path: root/Fluid_Mechanics_by_John_F._Douglas/Chapter_2.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 2: Pressure and Head"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.1, Page 30"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      " #Initializing  the  variables\n",
      "z1  =  0;                                                         #Taking  Ground  as  reference\n",
      "z2  =  -30                                                        #Depth\n",
      "rho  =  1025                                                      #Density\n",
      "g  =  9.81                                                        #Acceleration  due  to  gravity\n",
      "\n",
      " #Calculation\n",
      "pressureIncrease  =  -rho*g*(z2-z1);\n",
      "\n",
      "print \"Increase in Pressure (KN/m2):\",round(pressureIncrease/1000,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Increase in Pressure (KN/m2): 301.7\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.2, Page 34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "p1  =  22.4*10**3                                                    #Initial  Pressure\n",
      "z1  =  11000                                                            #Initial  Height\n",
      "z2  =  15000                                                            #final  Height\n",
      "g  =  9.81                                                                #Acceleration  due  to  gravity\n",
      "R  =  287;                                                                #Gas  Constant\n",
      "T  =  273-56.6                                                        #Temperature  \n",
      "\n",
      " #Calculations\n",
      "p2  =  p1*math.exp(-g*(z2-z1)/(R*T));\n",
      "rho2=p2/(R*T);\n",
      "  \n",
      "print \"Final Pressure (kN/m2):\",round(p2/1000,2)\n",
      "print \"Final Density  (kg/m3):\",round(rho2,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Final Pressure (kN/m2): 11.91\n",
        "Final Density  (kg/m3): 0.192\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.3, Page 37"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "p1  =  101*10**3                                                      #Initial  Pressure\n",
      "z1  =  0                                                              #Initial  Height\n",
      "z2  =  1200                                                           #Final  Height\n",
      "T1  =  15+273                                                         #Initial  Temperature\n",
      "g  =  9.81                                                            #Acceleration  due  to  gravity\n",
      "gamma  =  1.4                                                         #Heat  capacity  ratio\n",
      "R  =  287                                                                  #Gas  Constant\n",
      "\n",
      " #Calculations\n",
      "p2  =  p1*(1-g*(z2-z1)*(gamma-1)/(gamma*R*T1))**(gamma/(gamma-1));\n",
      "dT_dZ  =  -(g/R)*((gamma-1)/gamma);\n",
      "T2  =  T1  +  dT_dZ*(z2-z1);\n",
      "rho2 = p2/(R*T2);\n",
      "\n",
      "print \"Final Pressure (kN/m2)            :\",round(p2/1000,2)\n",
      "print \"Temprature     (in degree celcius):\",round(T2-273,1)\n",
      "print \"Density        (kg/m^3)           :\",round(rho2,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Final Pressure (kN/m2)            : 87.33\n",
        "Temprature     (in degree celcius): 3.3\n",
        "Density        (kg/m^3)           : 1.101\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.4, Page 39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "p1  =  101*10**3                                                      #Initial  Pressure\n",
      "z1  =  0                                                                    #Initial  Height\n",
      "z2  =  7000                                                              #Final  Height\n",
      "T1  =  15+273                                                          #Initial  Temperature\n",
      "g  =  9.81                                                                #Acceleration  due  to  gravity\n",
      "R  =  287                                                                  #Gas  Constant\n",
      "dT  =  6.5/1000                                                      #Rate  of  Variation  of  Temperature\n",
      "\n",
      " #Calculations\n",
      "p2  =  p1*(1-dT*(z2-z1)/T1)**(g/(R*dT));\n",
      "T2  =  T1  -  dT*(z2-z1);\n",
      "rho2  =  p2/(R*T2);\n",
      "\n",
      "\n",
      "print \"Final Pressure (kN/m^2) :\",round(p2/1000,2)\n",
      "print \"Final Density  (kg/m^3 ):\",round(rho2,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Final Pressure (kN/m^2) : 40.89\n",
        "Final Density  (kg/m^3 ): 0.588\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.5, Page 44"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "p  =  350*10**3;                                         #Gauge  Pressure\n",
      "pAtm  =  101.3*10**3;                                    #Atmospheric  Pressure    \n",
      "rhoW  =  1000;                                           #Density  of  Water\n",
      "sigma  =  13.6;                                          #Relative  Density  of  Mercury\n",
      "g  =  9.81                                               #Acceleration  due  to  gravity\n",
      "\n",
      " #Calculations\n",
      "def Head(rho):\n",
      "    head  =  p/(rho*g);\n",
      "    return head\n",
      "rhoM  =  sigma*rhoW;\n",
      "pAbs  =  p  +  pAtm;\n",
      "\n",
      "print \"\\nPart(a)- Equivalent head of water (m) :\",round(Head(rhoW),2)\n",
      "print \"\\nPart(b)- Equivalent head of water (m) :\",round(Head(rhoM),2)\n",
      "print \"\\nAbsolute pressure (kN/m^2)            :\",pAbs/1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Part(a)- Equivalent head of water (m) : 35.68\n",
        "\n",
        "Part(b)- Equivalent head of water (m) : 2.62\n",
        "\n",
        "Absolute pressure (kN/m^2)            : 451.3\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.6, Page 45"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "   \n",
      "\n",
      " #Initializing  the  variables\n",
      "rho  =  10**3;                                  #Density  of  water\n",
      "h  =  2;                                        #Height\n",
      "g  =  9.81;                                     #Acceleration  due  to  gravity\n",
      "\n",
      " #Calculations\n",
      "p=rho*h*g;  \n",
      "\n",
      "print \"Gauge pressure (k/m2) :\",p/1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Gauge pressure (k/m2) : 19.62\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.7, Page 46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "rho  =  0.8*10**3;                                                  #Density  of  fluid\n",
      "rhoM  =  13.6*10**3;                                              #Density  of  manometer  liquid\n",
      "g  =  9.81                                                                #Acceleration  due  to  gravity\n",
      "\n",
      " #Calculations\n",
      "def fluidPressure(h1,h2):\n",
      "    P  =  rhoM*g*h2-rho*g*h1;\n",
      "    return P\n",
      "\n",
      "p1=fluidPressure(0.5,0.9)/1000\n",
      "p2=fluidPressure(0.1,-0.2)/1000\n",
      "\n",
      "print \"!-----Part (a)-----! \\nGauge pressure (kN/m2) :\",round(p1,2)\n",
      "print \"\\n!-----Part (b)-----! \\nGauge pressure (kN/m2) :\",round(p2,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "!-----Part (a)-----! \n",
        "Gauge pressure (kN/m2) : 116.15\n",
        "\n",
        "!-----Part (b)-----! \n",
        "Gauge pressure (kN/m2) : -27.47\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.8, Page 47"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "rho  =  10**3;                                                          #Density  of  fluid\n",
      "rhoM  =  13.6*10**3;                                              #Density  of  manometer  liquid\n",
      "g  =  9.81;                                                              #Acceleration  due  to  gravity\n",
      "H  =  0.3;                                                                #  Differnce  in  height  =  b-a  as  in  text\n",
      "h  =  0.7;\n",
      "\n",
      " #Calculations\n",
      "result  =  rho*g*H  +  h*g*(rhoM-rho);\n",
      "\n",
      "print \"Pressure difference (kN/m^2):\", round(result/1000,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure difference (kN/m^2): 89.467\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.9, Page 50"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "rho  =  10**3;                                                          #Density  of  fluid\n",
      "rhoM  =  0.8*10**3;                                                #Density  of  manometer  liquid\n",
      "g  =  9.81;                                                              #Acceleration  due  to  gravity\n",
      "a  =  0.25;\n",
      "b  =  0.15;\n",
      "h  =  0.3;\n",
      " #Calculations\n",
      "def PressureDiff(a,b,h,rho,rhoM):\n",
      "    P  =  rho*g*(b-a)  +  h*g*(rho-rhoM);\n",
      "    return P\n",
      "print \"The presure difference,if the top of the manometer is filled with\"\n",
      "print \"(a) air                          :\",PressureDiff(a,b,h,rho,0)/1000, \" N/m^2\"\n",
      "print \"(b) oil of relative density 0.8. :\",PressureDiff(a,b,h,rho,rhoM), \"N/m^2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The presure difference,if the top of the manometer is filled with\n",
        "(a) air                          : 1.962  N/m^2\n",
        "(b) oil of relative density 0.8. : -392.4 N/m^2\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.10, Page 54"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      " #Initializing  the  variables\n",
      "phi  =  30;                                                              #30  degree\n",
      "h  =  1.2  ;                                                              #  Height  of  tank\n",
      "l  =  2;                                                                    #  Length  of  tank\n",
      "\n",
      " #Calculations\n",
      "def SurfaceAngle(a,phi):\n",
      "    g=9.81; # m/s**2    \n",
      "    Theta  =  math.atan(-a*math.cos(math.radians(phi))/(g+a*math.sin(math.radians(phi))));  \n",
      "    return Theta\n",
      "\n",
      " #case  (a)  a  =  4\n",
      "\n",
      "print \"ThetaA      (degree)      :\",round(180 + 180/math.pi*SurfaceAngle(4,phi),2)\n",
      "\n",
      " #Case  (b)  a  =  -  4.5\n",
      "tanThetaR  =  math.tan((SurfaceAngle(-4.5,phi)));\n",
      "\n",
      "print \"\\nThetaR      (degree)      :\",round(SurfaceAngle(-4.5,phi)*180/math.pi,2)\n",
      "\n",
      "Depth  =  h  -  l*tanThetaR/2;\n",
      "print \"\\nMaximum Depth of tank (m) :\",round(Depth,4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ThetaA      (degree)      : 163.65\n",
        "\n",
        "ThetaR      (degree)      : 27.27\n",
        "\n",
        "Maximum Depth of tank (m) : 0.6845\n"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}