path: root/Fluid_Mechanics_by_John_F_Douglas/Chapter_14.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 14: Steady Incompressible Flow in Pipe and Duct System"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.1, Page 468"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "L1  =  5;\n",
      "L2  =  10;\n",
      "d  =  0.1;\n",
      "f  =  0.08;\n",
      "Za_Zc  =  4;                                                 #difference  in  height  between  A  and  C  \n",
      "g  =  9.81  ;\n",
      "Pa  =  0;\n",
      "Va  =  0;  \n",
      "Za_Zb  =  -1.5;\n",
      "V  =  1.26;\n",
      "rho  =  1000;\n",
      "\n",
      " #Calculations\n",
      "D  =  1.5  +  4*f*(L1+L2)/d  ;                               #  Denominator  in  case  of  v**2  \n",
      "v  =  (2*g*Za_Zc/D)**0.5;\n",
      "Pb  =  rho*g*Za_Zb  -  rho*V**2/2*(1.5+4*f*L1/d);\n",
      "print \"Pressure in the pipe at B (kN/m2):\",round(Pb/1000,2)\n",
      "print \"Mean Velocity at C    (m/s)      :\",round(v,2)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure in the pipe at B (kN/m2): -28.61\n",
        "Mean Velocity at C    (m/s)      : 1.26\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.3, Page 473"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "from sympy import symbols,solve\n",
      "import sympy\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "Za_Zb  =  10;\n",
      "f  =  0.008;\n",
      "L  =  100;\n",
      "d1  =  0.05;\n",
      "g  =  9.81;\n",
      "d2  =  0.1;\n",
      "\n",
      " #Calculations\n",
      "\n",
      "def  flowRate(d):\n",
      "    D = 1.5 + 4*f*L/d ;                                     #  Denominator  in  case  of  v1**2\n",
      "    A  =  math.pi*d**2/4;\n",
      "    v  =  (2*g*Za_Zb/D)**0.5;\n",
      "    z  =  A*v;\n",
      "    return z     \n",
      "Q1  =  flowRate(d1);\n",
      "Q2  =  flowRate(d2);\n",
      "Q=round(Q1+Q2,4)\n",
      "\n",
      "\n",
      "D=symbols('D')\n",
      "roots=solve(241212*D**5  -3.2, D)\n",
      "dia=roots[0]\n",
      "\n",
      "print \"Rate flow for pipe 1            (m^3/s) :\",round(Q1,4)\n",
      "print \"Rate flow for pipe 2            (m^3/s) :\",round(Q2,4)\n",
      "print \"Combined Rate flow              (m^3/s) :\",round(Q,4)\n",
      "print \"Diameter of single equivalent pipe (mm) :\",round(dia,3)*1000\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rate flow for pipe 1            (m^3/s) : 0.0034\n",
        "Rate flow for pipe 2            (m^3/s) : 0.019\n",
        "Combined Rate flow              (m^3/s) : 0.0224\n",
        "Diameter of single equivalent pipe (mm) : 106.0\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.4, Page 476"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "import sympy\n",
      "from sympy import solve,symbols\n",
      "\n",
      " #Initializing  the  variables\n",
      "Za_Zb  =  16;\n",
      "Za_Zc  =  24;\n",
      "f  =  0.01;\n",
      "l1  =  120;\n",
      "l2  =  60;\n",
      "l3  =  40;\n",
      "d1  =  0.12;\n",
      "d2  =  0.075;\n",
      "d3  =  0.060;\n",
      "g  =  9.81;\n",
      " #Calculations\n",
      "\n",
      "v1=symbols('v1')\n",
      "ash=solve(v1-0.3906*(g-1.25*v1**2)**0.5-0.25*(17.657-1.5*v1**2)**0.5,v1)\n",
      "v1=round(abs(ash[0]),2)\n",
      "Q1=math.pi/4*d1**2*v1\n",
      "\n",
      "v2=(g-1.25*v1**2)**0.5\n",
      "Q2=math.pi/4*d2**2*v2\n",
      "\n",
      "v3=(17.657-1.5*v1**2)**0.5\n",
      "Q3=math.pi/4*d3**2*v3\n",
      "\n",
      "print \"Flow rate in pipe 1 (m^3/s):\",round(Q1,4)\n",
      "print \"Flow rate in pipe 2 (m^3/s):\",round(Q2,4)\n",
      "print \"Flow rate in pipe 3 (m^3/s):\",round(Q3,4)\n",
      "print \"continuity condition satisfied as Q1=Q2+Q3\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Flow rate in pipe 1 (m^3/s): 0.0206\n",
        "Flow rate in pipe 2 (m^3/s): 0.0105\n",
        "Flow rate in pipe 3 (m^3/s): 0.0101\n",
        "continuity condition satisfied as Q1=Q2+Q3\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.5, Page 480"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "D  =  0.3;\n",
      "Q  =  0.8;\n",
      "rho  =  1.2;\n",
      "f  =  0.008;\n",
      "L_entry  =  10;\n",
      "L_exit  =  30;\n",
      "Lt  =  20*D                              #Transition  may  be  represented  by  a  separation  loss  equivalent  length  of  20  *  the  approach  duct  diameter\n",
      "K_entry  =  4;\n",
      "K_exit  =  10\n",
      "l  =  0.4;                               #  length  of  cross  section\n",
      "b  =  0.2;                               #  width  of  cross  section\n",
      "\n",
      " #Calculations\n",
      "A  =  math.pi*D**2/4;\n",
      "Dp1  =  0.5*rho*Q**2/A**2*(K_entry  +  4*f*(L_entry+Lt)/D);\n",
      "area  =  l*b;\n",
      "perimeter  =2*(l+b);\n",
      "m  =  area/perimeter;\n",
      "Dp2  =  0.5*rho*Q**2/area**2*(K_exit  +  f*L_exit/m);\n",
      "Dfan  =    Dp1+Dp2;\n",
      "\n",
      "print \"fan Pressure input (N/m2) :\",round(Dfan,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fan Pressure input (N/m2) : 1254.6\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.6, Page 482"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      " #Initializing  the  variables\n",
      "D  =  [0.15 , 0.3];\n",
      "rho  =  1.2;\n",
      "f  =  0.008;\n",
      "L_entry  =  10;\n",
      "L_exit  =  20;\n",
      "Lt  =  20*D[1]              \n",
      "K  =  4;\n",
      "Q1  =  0.2;\n",
      "\n",
      " #Calculations\n",
      "Q2  =  4*Q1;\n",
      "A=[0.0,0.0]\n",
      "A[0]  =  math.pi*D[0]**2/4;\n",
      "A[1]  =  math.pi*D[1]**2/4;\n",
      "Dp1  =  0.5*rho*Q1**2/A[0]**2*(K  +  4*f*L_entry/D[0]);\n",
      "Dp2  =  0.5*rho*Q2**2/A[1]**2*(4*f*(L_exit  +  Lt)/D[1]);\n",
      "Dfan  =    Dp1+Dp2;\n",
      "\n",
      "print \"fan Pressure input (N/m2) :\",round(Dfan,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fan Pressure input (N/m2) : 684.51\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14.7, Page 487"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "from scipy.optimize import fsolve\n",
      " \n",
      " \n",
      " \n",
      " #Initializing  the  variables\n",
      "d  =  [0.1 , 0.125,  0.15,  0.1,  0.1  ];                    #  Corrosponding  to  AA1B  AA2B  BC  CD  CF\n",
      "l  =  [30 , 30 , 60,  15,  30];                                      #  Corrosponding  to  AA1B  AA2B  BC  CD  CF\n",
      "rho   =  1.2;\n",
      "f     =  0.006;\n",
      "Ha    =  100;\n",
      "Hf    =  60;\n",
      "He    =  40;\n",
      "K = [0.0, 0.0, 0.0, 0.0, 0.0]\n",
      " #Calculations\n",
      "for i in range(0,len(l)):\n",
      "    K[i]  =  f*l[i]/(3*d[i]**5);\n",
      "\n",
      "\n",
      "K_ab  =  K[0]*K[1]/((K[0])**0.5+(K[1])**0.5)**2;\n",
      "K_ac  =  K_ab  +  K[2];\n",
      "Hc  =  (K_ac*Hf  +K[4]*Ha/4)/(K_ac+K[4]/4);\n",
      "Q  =  ((Ha  -  Hc)/K_ac)**0.5;\n",
      "\n",
      "def  f(n):\n",
      "    z  =  He  -  Hc  +  (0.5*Q)**2  *(K[3]+(4000/n)**2);\n",
      "    return z\n",
      "\n",
      "n  =  fsolve(f,1);\n",
      "\n",
      "print \"total Volume flow rate (m3/s):\",round(Q, 4)\n",
      "print \"Head at C (m)                :\",round(Hc,2) \n",
      "print \"Percentage valve opening (%) :\",round(n,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total Volume flow rate (m3/s): 0.1016\n",
        "Head at C (m)                : 75.48\n",
        "Percentage valve opening (%) : 38.58\n"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}