{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 13 Fluid flow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.1 Pg:583"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "velocity in ft/s are:\n",
      "0.000000 \t1118.735268 \t1663.871913 \t1791.374302 \t2179.668416 \t2779.331106 \t\n",
      "\n",
      "Area in ft**2 are:\n",
      "0.000000 \t0.006600 \t0.005534 \t0.005495 \t0.005760 \t0.007656 \t\n",
      "\n",
      "The initial values of velocity and area are 0 and infinity respectively. Since, Infinity in calculations stops the code to display an error. It has been mentioned separately.\n"
     ]
    }
   ],
   "source": [
    "from numpy import nditer\n",
    "from math import sqrt\n",
    "#Initialization of variables\n",
    "h1=1329.1 #Btu/lbm\n",
    "v1=6.218 #ft**3/lbm\n",
    "J=778\n",
    "g=32.174\n",
    "m=1\n",
    "#calculations\n",
    "p=[80, 60 ,54.6, 40, 20]\n",
    "h=[ 1304.1, 1273.8, 1265 ,1234.2, 1174.8]\n",
    "v=[ 7.384, 9.208, 9.844 ,12.554, 21.279]\n",
    "Fc=1\n",
    "V2=[Fc*sqrt(2*J*g*(h1-hh)) for hh in h]\n",
    "A=[m*v1/V21 for v1,V21 in nditer([v,V2])]\n",
    "V2=[0]+V2\n",
    "A=[0]+A\n",
    "#results\n",
    "print 'velocity in ft/s are:'\n",
    "for vv in V2:\n",
    "    print '%.6f'%vv,'\\t', \n",
    "print '\\n\\nArea in ft**2 are:'\n",
    "for aa in A:\n",
    "    print '%.6f'%aa,'\\t',\n",
    "print '\\n\\nThe initial values of velocity and area are 0 and infinity respectively. Since, Infinity in calculations stops the code to display an error. It has been mentioned separately.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.2 Pg:584"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area required = 0.00464 ft**2\n",
      "\n",
      " Area in case 2 at the exit= 0.00379 ft**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Initialization of variables\n",
    "n=1.4\n",
    "p1=50 #psia\n",
    "J=778\n",
    "cp=0.24\n",
    "T1=520 #R\n",
    "k=n\n",
    "R=1545/29\n",
    "m=1\n",
    "p2=10 #psia\n",
    "#calculations\n",
    "rpt=(2/(n+1))**(n/(n-1))\n",
    "pt=p1*rpt\n",
    "Vtrev=223.77*sqrt(cp*T1*(1- rpt**((k-1)/k)))\n",
    "v1=R*T1/p1/144\n",
    "vt=v1*(p1/pt)**(1/k)\n",
    "At=m*vt/Vtrev\n",
    "V2rev=223.77*sqrt(cp*T1*(1-(p2/p1)**((k-1)/k)))\n",
    "v2=v1*(p1/p2)**(1/k)\n",
    "A2=m*v2/V2rev\n",
    "#results\n",
    "print \"Area required = %.5f ft**2\"%(At)\n",
    "print \"\\n Area in case 2 at the exit= %.5f ft**2\"%(A2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.3 Pg:585"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Throat area= 0.0056 ft**2\n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "J=778\n",
    "g=32.2\n",
    "pc=54.6 #psia\n",
    "h1=1329.1 #Btu/lbm\n",
    "h2=1265 #btu/lbm\n",
    "V2rev=1790 #ft/s\n",
    "cv=0.99\n",
    "m=1 #lbm\n",
    "cv2=0.96\n",
    "#calculations\n",
    "V2d=cv*V2rev\n",
    "hd=cv**2 *(h1-h2)\n",
    "h2d=h1-hd\n",
    "v2d=9.946\n",
    "A2d=m*v2d/V2d\n",
    "#results\n",
    "print \"Throat area= %.4f ft**2\"%(A2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.4 Pg:585"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average velocity = 31.3 ft/sec\n",
      "\n",
      " mass flow rate = 29.0 lbm/sec\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "zm=0.216\n",
    "pm=62.3 #lbm/ft**2\n",
    "p1=0.0736 #lbm/ft**2\n",
    "g=32.2\n",
    "d=4\n",
    "#calculations\n",
    "H=zm*(pm-p1)/12/p1\n",
    "V=sqrt(2*g*H)\n",
    "m=pi/4 *d**2 *V*p1\n",
    "#results\n",
    "print \"average velocity = %.1f ft/sec\"%(V)\n",
    "print \"\\n mass flow rate = %.1f lbm/sec\"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.5 Pg:586"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From table B-17,\n",
      "Area of throat = 0.00596 ft**2\n",
      "\n",
      " Area of exit = 0.00805 ft**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Initialization of variables\n",
    "p0=50 #psia\n",
    "T0=520 #R\n",
    "rho0=0.259 #lbm/ft**3\n",
    "p2=10 #psia\n",
    "mf=1 #lbm\n",
    "#calculations\n",
    "print \"From table B-17,\"\n",
    "pr=0.528\n",
    "Tr=0.833\n",
    "rhor=0.634\n",
    "ps=pr*p0\n",
    "Ts=Tr*T0\n",
    "rhos=rho0*rhor\n",
    "Vs=49.1*sqrt(Ts)\n",
    "As=mf/(Vs*rhos)\n",
    "p2r=p2/p0\n",
    "M2=1.71\n",
    "V2=1.487*Vs\n",
    "T2=0.632*Ts\n",
    "A2=As*1.35\n",
    "rho2=rhos*0.317\n",
    "#results\n",
    "print \"Area of throat = %.5f ft**2\"%(As)\n",
    "print \"\\n Area of exit = %.5f ft**2\"%(A2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.6 Pg:587"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of pipe = 406.3 ft\n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "M1=0.2\n",
    "M2=0.4\n",
    "D=0.5  #ft\n",
    "f=0.015\n",
    "#calculations\n",
    "f1=14.5\n",
    "f2=2.31\n",
    "dl=(f1-f2)*D/f\n",
    "#results\n",
    "print \"Length of pipe = %.1f ft\"%(dl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.7 Pg:588"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "from table B-19\n",
      "Change in entropy = 0.0224 Btu/lbm R\n"
     ]
    }
   ],
   "source": [
    "from math import log\n",
    "#Initialization of variables\n",
    "py=20 #psia\n",
    "px=3.55 #psia\n",
    "R=1.986/29\n",
    "#calculations\n",
    "pr=py/px\n",
    "print \"from table B-19\"\n",
    "Mx=2\n",
    "My=0.577\n",
    "pr2=0.721\n",
    "ds=R*log(1/pr2)\n",
    "#results\n",
    "print \"Change in entropy = %.4f Btu/lbm R\"%(ds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.8 Pg:588"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From table B-18 and B-17,\n",
      "Mach numbers before and after are 1.64 and 0.658 respectively\n",
      "\n",
      " Pressure before and after are 11.0 psia and 32.9 psia\n",
      "\n",
      " Exhaust pressure = 32.3 psia\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "pi=50 #psia\n",
    "pe=34.6 #psia\n",
    "#calculations\n",
    "print \"From table B-18 and B-17,\"\n",
    "pr1=1.35\n",
    "p0f=pi/pr1\n",
    "pfs=0.528*p0f\n",
    "per=pe/pfs\n",
    "Me=0.6\n",
    "p0e=1.19\n",
    "pyx=p0e/pr1\n",
    "Mx=1.64\n",
    "My=0.658\n",
    "px=0.22*pi\n",
    "py=32.9 #psia\n",
    "p2yx=0.852\n",
    "pe2=1.65*pfs\n",
    "#results\n",
    "print \"Mach numbers before and after are %.2f and %.3f respectively\"%(Mx,My)\n",
    "print \"\\n Pressure before and after are %.1f psia and %.1f psia\"%(px,py)\n",
    "print \"\\n Exhaust pressure = %.1f psia\"%(pe2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.9 Pg:589"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From table B-20\n",
      "Heat required = 272 Btu/lbm\n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "T1=550 #R\n",
    "T2=2660 #R\n",
    "ts1=0.207\n",
    "ts2=0.833\n",
    "cp=0.24\n",
    "#calculations\n",
    "Ts=T1/ts1\n",
    "Ts0=T2/ts2\n",
    "print \"From table B-20\"\n",
    "tr1=0.529\n",
    "tr2=0.174\n",
    "dq=cp*Ts0*(tr1-tr2)\n",
    "#results\n",
    "print \"Heat required = %d Btu/lbm\"%(dq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.10 Pg:590"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Internal thrust = 3651 lbf\n",
      "\n",
      " Net thrust = 2593 lbf\n",
      "The answers are a bit different due to rounding off error in textbook\n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "M1=0.5\n",
    "M2=1\n",
    "A1=0.5 #ft**2\n",
    "A2=1 #ft**2\n",
    "p1=14.7 #psia\n",
    "p2=14.7 #psia\n",
    "k=1.4\n",
    "#calculations\n",
    "thru=p2*144*A2*(1+k*M2**2)-p1*144*A1*(1+k*M1**2)\n",
    "net=thru-p1*144*(A2-A1)\n",
    "#results\n",
    "print \"Internal thrust = %d lbf\"%(thru)\n",
    "print \"\\n Net thrust = %d lbf\"%(net)\n",
    "print \"The answers are a bit different due to rounding off error in textbook\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.11 Pg:590"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mass flow rate = 0.572 lbm/sec\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "p1=50 #psia\n",
    "pr=0.58\n",
    "#calculations\n",
    "p=p1*pr\n",
    "s1=1.6585\n",
    "h1=1174.1 #Btu/lbm\n",
    "sf=0.3680\n",
    "sfg=1.3313\n",
    "hfg=945.3\n",
    "vg=13.746\n",
    "hf=218.82\n",
    "x= (s1-sf)/sfg\n",
    "v2=vg*x\n",
    "h2=hf+x*hfg\n",
    "V2rev=223.77*sqrt(h1-h2)\n",
    "m=pi/4 *1/144 *V2rev/v2\n",
    "#results\n",
    "print \"mass flow rate = %.3f lbm/sec\"%(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.12 Pg:591"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mass flow rate = 0.597 lbm/sec\n",
      "\n",
      " Meta stable under cooling = 52 F\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "k=1.31\n",
    "p1=7200 #lbf/ft**2\n",
    "v1=8.515 #ft**3/lbm\n",
    "pr=0.6\n",
    "m1=0.574\n",
    "T1=741 #R\n",
    "#calculations\n",
    "V2rev=8.02*sqrt(k/(k-1) *p1*v1*(1- (pr)**((k-1)/k)))\n",
    "v2=v1*(1/pr)**(1/k)\n",
    "m=pi/4 *1/144 *V2rev/v2\n",
    "C=m/m1\n",
    "T2=T1*(0.887)\n",
    "t=250+460 #R\n",
    "dt=t-T2\n",
    "#results\n",
    "print \"Mass flow rate = %.3f lbm/sec\"%(m)\n",
    "print \"\\n Meta stable under cooling = %d F\"%(dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.13 Pg:592"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area = 1.344 in**2\n",
      "\n",
      " diameter = 1.31 in\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "C=0.98\n",
    "m=1\n",
    "v=12.55 #ft**3/lbm\n",
    "V=1372 #ft/s\n",
    "#calculations\n",
    "A=m*v/(C*V) *144\n",
    "D=sqrt(A*4/pi)\n",
    "#results\n",
    "print \"Area = %.3f in**2\"%(A)\n",
    "print \"\\n diameter = %.2f in\"%(D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.14 Pg:593"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area = 0.92 in**2\n",
      "\n",
      " diameter = 1.080 in\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "nn=0.95\n",
    "p1=50 #psia\n",
    "p2=30 #psia\n",
    "v1=8.515\n",
    "m=1 #lbm\n",
    "#calculations\n",
    "cv=sqrt(nn)\n",
    "V2rev=1372\n",
    "V2act=cv*V2rev\n",
    "n=1.283\n",
    "v2=v1*(p1/p2)**(1/n)\n",
    "A=m*v2/V2act *144\n",
    "D=sqrt(A*4/pi)\n",
    "#results\n",
    "print \"Area = %.2f in**2\"%(A)\n",
    "print \"\\n diameter = %.3f in\"%(D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.15 Pg:593"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient of discharge = 0.991 \n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "dFf=110.5 #ft-lbf/lbm\n",
    "Vd=1028 #ft/s\n",
    "gc=32.2 #ft/s**2\n",
    "p0=100 #psia\n",
    "k=1.4\n",
    "v0=2.08\n",
    "p1=55 #psia\n",
    "p2=99.2 #psia\n",
    "#calculations\n",
    "dFe=0.01*Vd**2 /(2*gc)\n",
    "dF=dFf+dFe\n",
    "V2ig=(p0*144)**(1/k) *v0/(1-1/k) *((p1*144)**(1-1/k) -(p2*144)**(1-1/k))\n",
    "C2=(V2ig+dF)/V2ig\n",
    "C=sqrt(C2)\n",
    "#results\n",
    "print \"Coefficient of discharge = %.3f \"%(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.16 Pg:594"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pressure drop in the nozzle = 3.60 lbf/ft**2\n",
      "\n",
      " Coefficient of discharge = 0.982 \n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import pi,sqrt\n",
    "#Initialization of variables\n",
    "dL=1/6 #ft\n",
    "mf=0.430 #lbm/sec\n",
    "rho=62.4 \n",
    "gc=32.2 #ft/s**2\n",
    "d=0.81/12 #ft\n",
    "#calculations\n",
    "V=mf*4/(rho*pi)\n",
    "VD=V/dL**2\n",
    "Vd=1.92 #ft/s\n",
    "dFf=0.031/(2*gc) *2.31\n",
    "dFe=0.04*Vd**2 /(2*gc)\n",
    "dF=dFf+dFe\n",
    "dp=rho*(3.5/(2*gc) +dF)\n",
    "vd22=(2*gc)/rho *dp /(1-(d/dL)**4)\n",
    "vd2=sqrt(vd22)\n",
    "C=Vd/vd2\n",
    "#results\n",
    "print \"Pressure drop in the nozzle = %.2f lbf/ft**2\"%(dp)\n",
    "print \"\\n Coefficient of discharge = %.3f \"%(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:13.17 Pg:595"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mass flow rate = 1.176 lbm/sec\n",
      "\n",
      " Coefficient of discharge = 0.598\n"
     ]
    }
   ],
   "source": [
    "#Initialization of variables\n",
    "K=0.6003\n",
    "Y1=0.91\n",
    "D1=6.065\n",
    "D2=1.820\n",
    "rho1=0.156\n",
    "p1=30\n",
    "p2=20.18\n",
    "#calculations\n",
    "bet=D2/D1\n",
    "m=0.525*K*Y1 *D2**2 *sqrt(rho1*(p1-p2))\n",
    "C=K*sqrt(1-bet**4)\n",
    "#results\n",
    "print \"mass flow rate = %.3f lbm/sec\"%(m)\n",
    "print \"\\n Coefficient of discharge = %.3f\"%(C)"
   ]
  }
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