{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 12: Pipes and Cisterns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.1, Page number 12.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken by leak to empty the cistern is 45.0 hours\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f=4+(1/2);       #time(hours)\n",
    "x=1/2;     #time(hours)\n",
    "\n",
    "#Calculation\n",
    "E=f*(1+(f/x));      #time taken by leak to empty the cistern(hours)\n",
    "\n",
    "#Result\n",
    "print \"time taken by leak to empty the cistern is\",E,\"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.2, Page number 12.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time taken by leak to empty the cistern is 112.0 hours\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x=32/60;     #time(hours)\n",
    "f1=14;    #time for 1st pipe(hours)\n",
    "f2=16;    #time for 2nd pipe(hours)\n",
    "\n",
    "#Calculation\n",
    "T=f1*f2/(f1+f2);      #time(h)\n",
    "E=T*(1+(T/x));      #time taken by leak to empty the cistern(hours)\n",
    "\n",
    "#Result\n",
    "print \"time taken by leak to empty the cistern is\",E,\"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.3, Page number 12.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time to fill is 12.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f1=20;    #time for 1st pipe(minutes)\n",
    "f2=30;    #time for 2nd pipe(minutes)\n",
    "\n",
    "#Calculation\n",
    "T=f1*f2/(f1+f2);      #total time to fill(minutes)\n",
    "\n",
    "#Result\n",
    "print \"total time to fill is\",T,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.4, Page number 12.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fill or empty time is 50.0 minutes\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f=25;     #time(minutes)\n",
    "e=50;     #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "Et=1/((1/f)-(1/e));       #fill or empty time(minutes)\n",
    "\n",
    "#Result\n",
    "print \"fill or empty time is\",Et,\"minutes\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.5, Page number 12.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill half the cistern is 8.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x1=3/4;    #part of cistern\n",
    "x2=1/2;    #part of cistern\n",
    "f1=12;     #time to fill(minutes)\n",
    "\n",
    "#Calculation\n",
    "f2=f1*x2/x1;    #time to fill(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill half the cistern is\",f2,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.6, Page number 12.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " part of cistern to be emptied is 3/8\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "e1=20;     #time(minutes)\n",
    "e2=9;      #time(minutes)\n",
    "y1=5/6;    #part of cistern\n",
    "\n",
    "#Calculation\n",
    "y2=e2*y1/e1;    #part of cistern to be emptied\n",
    "\n",
    "#Result\n",
    "print \"part of cistern to be emptied is\",Fraction(y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.7, Page number 12.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 8.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a1=3;     #time(minutes)\n",
    "a2=15;    #time(minutes)\n",
    "b=10;     #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "T=b*(1-(a1/a2));     #time to fill the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",T,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.8, Page number 12.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 9.143 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "At=12;     #alone fill time of A(minutes)\n",
    "Bt=16;     #alone fill time of B(minutes)\n",
    "t=4;      #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "l=At*Bt/gcd(At,Bt);     #lcm of At and Bt\n",
    "a=l/At;\n",
    "b=l/Bt;\n",
    "T=(l+(t*a))/(a+b);      #time to fill the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",round(T,3),\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.9, Page number 12.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 20.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "At=10;    #time to fill cistern for A(minutes)\n",
    "Bt=15;    #time to fill cistern for B(minutes)\n",
    "Ct=5;     #time to empty cistern for C(minutes)\n",
    "t=4;      #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "l1=At*Bt/gcd(At,Bt);     #lcm of At and Bt\n",
    "l=l1*Ct/gcd(l1,Ct);     #lcm of At,Ct and Bt\n",
    "a=l/At;\n",
    "b=l/Bt;\n",
    "c=l/Ct;\n",
    "T=(-(t*a)-(t*b))/(a+b-c);     #time to empty the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",T,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.10, Page number 12.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 3.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import gcd\n",
    "\n",
    "#Variable declaration\n",
    "At=3;    #time to fill cistern for A(minutes)\n",
    "Bt=6;    #time to fill cistern for B(minutes)\n",
    "Ct=4;     #time to empty cistern for B(minutes)\n",
    "t=2;      #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "x=1+(t/Ct);\n",
    "l=At*Bt/gcd(At,Bt);     #lcm of At and Bt\n",
    "a=l/At;\n",
    "b=l/Bt;\n",
    "T=x*l/(a+b);     #time to fill the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",T,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.11, Page number 12.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time to fill is 16.0 hours\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f1=20;    #time for 1st pipe(hours)\n",
    "f2=30;    #time for 2nd pipe(hours)\n",
    "\n",
    "#Calculation\n",
    "F=f1*f2/(f1+f2);      \n",
    "T=F+(F/3);      #total time to fill(hours)\n",
    "\n",
    "\n",
    "#Result\n",
    "print \"total time to fill is\",T,\"hours\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.12, Page number 12.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "capacity of cistern is 40.0 litres\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f1=15;    #time for 1st pipe(hours)\n",
    "f2=10;    #time for 2nd pipe(hours)\n",
    "p=7;     #capacity of carrying(litres/min)\n",
    "E=2*60;    #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "c=p/((1/f1)+(1/f2)+(1/E));      #capacity of cistern(litres)\n",
    "\n",
    "#Result\n",
    "print \"capacity of cistern is\",c,\"litres\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.13, Page number 12.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 3.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "ta=6;    #fraction of time for A\n",
    "t=21;    #time to fill for B(minutes)\n",
    "\n",
    "#Calculation\n",
    "F=t/(1+ta);    #time to fill the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",F,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.14, Page number 12.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time to fill the cistern is 8.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "K=4;     #time(minutes)\n",
    "L=30;   #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "F=K*L/(K**2-1);      #time to fill the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time to fill the cistern is\",F,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.15, Page number 12.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total time to empty the cistern is 18.0 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f1=10;    #time for 1st pipe(minutes)\n",
    "f2=15;    #time for 2nd pipe(minutes)\n",
    "tex=2;    #extra time taken to fill(minutes)\n",
    "\n",
    "#Calculation\n",
    "T=f1*f2/(f1+f2);      #total time to fill(minutes)\n",
    "E=T**2/tex;     #total time to empty the cistern(minutes)\n",
    "\n",
    "#Result\n",
    "print \"total time to empty the cistern is\",E,\"minutes\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.16, Page number 12.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of filling pipes are 4.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "f=9;    #fill rate(hours)\n",
    "e=6;    #empty rate(hours)\n",
    "F=9;    #total time(hours)\n",
    "\n",
    "#Calculation\n",
    "a=(1/F)+1;\n",
    "nf=a*f*e/(f+e);      #number of filling pipes\n",
    "\n",
    "#Result\n",
    "print \"number of filling pipes are\",nf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.17, Page number 12.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average sailing rate is 5.5 km/h\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "ra=2/6;    #rate of admission of water(tonnes/min)\n",
    "rp=12/60;    #rate of pumping out water(tonnes/min)\n",
    "q=80;    #quantity of water(tonnes)\n",
    "d=55;    #distance(km)\n",
    "\n",
    "#Calculation\n",
    "r=ra-rp;     #rate of accumulation(tonnes/min)\n",
    "T=q/(r*60);      #time to accumulate water(hours)\n",
    "Asr=d/T;    #average sailing rate(km/h)\n",
    "\n",
    "#Result\n",
    "print \"average sailing rate is\",Asr,\"km/h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12.18, Page number 12.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time before the full flow began is 4.5 minutes\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "p1=7/8;     #part1\n",
    "p2=5/6;     #part2\n",
    "t1=12;      #time(minutes)\n",
    "t2=16;      #time(minutes)\n",
    "t=3;     #time(minutes)\n",
    "\n",
    "#Calculation\n",
    "a=(p1/t1)+(p2/t2);\n",
    "b=1-(t/t1)-(t/t2);\n",
    "x=b/a;     #time before the full flow began(minutes)\n",
    "\n",
    "#Result\n",
    "print \"time before the full flow began is\",x,\"minutes\""
   ]
  }
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