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 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 10 : Liquid Flow in Open Channels"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.1 Pageno : 353"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "\n",
      "# variables\n",
      "yo = Symbol(\"yo\")\n",
      "A = 20*yo\n",
      "P = 20 + 2*yo\n",
      "Rh= 20*yo/(20+2*yo)\n",
      "n = 0.017        # ft\n",
      "\n",
      "# calculations\n",
      "ans = solve((1.49/n)*A*Rh**(2./3)*(0.0001)**(1./2) - 400) #*yo*Rh**(2./3)\n",
      "\n",
      "# result\n",
      "print \"Yo = %.2f ft\"%ans[0]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Yo = 8.32 ft\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.2 pageno : 356"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculations\n",
      "Rh = 20*8.34/(20+2*8.34)\n",
      "\n",
      "# result\n",
      "print \"Rh = %.2f ft\"%Rh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rh = 4.55 ft\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.3 pageno : 362"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "\n",
      "# variables\n",
      "yo = Symbol(\"yo\")\n",
      "n = 0.017      #ft 1/6\n",
      "A = 2*yo**2\n",
      "Rh = yo/2\n",
      "\n",
      "# Calculations\n",
      "ans = solve((1.49/n)*A*Rh**(2./3) * (0.0001)**(1./2) - 400,yo)\n",
      "Yo = ans[0]\n",
      "B = 2*Yo\n",
      "\n",
      "#result\n",
      "print \"Yo**(8/3) = %.f \"%(Yo**(8./3))\n",
      "print \"Yo  = %.2f ft \"%(Yo)\n",
      "print \"B = %.2f ft \"%(B)\n",
      "\n",
      "# note : answer are slightly differenet because of solve method of sympy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Yo**(8/3) = 362 \n",
        "Yo  = 9.11 ft \n",
        "B = 18.22 ft \n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.4 Page no : 367"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from sympy import Symbol, solve\n",
      "\n",
      "# variables\n",
      "q = 500./40        # cfs/ft\n",
      "ye = ((12.5)**2 / 32.2)**(1./3)\n",
      "n = 0.017\n",
      "So = Symbol(\"So\")\n",
      "\n",
      "# calculations\n",
      "Sc = 32.2 * n**2 / (2.2 * ye**(1./3))\n",
      "ans = solve((1.49/n)*160*(3.33)**(2./3)*So**(1./2) - 500)\n",
      "So = ans[0]\n",
      "\n",
      "# result\n",
      "print \"Sc = %.4f\"%Sc\n",
      "print \"So = %f\"%So\n",
      "print \"So is a mild slope since it is less than Se\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sc = 0.0035\n",
        "So = 0.000256\n",
        "So is a mild slope since it is less than Se\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.5 page no : 369"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import solve,Symbol\n",
      "import math\n",
      "\n",
      "# variables\n",
      "y = Symbol(\"y\")\n",
      "A = 10*y + 2*y**2\n",
      "n = 0.017\n",
      "b = 10 + 4*y\n",
      "P = 10 + 2*math.sqrt(5)*y\n",
      "\n",
      "# calculations\n",
      "ans = solve(A**3/b *32.2/1000**2 - 1)\n",
      "yo = ans[1]\n",
      "Ae = 97.3         # sqft\n",
      "be = 29.65        # ft\n",
      "Rhe = Ae/32       # ft\n",
      "Sc = 32.2*n**2/2.2 * (Ae/(be*Rhe**(4./3)))\n",
      "\n",
      "# result\n",
      "print \"Yo = %.2f ft\"%yo\n",
      "print \"Sc = %.5f\"%Sc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Yo = 4.91 ft\n",
        "Sc = 0.00315\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10.6  page no : 373"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import Symbol,solve\n",
      "\n",
      "# variables\n",
      "Q = round((1.49/0.015)*50*(50./20)**(2./3)*(0.001)**(1./2))        # cfs\n",
      "E = 5.52           # ft\n",
      "\n",
      "# calculations and results\n",
      "Ye = ((Q/10)**2/32.2)**(1./3)\n",
      "Emin = 3 * Ye/2\n",
      "\n",
      "print \"Ye = %.2f ft\"%Ye\n",
      "print \"Minimum height of hump : Emin = %.2f ft\"%Emin\n",
      "\n",
      "Ye = 2 * 5.52/3\n",
      "b = Symbol(\"b\")\n",
      "ans = solve( ( (289/b)**2 / 32.2  )**(1./3) - Ye)\n",
      "b = ans[1]\n",
      "\n",
      "print \"Ye = %.2f ft\"%Ye\n",
      "print \"Maximum width of contraction : b = %.1f ft\"%b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Ye = 2.96 ft\n",
        "Minimum height of hump : Emin = 4.44 ft\n",
        "Ye = 3.68 ft"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Maximum width of contraction : b = 7.2 ft\n"
       ]
      }
     ],
     "prompt_number": 37
    }
   ],
   "metadata": {}
  }
 ]
}