path: root/Fluid_Mechanics_by_John_F._Douglas/Chapter_5.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5: The Momentum Equation and its Applications"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.1, Page 119"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      " #Initializing  the  variables  \n",
      "\n",
      "l  =  60  ;                                                                #Length  of  pipeline\n",
      "rho  =  1000;                                                          #  Density  of  liquid\n",
      "a  =  0.02;                                                              #Acceleration  of  fluid\n",
      "\n",
      " #Calculations\n",
      "delP  =  rho*l*a;                                                  #Change  in  pressure\n",
      "print \"Increase of pressure difference required (kN/m2):\",delP/1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Increase of pressure difference required (kN/m2): 1.2\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.2, Page 121"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      " #Initializing  the  variables  \n",
      "v  =  5;                                 #Velocity  of  jet          \n",
      "rho  =  1000;                            #density  of  water\n",
      "d  =  0.025;                             #Diameter  of  fixed  nozzle\n",
      "\n",
      " #Calculations\n",
      " #--Part(a)  Variation  of  force  exerted  normal  to  the  plate  with  plate  angle--//\n",
      "header  =  \"Theta\\t vcos(x)\\t pAv\\t Force\"\n",
      "unit  =    \"deg\\t m/s\\t kg/s\\t N\"\n",
      "\n",
      "A  =  math.pi*d**2/4;\n",
      "x  =  range(0,91,15);\n",
      "for c in range(len(x)):\n",
      "    x[c]=1.0*x[c]\n",
      "m  =  round(rho*A*v,2);\n",
      "ma  =  [m,m,m,m,m,m,m];\n",
      "vcomp=[]\n",
      "force=[]\n",
      "for c in x:\n",
      "    vcomp.append(round(v*math.cos(math.radians(c)),2))\n",
      "    force.append(round((rho*A*v**2)*math.cos(math.radians(c)),2))\n",
      "\n",
      "print header\n",
      "print unit\n",
      "for c in range(len(x)):\n",
      "    mm=str(x[c])+' \\t '+str(vcomp[c])+' \\t'+str(ma[c])+' \\t'+str(force[c])\n",
      "    print mm\n",
      "##value  = [x,vcomp,ma,force]\n",
      "##print value,unit, header\n",
      "\n",
      " #--Part(b)  Variation  of  force  exerted  normal  to  the  plate  with  plate  velocity--//        \n",
      "header  =\"Theta\\t v\\t u\\t v-u\\t pA(v-u)\\t Force\\t\"\n",
      "unit    =\"deg\\t m/s\\t m/s\\t m/s\\t kg/s\\t N\\t\"\n",
      "x  =  [0,0,0,0,0]\n",
      "v  =  [5,5,5,5,5]\n",
      "u  =  range(2,-3,-1);\n",
      "D=[]\n",
      "Prod=[]\n",
      "Force=[]\n",
      "for c in range(5):\n",
      "    D.append(v[c]-u[c])\n",
      "    Prod.append(round((rho*A*D[c]),2))\n",
      "    Force.append(round((rho*A*D[c]**2),2))\n",
      "    \n",
      "print '\\n',\"(b)\",\"\\n\",header\n",
      "print unit\n",
      "for c in range(len(x)):\n",
      "    mm=str(x[c])+' \\t '+str(v[c])+' \\t '+str(u[c])+' \\t '+str(D[c])+' \\t '+str(Prod[c])+' \\t '+str(Force[c])\n",
      "    print mm\n",
      "    \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Theta\t vcos(x)\t pAv\t Force\n",
        "deg\t m/s\t kg/s\t N\n",
        "0.0 \t 5.0 \t2.45 \t12.27\n",
        "15.0 \t 4.83 \t2.45 \t11.85\n",
        "30.0 \t 4.33 \t2.45 \t10.63\n",
        "45.0 \t 3.54 \t2.45 \t8.68\n",
        "60.0 \t 2.5 \t2.45 \t6.14\n",
        "75.0 \t 1.29 \t2.45 \t3.18\n",
        "90.0 \t 0.0 \t2.45 \t0.0\n",
        "\n",
        "(b) \n",
        "Theta\t v\t u\t v-u\t pA(v-u)\t Force\t\n",
        "deg\t m/s\t m/s\t m/s\t kg/s\t N\t\n",
        "0 \t 5 \t 2 \t 3 \t 1.47 \t 4.42\n",
        "0 \t 5 \t 1 \t 4 \t 1.96 \t 7.85\n",
        "0 \t 5 \t 0 \t 5 \t 2.45 \t 12.27\n",
        "0 \t 5 \t -1 \t 6 \t 2.95 \t 17.67\n",
        "0 \t 5 \t -2 \t 7 \t 3.44 \t 24.05\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.3, Page 123"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "  \n",
      "\n",
      " #Initializing  the  variables  \n",
      "x  =  60;                                                     #Angle  of  deflection theta\n",
      "rho  =  1000;                                                 #  Density  of  liquid\n",
      "V1  =  30;                                                    #Acceleration  of  fluid\n",
      "V2  =  25;\n",
      "m  =  .8;                                                     #Discharge  through  A\n",
      "\n",
      " #Calculations\n",
      "def  Reaction(Vin , Vout):\n",
      "    R  =  m*(Vin  -Vout)  ;\n",
      "    return R\n",
      "Rx  =  Reaction(V1,V2*math.cos(math.radians(x)));\n",
      "Ry  =  -Reaction(0,V2*math.sin(math.radians(x)));\n",
      "print \"Reaction in X-direction (N)                              :\",Rx\n",
      "print \"Reaction in Y-direction (N)                              :\",round(Ry,2)\n",
      "print \"Net Reaction            (N)                              :\",round((Rx**2 +Ry**2)**0.5,2)\n",
      "print \"Inclination of Resultant Force with x-direction (Degrees):\",round(180/math.pi*math.atan(Ry/Rx),2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reaction in X-direction (N)                              : 14.0\n",
        "Reaction in Y-direction (N)                              : 17.32\n",
        "Net Reaction            (N)                              : 22.27\n",
        "Inclination of Resultant Force with x-direction (Degrees): 51.05\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.4, Page 125"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables  \n",
      "v1  =  36  ;                                                              #Exit  velocity\n",
      "u  =  15;                                                                  #Velocity  of  vane\\\n",
      "x  =  30;                                                                  #  Angle  between  vanes  and  flow\n",
      "rho  =  1000;                                                          #  Density  of  water\n",
      "d  =  .1;                                                                  #  Diameter  of  jet\n",
      "\n",
      " #Calculations\n",
      "alp  =  (180/math.pi)*math.atan((v1*math.sin(math.radians(x))/(v1*math.cos(math.radians(x))-u)));\n",
      "v2  =  0.85*v1*math.sin(math.radians(x));\n",
      "bta  =    (180/math.pi)*math.acos((u*math.sin(math.radians(alp))/v2));\n",
      "m  =  (rho*math.pi*v1*d**2)/4;\n",
      "Vin  =  v1*math.cos(math.radians(x));\n",
      "Vout  =  v2*math.cos(math.radians(90));\n",
      "Rx  =  m*(Vin-Vout);\n",
      "\n",
      "\n",
      "print \"Inlet Angle            (Degrees) :\", round(alp,2)\n",
      "print \"Outlet Angle           (Degrees) :\", round(bta,2)\n",
      "print \"Force exerted by vanes (N)       :\", round(Rx) \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Inlet Angle            (Degrees) : 48.05\n",
        "Outlet Angle           (Degrees) : 43.18\n",
        "Force exerted by vanes (N)       : 8815.0\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.5, Page 127"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables  \n",
      "rho  =  850  ;                                                          #  Density  of  liquid\n",
      "a  =  0.02                                                                #Acceleration  of  fluid\n",
      "x  =  45  ;\n",
      "d1  =  .5  ;\n",
      "d2  =  .25;\n",
      "p1  =  40*10**3;\n",
      "p2  =  23*10**3;\n",
      "Q  =  .45;\n",
      "   \n",
      " #Calculations\n",
      "A1  =  (math.pi*d1**2)/4;\n",
      "A2  =  (math.pi*d2**2)/4;\n",
      "v1  =  Q/A1;\n",
      "v2  =  Q/A2;\n",
      "\n",
      "Rx  =  p1*A1  -  p2*A2*math.cos(math.radians(x))  -  rho*Q*(v2*math.cos(math.radians(x))-v1);\n",
      "Ry  =  p2*A2*math.sin(math.radians(x))  +  rho*Q*v2*math.sin(math.radians(x));\n",
      "\n",
      "print \"Resultant force on the bend                     (kN)     :\",round((Rx**2 +Ry**2)**0.5/1000,3)\n",
      "print \"Inclination of Resultant Force with x-direction (Degrees):\",round(math.atan(Ry/Rx)*180/math.pi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Resultant force on the bend                     (kN)     : 6.362\n",
        "Inclination of Resultant Force with x-direction (Degrees): 31.0\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.6, Page 129"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables  \n",
      "v  =  4.9;                                                                #Velocity  of  Jet\n",
      "rho  =  1000;                                                          #  Density  of  water\n",
      "d  =  0.05;\n",
      "u  =  1.2                                                                  #  Velocity  of  tank\n",
      " #Calculations\n",
      "Vout  =  v;\n",
      "Vin  =  0;\n",
      "m  =  rho*math.pi*d**2*v/4;\n",
      "R  =  m*(Vout-Vin);\n",
      "print \"Reaction of jet on tank (N) :\",round(R,2)\n",
      "print \"Work done per second    (W) :\",round(R*u,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reaction of jet on tank (N) : 47.14\n",
        "Work done per second    (W) : 56.57\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.7, Page 130"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "from scipy import integrate\n",
      " \n",
      " \n",
      "\n",
      " #Initializing  the  variables  \n",
      "Vj  =  5*10**6;                               # Velocity  of  Jet\n",
      "Mr  =  150000;                                # Mass  of  Rocket\n",
      "Mf0  =  300000;                               # Mass  of  initial  fuel\n",
      "Vr  =  3000;                                  # Velocity  of  jet  relative  to  rocket\n",
      "g  =  9.81;                                   # Acceleration  due  to  gravity\n",
      "\n",
      " #Calculations\n",
      "m  =  Vj/Vr;                                  #Rate  of  fuel  consumption\n",
      "T  =  Mf0/m;                                  #  Burning  time\n",
      "\n",
      "def f(t,m,Vr,Mr,Mf0,g):\n",
      "    return m*Vr  /(Mr  +  Mf0  -  m*t)  -  g;\n",
      " \n",
      "args = (5000/3,3000,150000,300000,9.81)\n",
      "Vt = integrate.quad(f, 0.0, 180, args)\n",
      "\n",
      "def h(t,Vr,g):\n",
      "    return -g*t - Vr*math.log(1 - t/269.95);\n",
      " \n",
      "args = (3000,9.81)\n",
      "Z1 = integrate.quad(h, 0.0, 180, args)\n",
      "Z2 =  Vt[0]**2/(2*g);\n",
      "\n",
      "print \"(a)Burning time (s)                             :\",T\n",
      "print \"(b)Speed of rocket when all fuel is burned (m/s):\",round(Vt[0],2)\n",
      "print \"(c)Maximum height reached (km)                  :\",round((Z2+Z1[0])/1000,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Burning time (s)                             : 180.0\n",
        "(b)Speed of rocket when all fuel is burned (m/s): 1530.04\n",
        "(c)Maximum height reached (km)                  : 203.8\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.8, Page 134"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables  \n",
      "V  =  200;                                                                #Velocity  in  still  air\n",
      "Vr  =  700;                                                              #velocity  of  gas  relative  to  engine\n",
      "mf  =  1.1;                                                              #  Fuel  Consumption\n",
      "r  =  1/40  ;        \n",
      "P1  =0;\n",
      "P2  =  0;\n",
      "\n",
      " #Calculations\n",
      "m1  =    mf/r;\n",
      "T  =  m1*((1+r)*Vr  -V);\n",
      "print \"(a)Thrust               (kN) :\",T/1000\n",
      "\n",
      "W  =  T*V;\n",
      "print \"(b)Work done per second (kW) :\",W/1000\n",
      "\n",
      "Loss  =  0.5*m1*(1+r)*(Vr-V)**2;\n",
      "print \"(c)Efficiency           (%)  :\",round(W/(W+Loss)*100,1) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Thrust               (kN) : 22.77\n",
        "(b)Work done per second (kW) : 4554.0\n",
        "(c)Efficiency           (%)  : 44.7\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.10, Page 140"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      " #Initializing  the  variables  \n",
      "rho  =  1000;                                                          #  Density  of  water\n",
      "Q  =  10;                                                                  #Acceleration  of  fluid\n",
      "r2  =  1.6;\n",
      "r1  =  1.2;\n",
      "V1  =  2.3;\n",
      "V2  =  0.2;\n",
      "rot  =  240;  \n",
      "\n",
      " #Calculations\n",
      "Tf  =  rho*Q*(V2*r2  -  V1*r1);\n",
      "T  =  -Tf;\n",
      "n  =  rot  /  60;\n",
      "P  =  2*round(math.pi,3)*n*T;\n",
      "\n",
      "print \"Torque exerted by fluid  (N.m):\",T\n",
      "print \"Theoretical power output (kW) :\",round(P/1000,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Torque exerted by fluid  (N.m): 24400.0\n",
        "Theoretical power output (kW) : 613.32\n"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}