN IT IS RAISED BY 2 cm\n",
      "N1=(895./h1)**.5##           SPEED AT h1 IN rpm\n",
      "n=(N1-N2)/N2*100.##         PERCENTAGE CHANGE IN SPEED\n",
      "##==========================================================================================\n",
      "print'%s %.1f %s'%('PERCENTAGE CHANGE IN SPEED=',n,' PERCENTAGE')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "PERCENTAGE CHANGE IN SPEED= 3.0  PERCENTAGE\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg197"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 2 PAGE NO 197\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.5(A),7.5(B)\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "OA=.3##                          LENGTH OF UPPER ARM IN m\n",
      "m=6.##                            MASS OF EACH BALL IN Kg\n",
      "M=18.##                           MASS OF SLEEVE IN Kg\n",
      "r2=.2##                          RADIUS OF ROTATION AT BEGINING IN m\n",
      "r1=.25##                         RADIUS OF ROTATION AT MAX SPEED IN m\n",
      "##===========================================================================================\n",
      "h1=(OA**2.-r1**2.)**.5##             HIEGHT OF GOVERNOR AT MAX SPEED IN m\n",
      "N1=(895.*(m+M)/(h1*m))**.5##      MAX SPEED IN rpm\n",
      "h2=(OA**2.-r2**2.)**.5##             HEIGHT OF GONERNOR AT BEGINING IN m\n",
      "N2=(895.*(m+M)/(h2*m))**.5##      MIN SPEED IN rpm\n",
      "##===========================================================================================\n",
      "print'%s %.1f %s %.1f %s %.1f %s'%('MAX SPEED = ',N1,' rpm'' MIN SPEED = ',N2,' rpm''RANGE OF SPEED = ',N1-N2,' rpm')\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MAX SPEED =  146.9  rpm MIN SPEED =  126.5  rpmRANGE OF SPEED =  20.4  rpm\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg197"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 3 PAGE NO 197\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.6\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "OA=.25##                                 LENGHT OF UPPER ARM IN m\n",
      "CD=.03##                                 DISTANCE BETWEEN LEEVE AND LOWER ARM IN m\n",
      "m=6.##                                    MASS OF BALL IN Kg\n",
      "M=48.##                                   MASS OF SLEEVE IN Kg\n",
      "AE=.17##                                  FROM FIGURE 7.6\n",
      "AE1=.12##                                 FROM FIGURE 7.6\n",
      "r1=.2##                                  RADIUS OF ROTATION AT MAX SPEED IN m\n",
      "r2=.15##                                 RADIUS OF ROTATION AT MIN SPEED IN m\n",
      "##============================================================================================\n",
      "h1=(OA**2-r1**2)**.5##                     HIEGHT OF GOVERNOR AT MIN SPEED IN m\n",
      "TANalpha=r1/h1\n",
      "TANbeeta=AE/(OA**2-AE**2)**.5\n",
      "k=TANbeeta/TANalpha\n",
      "N1=(895.*(m+(M*(1.+k)/2.))/(h1*m))**.5##    MIN SPEED IN rpm\n",
      "h2=(OA**2-r2**2)**.5##                    HIEGHT OF GOVERNOR AT MAX SPEED IN m\n",
      "CE=(OA**2-AE1**2)**.5\n",
      "TANalpha1=r2/h2\n",
      "TANbeeta1=(r2-CD)/CE\n",
      "k=TANbeeta1/TANalpha1\n",
      "N2=(895.*(m+(M*(1.+k)/2.))/(h2*m))**.5##    MIN SPEED IN rpm\n",
      "##========================================================================================================\n",
      "print'%s %.1f %s %.1f %s %.1f %s'%('MAX SPEED = ',N1,' rpm'' MIN SPEED = ',N2,' rpm''RANGE OF SPEED = ',N1-N2,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MAX SPEED =  215.5  rpm MIN SPEED =  188.2  rpmRANGE OF SPEED =  27.2  rpm\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex4-pg199"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 4 PAGE NO 199\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.7\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "g=9.81##                   ACCELERATION DUE TO GRAVITY \n",
      "OA=.20##                  LENGHT OF UPPER ARM IN m\n",
      "AC=.20##                  LENGTH OF LOWER ARM IN m\n",
      "CD=.025##                 DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n",
      "AB=.1##                   RADIUS OF ROTATION OF BALLS IN m\n",
      "N2=250##                  SPEED OF THE GOVERNOR IN rpm\n",
      "X=.05##                   SLEEVE LIFT IN m\n",
      "m=5.##                     MASS OF BALL IN Kg\n",
      "M=20.##                    MASS OF SLEEVE IN Kg\n",
      "##===========================================================\n",
      "h2=(OA**2.-AB**2.)**.5##               OB DISTANCE IN m IN FIGURE\n",
      "h21=(AC**2.-(AB-CD)**2.)**.5##         BD DISTANCE IN m IN FIGURE\n",
      "TANbeeta=(AB-CD)/h21##            TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n",
      "TANalpha=AB/h2##                  TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
      "k=TANbeeta/TANalpha\n",
      "c=X/(2.*(h2*(1.+k)-X))##            PERCENTAGE INCREASE IN SPEED \n",
      "n=c*N2##                          INCREASE IN SPEED IN rpm\n",
      "N1=N2+n##                          SPEED AFTER LIFT OF SLEEVE\n",
      "E=c*g*((2.*m/(1.+k))+M)##            GOVERNOR EFFORT IN N\n",
      "P=E*X##                            GOVERNOR POWER IN N-m\n",
      "\n",
      "print'%s %.1f %s  %.2f %s  %.1f %s '%('SPEED OF THE GOVERNOR WHEN SLEEVE IS LIFT BY 5 cm = ',N1,' rpm'' GOVERNOR EFFORT = ',E,' N' 'GOVERNOR POWER = ',P,' N-m')\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SPEED OF THE GOVERNOR WHEN SLEEVE IS LIFT BY 5 cm =  275.6  rpm GOVERNOR EFFORT =   25.95  NGOVERNOR POWER =   1.3  N-m \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex5-pg200"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 5 PAGE NO 200\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.8\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "g=9.81##                   ACCELERATION DUE TO GRAVITY \n",
      "OA=.30##                  LENGHT OF UPPER ARM IN m\n",
      "AC=.30##                  LENGTH OF LOWER ARM IN m\n",
      "m=10.##                     MASS OF BALL IN Kg\n",
      "M=50.##                    MASS OF SLEEVE IN Kg\n",
      "r=.2##                    RADIUS OF ROTATION IN m\n",
      "CD=.04##                  DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n",
      "F=15.##                    FRICTIONAL LOAD ACTING IN N\n",
      "##============================================================\n",
      "h=(OA**2-r**2)**.5##           HIEGTH OF THE GOVERNOR IN m\n",
      "AE=r-CD##                   AE VALUE IN m\n",
      "CE=(AC**2-AE**2)**.5##         BD DISTANCE IN m\n",
      "TANalpha=r/h##              TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
      "TANbeeta=AE/CE##            TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n",
      "k=TANbeeta/TANalpha\n",
      "N=((895./h)*(m+(M*(1.+k)/2.))/m)**.5##      EQULIBRIUM SPEED IN rpm\n",
      "N1=((895./h)*((m*g)+(M*g+F)/2.)*(1.+k)/(m*g))**.5##        MAX SPEED IN rpm\n",
      "N2=((895./h)*((m*g)+(M*g-F)/2.)*(1.+k)/(m*g))**.5##        MIN SPEED IN rpm\n",
      "R=N1-N2##                                   RANGE OF SPEED\n",
      "print'%s %.1f %s %.1f %s '%('EQUILIBRIUM SPEED OF GOVERNOR = ',N,' rpm'' RANGE OF SPEED OF GOVERNOR= ',R,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "EQUILIBRIUM SPEED OF GOVERNOR =  145.1  rpm RANGE OF SPEED OF GOVERNOR=  3.4  rpm \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg202"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 6 PAGE NO 202\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.9\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "g=9.81##                   ACCELERATION DUE TO GRAVITY \n",
      "OA=.30##                  LENGHT OF UPPER ARM IN m\n",
      "AC=.30##                  LENGTH OF LOWER ARM IN m\n",
      "m=5.##                     MASS OF BALL IN Kg\n",
      "M=25.##                    MASS OF SLEEVE IN Kg\n",
      "X=.05##                   LIFT OF THE SLEEVE\n",
      "alpha=30.##                ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
      "##==============================================\n",
      "h2=OA*math.cos(alpha/57.3)##        HEIGHT OF THE GOVERNOR AT LOWEST POSITION OF SLEEVE\n",
      "h1=h2-X/2.##                HEIGHT OF THE GOVERNOR AT HEIGHT POSITION OF SLEEVE\n",
      "F=((h2/h1)*(m*g+M*g)-(m*g+M*g))/(1.+h2/h1)##      FRICTION AT SLEEVE IN N\n",
      "N1=((m*g+M*g+F)*895./(h1*m*g))**.5##          MAX SPEEED OF THE GOVVERNOR IN rpm\n",
      "N2=((m*g+M*g-F)*895./(h2*m*g))**.5##          MIN SPEEED OF THE GOVVERNOR IN rpm\n",
      "R=N1-N2##                                   RANGE OF SPEED IN rpm\n",
      "\n",
      "print'%s %.1f %s %.1f %s'%('THE VALUE OF FRICTIONAL FORCE= ',F,' F'' RANGE OF SPEED OF THE GOVERNOR = ',R,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "THE VALUE OF FRICTIONAL FORCE=  14.9  F RANGE OF SPEED OF THE GOVERNOR =  14.9  rpm\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex7-pg203"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 7 PAGE NO 203\n",
      "##TITLE:GOVERNORS\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "PI=3.147\n",
      "m=3##                 MASS OF EACH BALL IN Kg\n",
      "a=.12##               LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
      "b=.08##               LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
      "r2=.12##              RADIUS OF ROTATION OF THE BALL FOR LOWEST POSITION IN m\n",
      "N2=320.##               SPEED OF GOVERNOR AT THE BEGINING IN rpm\n",
      "S=20000.##                 STIFFNESS OF THE SPRING IN N/m\n",
      "h=.015##                  SLEEVE LIFT IN m\n",
      "##==================================================\n",
      "Fc2=m*(2.*PI*N2/60.)**2*r2##               CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n",
      "L=2*a*Fc2/b##                           INITIAL LOAD ON SPRING IN N\n",
      "r1=a/b*h+r2##                           MAX RADIUS OF ROTATION IN m\n",
      "Fc1=(S*(r1-r2)*(b/a)**2/2)+Fc2##         CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n",
      "N1=(Fc1/(m*r1)*(60./2./PI)**2)**.5\n",
      "print'%s %.1f %s %.1f %s '%('INITIAL LOAD ON SPRING =',L,' N'' EQUILIBRIUM SPEED CORRESPONDING TO LIFT OF 15 cm =',N1,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "INITIAL LOAD ON SPRING = 1217.0  N EQUILIBRIUM SPEED CORRESPONDING TO LIFT OF 15 cm = 327.9  rpm \n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex7-pg204"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 8 PAGE NO 204\n",
      "##TITLE:GOVERNORS\n",
      "\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "PI=3.147\n",
      "m=3##                           MASS OF BALL IN Kg\n",
      "r2=.2##                         INITIAL RADIUS OF ROTATION IN m\n",
      "a=.11##               LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
      "b=.15##               LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
      "h=.004##                  SLEEVE LIFT IN m\n",
      "N2=240.##                INITIAL SPEED IN rpm\n",
      "n=7.5##                    FLUCTUATION OF SPEED IN %\n",
      "##===================================\n",
      "w2=2.*PI*N2/60.##                  INITIAL ANGULAR SPEED IN rad/s\n",
      "w1=(100.+n)*w2/100.##              FINAL ANGULAR SPEED IN rad/s\n",
      "F=2.*a/b*m*w2**2.*r2##              INITIAL COMPRESSIVE FORCE IN N\n",
      "r1=r2+a/b*h##                    MAX RDIUS OF ROTATION IN m\n",
      "S=2.*((m*w1**2.*r1)-(m*w2**2.*r2))/(r1-r2)*(a/b)**2.\n",
      "print'%s %.1f %s %.1f %s'%('INITIAL COMPRESSIVE FPRCE = ',F,' N'' STIFFNESS OF THE SPRING = ',S/1000,' N/m')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "INITIAL COMPRESSIVE FPRCE =  557.8  N STIFFNESS OF THE SPRING =  24.1  N/m\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex9-pg204"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 9 PAGE NO 204\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.3(C)\n",
      "\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "g=9.81##                   ACCELERATION DUE TO GRAVITY \n",
      "PI=3.147\n",
      "r=.14##                          DISTANCE BETWEEN THE CENTRE OF PIVOT OF BELL CRANK LEVER AND AXIS OF GOVERNOR SPINDLE IN m\n",
      "r2=.11##                         INITIAL RADIUS OF ROTATION IN m\n",
      "a=.12##                          LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
      "b=.10##                          LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
      "h=.05##                         SLEEVE LIFT IN m\n",
      "N2=240##                         INITIAL SPEED IN rpm\n",
      "F=30##                           FRICTIONAL FORCE ACTING IN N\n",
      "m=5##                            MASS OF EACH BALL IN Kg\n",
      "##==========================================\n",
      "r1=r2+a/b*h##                    MAX RADIUS OF ROTATION IN m\n",
      "N1=41.*N2/39.##                 MAX SPEED OF ROTATION IN rpm\n",
      "N=(N1+N2)/2.##                 MEAN SPEED IN rpm\n",
      "Fc1=m*(2.*PI*N1/60.)**2.*r1##     CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n",
      "Fc2=m*(2.*PI*N2/60.)**2.*r2##     CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n",
      "c1=r1-r##                     FROM FIGURE 7.3(C) IN m\n",
      "a1=(a**2.-c1**2.)**.5##            FROM FIGURE 7.3(C) IN m\n",
      "b1=(b**2.-(h/2.)**2.)**.5##             FROM FIGURE 7.3(C) IN m\n",
      "c2=r-r2##                     FROM FIGURE 7.3(C) IN m\n",
      "a2=a1##                       FROM FIGURE 7.3(C) IN m\n",
      "b2=b1##                       FROM FIGURE 7.3(C) IN m\n",
      "S1=2.*((Fc1*a1)-(m*g*c1))/b1##          SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n",
      "S2=2.*((Fc2*a2)-(m*g*c2))/b2##          SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n",
      "S=(S1-S2)/h##                   STIFFNESS OF THE SPRING IN N/m\n",
      "Is=S2/S##                       INITIAL COMPRESSION OF SPRING IN m\n",
      "P=S2+(h/2.*S)##                  SPRING FORCE OF MID PORTION IN N\n",
      "n1=N*((P+F)/P)**.5##             SPEED,WHEN THE SLEEVE BEGINS TO MOVE UPWARDS FROM MID POSITION IN rpm\n",
      "n2=N*((P-F)/P)**.5##             SPEED,WHEN THE SLEEVE BEGINS TO MOVE DOWNWARDS FROM MID POSITION IN rpm\n",
      "A=n1-n2##                        ALTERATION IN SPEED IN rpm\n",
      "print'%s %.1f %s %.1f %s '%('INTIAL COMPRESSION OF SPRING= ',Is*100,' cm''ALTERATION IN SPEED = ',A,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "INTIAL COMPRESSION OF SPRING=  6.8  cmALTERATION IN SPEED =  6.7  rpm \n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex10-pg206"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 10 PAGE NO 206\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.10\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "PI=3.147\n",
      "AE=.25##                  LENGTH OF UPPER ARM IN m\n",
      "CE=.25##                  LENGTH OF LOWER ARM IN m\n",
      "EH=.1##                   LENGTH OF EXTENDED ARM IN m\n",
      "EF=.15##                  RADIUS OF BALL PATH IN m\n",
      "m=5.##                     MASS OF EACH BALL IN Kg\n",
      "M=40.##                    MASS OF EACH BALL IN Kg\n",
      "##===================================================================\n",
      "h=(AE**2.-EF**2.)**.5##           HEIGHT OF THE GOVERNOR IN m\n",
      "EM=h\n",
      "HM=EH+EM##                   FROM FIGURE 7.10\n",
      "N=((895./h)*(EM/HM)*((m+M)/m))**.5\n",
      "print'%s %.1f %s'%('EQUILIBRIUM SPEED OF GOVERNOR =',N,' rpm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "EQUILIBRIUM SPEED OF GOVERNOR = 163.9  rpm\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex11-pg207"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 11 PAGE NO 207\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.11\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "PI=3.147\n",
      "g=9.81##                  ACCELERATION DUE TO GRAVITY IN N/mm**2\n",
      "AE=.25##                  LENGTH OF UPPER ARM IN m\n",
      "CE=.25##                  LENGTH OF LOWER ARM IN m\n",
      "ER=.175##                 FROM FIGURE 7.11\n",
      "AP=.025##                 FROM FIGURE 7.11\n",
      "FR=AP##                   FROM FIGURE 7.11\n",
      "CQ=FR##                   FROM FIGURE 7.11\n",
      "m=3.2##                     MASS OF BALL IN Kg\n",
      "M=25.##                    MASS OF SLEEVE IN Kg\n",
      "h=.2##                    VERTICAL HEIGHT OF GOVERNOR IN m\n",
      "EM=h##                    FROM FIGURE 7.11\n",
      "AF=h##                    FROM FIGURE 7.11\n",
      "N=160.##                   SPEED OF THE GOVERNOR IN rpm\n",
      "HM=(895.*EM*(m+M)/(h*N**2.*m))\n",
      "x=HM-EM##                LENGTH OF EXTENDED LINK IN m\n",
      "T1=g*(m+M/2.)*AE/AF##     TENSION IN UPPER ARM IN N\n",
      "print'%s %.3f %s %.1f %s'%('LENGTH OF EXTENDED LINK = ',x,' m''TENSION IN UPPER ARM =',T1,' N')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "LENGTH OF EXTENDED LINK =  0.108  mTENSION IN UPPER ARM = 192.5  N\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex12-pg208"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "##CHAPTER 7 ILLUSRTATION 12 PAGE NO 208\n",
      "##TITLE:GOVERNORS\n",
      "##FIGURE 7.12,7.13\n",
      "import math\n",
      "##===========================================================================================\n",
      "##INPUT DATA\n",
      "PI=3.147\n",
      "EF=.20##               MINIMUM RADIUS OF ROTATION IN m\n",
      "AE=.30##               LENGTH OF EACH ARM IN m\n",
      "A1E1=AE##              COMPARING FIRUES 7.12&7.13\n",
      "EC=.30##               LENGTH OF EACH ARM IN m\n",
      "E1C1=EC##              LENGTH OF EACH ARM IN m\n",
      "ED=.165##              FROM FIGURE 7.12 IN m\n",
      "MC=ED##                FROM FIGURE 7.12\n",
      "EH=.10##                FROM FIGURE 7.12 IN m\n",
      "m=8.##                  MASS OF BALL IN Kg \n",
      "M=60.##                 MASS OF SLEEVE IN Kg\n",
      "DF=.035##              SLEEVE DISTANCE FROM AXIS IN m\n",
      "E1F1=.25##             MAX RADIUS OF ROTATION IN m\n",
      "g=9.81\n",
      "##=========================================================\n",
      "alpha=math.asin((EF/AE))*57.3##     ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL IN DEGREES\n",
      "beeta=math.asin((ED/EC))*57.3##     ANGLE OF INCLINATION OF THE ARM TO THE HORIZONTAL IN DEGREES\n",
      "k=math.tan(beeta/57.3)/math.tan(alpha/57.3)\n",
      "h=(AE**2.-EF**2.)**.5##        HEIGHT OF GOVERNOR IN m\n",
      "EM=(EC**2.-MC**2.)**.5##       FROM FIGURE 7.12 IN m\n",
      "HM=EM+EH\n",
      "N2=(895.*EM*(m+(M/2.*(1.+k)))/(h*HM*m))**.5##      EQUILIBRIUM SPEED AT MAX RADIUS\n",
      "HC=(HM**2.+MC**2.)**.5##                      FROM FIGURE 7.13 IN m\n",
      "H1C1=HC\n",
      "gama=math.atan((MC/HM))*57.3\n",
      "alpha1=math.asin((E1F1/A1E1))*57.3\n",
      "E1D1=E1F1-DF##                             FROM FIGURE 7.13 IN m\n",
      "beeta1=math.asin((E1D1/E1C1))*57.3\n",
      "gama1=gama-beeta+beeta1\n",
      "r=H1C1*math.sin(gama1/57.3)+DF##                      RADIUS OF ROTATION IN m\n",
      "H1M1=H1C1*math.cos((gama1/57.3))\n",
      "I1C1=E1C1*math.cos(beeta1/57.3)*(math.tan(alpha1/57.3)+math.tan(beeta1/57.3))## FROM FIGURE IN m\n",
      "M1C1=H1C1*math.sin(gama1/57.3)\n",
      "w1=(((m*g*(I1C1-M1C1))+(M*g*I1C1)/2.)/(m*r*H1M1))**.5##   ANGULAR SPEED IN rad/s\n",
      "N1=w1*60./(2.*PI)##                         ##SPEED IN m/s\n",
      "print'%s %.1f %s %.1f %s '%('MINIMUM SPEED OF ROTATION =',N2,' rpm'' MAXIMUM SPEED OF ROTATION = ',N1,' rpm')\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MINIMUM SPEED OF ROTATION = 146.6  rpm MAXIMUM SPEED OF ROTATION =  156.3  rpm \n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ],
   "metadata": {}
  }
 ]
}