{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7 : Steam generators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.1 Pg: 510"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum area of the nozzles is 7.626 sq.cm\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=10#Initial pressure in bar\n",
    "T1=300+273#Initial temperature in K\n",
    "p2=2#Final pressure in bar\n",
    "m=1#Mass flow rate of steam in kg/s\n",
    "\n",
    "#Calculations\n",
    "px=(0.546*p1)#Critical pressure in bar\n",
    "ho=3052.2#Enthalpy in kJ/kg\n",
    "so=7.1229#Entropy in kJ/kg.K\n",
    "sx=so#Entropy in kJ/kg.K\n",
    "hx=2905.9#Enthalpy in kJ/kg\n",
    "vx=0.4125#Specific volume in m**3/kg\n",
    "Vx=(44.72*sqrt(ho-hx))#Critical velocity in m/s\n",
    "Ax=(vx/Vx)*10**4#Minimum area of the nozzle in sq.cm\n",
    "\n",
    "#Output\n",
    "print \"Minimum area of the nozzles is %3.3f sq.cm\"%(Ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.2 Pg: 511"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Minimum area of the nozzles is 7.98 cm**2 \n",
      " the number of nozzles are   4\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=10#Initial pressure in bar\n",
    "T1=300+273#Initial temperature in K\n",
    "p2=1#Final pressure in bar\n",
    "x=0.15#Friction loss of the isentropic enthalpy drop\n",
    "ms=1#Steam flow rate in kg/s\n",
    "d=25#Exit diameter of the nozzles in mm\n",
    "\n",
    "#Calculations\n",
    "px=(0.546*p1)#Critical pressure in bar\n",
    "h1=3052.2#Enthalpy in kJ/kg\n",
    "s1=7.1276#Entropy in kJ/kg\n",
    "s2s=s1#Entropy in kJ/kg\n",
    "h2s=2916.2#Enthalpy in kJ/kg\n",
    "Vx=(44.72*sqrt(h1-h2s))#Critical velocity in m/s\n",
    "h3s=2605#Enthalpy in kJ/kg\n",
    "V1=(44.72*sqrt((h1-h2s)+(0.85*(h2s-h3s))))#Velocity in m/s\n",
    "s3s=s1#Entropy in kJ/kg\n",
    "x3s=(s3s-1.3025)/6.0579#Dryness fraction\n",
    "h3s=(417.46+(x3s*2258.01))#Enthalpy in kJ/kg\n",
    "h2s3=((1-x)*(h2s-h3s))#Enthalpy in kJ/kg\n",
    "h3=h2s-h2s3#Enthalpy in kJ/kg\n",
    "x3=(h3-417.46)/2258.01#Dryness fraction\n",
    "v3=(0.001043+(x3*1.694))#Specific volume in m**3/kg\n",
    "v2s=0.416#Specific volume in m**3/kg\n",
    "vx=v2s#Specific volume in m**3/kg\n",
    "Ax=(ms/Vx)*vx*10**4#Minimum area in cm**2\n",
    "A1=(ms*v3)/V1*10**4#Area in cm**2\n",
    "n=(A1*4)/(3.14*(d/10)**2)#Number of nozzles\n",
    "\n",
    "#Output\n",
    "print \" Minimum area of the nozzles is %3.2f cm**2 \\n the number of nozzles are %3.0f\"%(Ax,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.3 Pg: 512"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Area of throat is 2430 mm**2 \n",
      " Exit area is 4029 mm**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=7.8#Pressure in bar\n",
    "t1=180+273#Temperature in K\n",
    "p2=1.03#pressure in bar\n",
    "m=3.6#flow rate of air in kg/s\n",
    "g=1.4#Ratio of specific heats\n",
    "R=287#Characteristic gas constant in J/kg.K\n",
    "cp=1.005#Specific heat in kJ/kg.K\n",
    "\n",
    "#Calculations\n",
    "pxpo=(2/(g+1))**(g/(g-1))#Ratio of pressure\n",
    "px=pxpo*p1#Critical pressure in bar\n",
    "txto=(2/(g+1))#Ratio of temperatures\n",
    "tx=t1*txto#Critical temperature in K\n",
    "vx=(R*tx)/(px*10**5)#Critical specific volume in m**3/kg\n",
    "Vx=sqrt(g*R*tx)#Critical velocity in m/s\n",
    "Ax=((m*vx)/Vx)*10**6#Critical area in mm**2\n",
    "tot1=(p1/p2)**((g-1)/g)#Ratio of temperatures\n",
    "t1i=t1/tot1#Temperature in K\n",
    "v1=(R*t1i)/(p2*10**5)#Specific volume in m**3/kg\n",
    "V1=44.72*sqrt(cp*(t1-t1i))#Velocity in m/s\n",
    "A1=((m*v1)/V1)*10**6#Area in mm**2\n",
    "\n",
    "#Output\n",
    "print \" Area of throat is %3.0f mm**2 \\n Exit area is %d mm**2\"%(Ax,A1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.4 Pg: 514"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Throat raea is 0.0286 m**2 \n",
      " Exit arae is 0.0370 m**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=3.8#pressure in bar\n",
    "T1=450+273#Tempereture in K\n",
    "p2=1#pressure in bar\n",
    "m=16#Flow rate in kg/s\n",
    "Cd=0.98#coefficient of discharge\n",
    "nv=0.93#nozzile effeciency\n",
    "cp=1.11#Specific heat in kJ/kg.K\n",
    "g=1.333#Ratio of specific heats\n",
    "\n",
    "#Calculations\n",
    "pxpo=(2/(g+1))**(g/(g-1))#Pressure ratio\n",
    "px=pxpo*p1#Critical pressure in bar\n",
    "TxTo=2/(g+1)#Temperature ratio\n",
    "Tx=T1*TxTo#Critical temperature in K\n",
    "Vx=44.72*sqrt(cp*(T1-Tx))#critical velocity in m/s\n",
    "R=(cp*(g-1)*1000)/g#Characteristic gas constant in J/kg.K\n",
    "vx=(R*Tx)/(px*10**5)#Critical specific volume in m**3/kg\n",
    "ws=(m/Cd)#Mass flow rate in kg/s\n",
    "Ax=(ws*vx)/Vx#Critical area in m**2\n",
    "T1sTo=(p2/p1)**((g-1)/g)#Temperature ratio\n",
    "T1s=T1*T1sTo#Temperature in K\n",
    "T1i=(T1-(nv*(T1-T1s)))#Temperature in K\n",
    "v1=(R*T1i)/(p2*10**5)#Specific volume in m**3/kg\n",
    "V1=44.72*sqrt(cp*(T1-T1i))#Velocity in m/s\n",
    "A1=(ws*v1)/V1#Area in m**2\n",
    "\n",
    "#Output\n",
    "print \" Throat raea is %3.4f m**2 \\n Exit arae is %3.4f m**2\"%(Ax,A1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.5 Pg: 515"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) Area of throat is 112.6 mm**2 \n",
      " Exit area is 184.5 mm**2 \n",
      "\n",
      " (b) Area of throat is 143.6 mm**2 \n",
      " Exit area is 219.0 mm**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=20#pressure in bar\n",
    "T1=300+273#Tempereture in K\n",
    "p2=3#pressure in bar\n",
    "m=0.3#Flow rate in kg/s\n",
    "n=1.3#Adiabatic constant\n",
    "Cd=0.98#Coefficient of discharge\n",
    "Cv=0.92#Coefficient of velocity\n",
    "\n",
    "#Calculations\n",
    "vo=0.1255#Specific volume in m**3/kg\n",
    "px=(0.546*p1)#Critical pressure in bar\n",
    "vx=(p1/px)**(1/n)*vo#Critical specific volume in m**3/kg\n",
    "Vx=sqrt(n*px*10**5*vx)#Critical velocity in m/s\n",
    "Ax=((m*vx)/Vx)*10**6#Critical area in m**2\n",
    "v1vo=(p1/p2)**(1/n)#Ratio of specific volumes\n",
    "v1=(vo*v1vo)#Specific volume in m**3/kg\n",
    "V1=sqrt(2*((n/(n-1))*10**5*((p1*vo)-(p2*v1))))#Velocity in m/s\n",
    "A1=((m*v1)/V1)*10**6#Area in mm**2\n",
    "ho=3050#Enthalpy in kJ/kg\n",
    "hx=2920#Enthalpy in kJ/kg\n",
    "h1s=2650#Enthalpy in kJ/kg\n",
    "ws=(m/Cd)#Flow rate in kg/s\n",
    "Vsx=44.72*sqrt(ho-hx)#Velocity in m/s\n",
    "V1s=44.72*sqrt(ho-h1s)#Velocity in m/s\n",
    "Vo1=(V1s*Cv)#Velocity in m/s\n",
    "hoh1=(V1/44.72)**2#Change in enthalpy in kJ/kg\n",
    "h1=ho-hoh1#Enthalpy in kJ/kg\n",
    "x1=(h1-561.47)/2163.8#Dryness fraction\n",
    "vo1=(0.001073+(x1*0.6047))#Specific volume in m**3/kg\n",
    "Ao1=((ws*vo1)/Vo1)*10**6#Exit nozzle area in mm**2\n",
    "Vox=(Vsx*Cv)#Velocity in m/s\n",
    "hohx=(Vox/44.72)**2#Change in enthalpy in kJ/kg\n",
    "hox=(ho-hohx)#Enthalpy in kJ/kg\n",
    "vox=0.22#Specific volume in m**3/kg\n",
    "Aox=((ws*vox)/Vox)*10**6#Critical area in m**2\n",
    "\n",
    "#Output\n",
    "print \"(a) Area of throat is %3.1f mm**2 \\n Exit area is %3.1f mm**2 \\n\\n (b) Area of throat is %3.1f mm**2 \\n Exit area is %3.1f mm**2\"%(Ax,A1,Aox,Ao1)\n",
    "#In textbook, Ao1 is given wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.6 Pg: 517"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Mass flow rate is 0.966 kg/s \n",
      " Nozzle efficiency is 0.971\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=5#Pressure of steam in bar\n",
    "V=100#Velocity in m/s\n",
    "p2=1.5#Exit pressure in bar\n",
    "At=1280#Throat area in mm**2\n",
    "Ae=1600#Exit area in mm**2\n",
    "rp=0.58#Critical pressure ratio\n",
    "\n",
    "#Calculations\n",
    "ho=2749#Enthalpy in kJ/kg\n",
    "so=6.822#Entropy in kJ/kg.K\n",
    "px=(rp*p1)#Critical pressure in bar\n",
    "sx=so#Entropy in kJ/kg.K\n",
    "xx=(sx-1.660)/5.344#Dryness fraction\n",
    "hx=(556+(xx*2168))#Enthalpy in kJ/kg\n",
    "Vx=sqrt(((ho+((V**2*10**-3))/2)-hx)*(2/10**-3))#Velocity in m/s\n",
    "vx=(xx*0.6253)#Specific volume in m**3/kg\n",
    "w=(At*10**-6*Vx)/vx#Mass flow rate in kg/s\n",
    "s1s=sx#Entropy in kJ/kg.K\n",
    "x1s=(so-1.434)/5.789#Dryness fraction\n",
    "h1s=(467+x1s*2226)#ENthalpy in kJ/kg\n",
    "z=((Vx**2*10**-3)/2)-hx#z value\n",
    "#By iteratio scheme\n",
    "x1=0.932#Dryness fraction\n",
    "v1=1.080#Specific volume in m**3/kg\n",
    "h1=2542#Enthalpy in kJ/kg\n",
    "V1=652.2#Velocity in m/s\n",
    "nn=((hx-h1)/(hx-h1s))#Nozzle efficiency\n",
    "\n",
    "#Output\n",
    "print \" Mass flow rate is %3.3f kg/s \\n Nozzle efficiency is %3.3f\"%(w,nn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.7 Pg: 819"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) Exit area when the flow is in equilibrium throughout is 398 mm**2 \n",
      " (b) Exit area when the flow is supersaturated is 435.4 mm**2 \n",
      " (i) The degree of supercooling is 10.38 degree C \n",
      " (ii) The degree of supersaturation is 1.396\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=5#Pressure in bar\n",
    "T1=200+273#Temperature in K\n",
    "p2=2#Pressure in bar\n",
    "m=0.3#Mass flow rate in kg/s\n",
    "n=1.3#Adiabatic index\n",
    "\n",
    "#Calculations\n",
    "vo=0.4249#Specific volume in m**3/kg\n",
    "ho=2855.4#Enthalpy in kJ/kg\n",
    "so=7.0592#Entropy in kJ/kg.K\n",
    "x1=0.972#Dryness fraction \n",
    "h1=(504.7+x1*2201.9)#Enthalpy in kJ/kg\n",
    "v1=x1*0.8857#Specific volume in m**3/kg\n",
    "V1=44.72*sqrt(ho-h1)#Velocity in m/s\n",
    "A1=((m*v1)/V1)*10**6#Area in mm**2\n",
    "rp=(p1/p2)**(1/n)#Specific volume ratio\n",
    "vR=(vo*rp)#Specific volume in m**3/kg\n",
    "VR=sqrt(2*((n/(n-1))*(p1*vo-p2*vR)*10**5))#Velocity in m/s\n",
    "AR=((m*vR)/VR)*10**6#Area in mm**2\n",
    "TR=T1/(p1/p2)**((n-1)/n)#Temperature in K\n",
    "tR=(TR-273)#Temperature in degree C\n",
    "ts=120.23#Saturation temperature at pressure p1 in degree C\n",
    "ds=ts-tR#Degree of subcooling in degree C\n",
    "ps=1.4327#Saturation pressure at tR in bar\n",
    "dsu=(p2/ps)#Degree of supersaturation\n",
    "\n",
    "#Output\n",
    "print \" (a) Exit area when the flow is in equilibrium throughout is %3.0f mm**2 \\n (b) Exit area when the flow is supersaturated is %3.1f mm**2 \\n (i) The degree of supercooling is %3.2f degree C \\n (ii) The degree of supersaturation is %3.3f\"%(A1,AR,ds,dsu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.8 Pg: 520"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exit area is 403.2 mm**2 which upon checking is 400 mm**2\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "#Input data\n",
    "p1=5#Pressure in bar\n",
    "T1=200#Temperature in degree C\n",
    "p2=2#Pressure in bar\n",
    "m=0.3#Mass flow rate in kg/s\n",
    "n=1.3#Adiabatic index\n",
    "nn=0.92#Nozzle efficiency\n",
    "cp=1.925#mean specific heat in kJ/kg.K\n",
    "x=[0,2.308,1943]#pv*10**3 = 2.308(h-1943)\n",
    "\n",
    "#Calculations\n",
    "vo=0.4249#Specific volume in m**3/kg\n",
    "ho=2855.4#Enthalpy in kJ/kg\n",
    "so=7.0592#Entropy in kJ/kg.K\n",
    "x1=0.972#Dryness fraction \n",
    "h1=(504.7+x1*2201.9)#Enthalpy in kJ/kg\n",
    "v1=x1*0.8857#Specific volume in m**3/kg\n",
    "V1=44.72*sqrt(ho-h1)#Velocity in m/s\n",
    "h=ho-h1#Change in enthalpy in kJ/kg\n",
    "hoq=nn*h#Change in enthalpy in kJ/kg\n",
    "VQ=44.72*sqrt(hoq)#Velocity in m/s\n",
    "toq=(hoq/cp)#Temperature difference in degree C\n",
    "tQ=(T1-toq)#Temperature in degree C\n",
    "TQ=tQ+273#Temperature in K\n",
    "vQ=((p1*100*vo)/(T1+273))*(TQ/T1)#Specific volume in m**3/kg\n",
    "A1=((m*vQ)/VQ)*10**6#Area in mm**2\n",
    "vQ=(x[(1)]*(ho-hoq-x[(2)]))/(10**3*p2)#Specific volume in m**3/kg\n",
    "A11=((m*vQ)/VQ)*10**6#Area in mm**2\n",
    "\n",
    "#Output\n",
    "print \"Exit area is %3.1f mm**2 which upon checking is %3.0f mm**2\"%(A1,A11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.9 Pg: 422"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Blade Angle is 32.36 degrees \n",
      "\n",
      " Neglecting the friction effects \n",
      " Tangential force is 809.49 N \n",
      " Axial thrust is 0 N \n",
      " Diagram efficiency is 86.3 percent \n",
      "\n",
      " Considering the friction effects \n",
      " Axial thrust is 51.3 N \n",
      " Diagram Power is 291.42 kW \n",
      " Diagram efficiency is 77.71 percent\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "V1=1000#Speed in m/s\n",
    "Vb=400#Peripheral velocity in m/s\n",
    "a=20#Nozzle angle in degree\n",
    "m=0.75#Mass flow in kg/s\n",
    "f=80#Percentage reduction of relative velocity\n",
    "\n",
    "#Calculations\n",
    "b1=degrees(atan((V1*sin(a*pi/180))/((V1*cos(a*pi/180))-Vb)))#Blade angle in degree\n",
    "V=342#Velocity from E7.9 in m/s\n",
    "Vr1=V/sin(b1*pi/180)#Velocity in m/s\n",
    "dVw=(2*Vr1*cos(b1*pi/180))#Velocity in m/s\n",
    "Pt=(m*dVw)#Tangential thrust in N\n",
    "WD=(Pt*Vb)/1000#Diagram power in kW\n",
    "nD=(WD/(0.5*m*V1**2*10**-3))*100#Diagram efficiency in percent\n",
    "Pa=0#Axial thrust in N\n",
    "Vr2=(f/100)*Vr1#Velocity in m/s\n",
    "Pa2=m*sin(b1*pi/180)*(Vr1-Vr2)#Axial thrust in N\n",
    "WD2=(m*(Vr1+Vr2)*cos(b1*pi/180)*Vb)/1000#Diagram power in kW\n",
    "nD2=(WD2/(0.5*m*V1**2*10**-3))*100#Diagram efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \" Blade Angle is %3.2f degrees \\n\\n Neglecting the friction effects \\n Tangential force is %3.2f N \\n Axial thrust is %d N \\n Diagram efficiency is %3.1f percent \\n\\n Considering the friction effects \\n Axial thrust is %3.1f N \\n Diagram Power is %3.2f kW \\n Diagram efficiency is %3.2f percent\"%(b1,Pt,Pa,nD,Pa2,WD2,nD2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:7.10 Pg: 523"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) Work done in the stage per kg of steam is 42.56 kJ/kg \n",
      " Stage efficiency is 66.4 percent \n",
      "\n",
      " (b) Number of stages are  15\n"
     ]
    }
   ],
   "source": [
    "from math import atan, sin, cos, degrees, ceil,pi\n",
    "#Input data\n",
    "a=20#Nozzle angle in degrees\n",
    "b2=30#Blade exit angle in degrees\n",
    "Vb=130#Mean blade speed in m/s\n",
    "V1=330#Velocity of steam in m/s\n",
    "f=0.8#Friction factor\n",
    "nn=0.85#Nozzle efficiency\n",
    "p1=20#Pressure in bar\n",
    "T1=250+273#Temperature in K\n",
    "p2=0.07#Pressure in bar\n",
    "rf=1.06#Reheat factor\n",
    "\n",
    "#Calculations\n",
    "b1=degrees(atan((V1*sin(a*pi/180))/((V1*cos(a*pi/180))-Vb)))#Blade angle in degrees\n",
    "Vr1=((V1*sin(a*pi/180))/sin(b1*pi/180))#Velocity in m/s\n",
    "Vr2=(f*Vr1)#Velocity in m/s\n",
    "dVw=(Vr1*cos(b1*pi/180))+(Vr2*cos(b2*pi/180))#Vecoity in m/s\n",
    "WD=(dVw*Vb)/1000#Workdone in kJ/kg\n",
    "nb1=((2*dVw*Vb)/V1**2)*100#Efficiency in percent\n",
    "nst=(nn*nb1)#Efficiency in percent\n",
    "nin=(nst*rf)*100#Efficiency in percent\n",
    "h1=2902.3#Enthalpy in kJ/kg\n",
    "s1=6.5466#Entropy in kJ/kg.K\n",
    "x2s=(s1-0.5582)/7.7198#Dryness fraction\n",
    "h2s=(163.16+x2s*2409.54)#Enthalpy in kJ/kg\n",
    "h12=(0.7041*(h1-h2s))#Change in enthalpy in kJ/kg\n",
    "n=ceil(h12/WD)#Number of stages\n",
    "\n",
    "#Output\n",
    "print \" (a) Work done in the stage per kg of steam is %3.2f kJ/kg \\n Stage efficiency is %3.1f percent \\n\\n (b) Number of stages are %3.0f\"%(WD,nst,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.10 Pg: 525"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Power deveoped in the blading is 355.89 kW\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import atan, sin, cos, degrees, ceil,pi\n",
    "#Input data\n",
    "d=800#Diameter in mm\n",
    "N=3000#Speed in rpm\n",
    "V1=300#Velocity in m/s\n",
    "a=20#Nozzle angle in degrees\n",
    "f=0.86#Frictional factor\n",
    "T=140#Axial thrust in N\n",
    "\n",
    "#Calculations\n",
    "Vb=((3.14*(d/1000)*N)/60)#Velocity in m/s\n",
    "b1=degrees(atan((V1*sin(a*pi/180))/((V1*cos(a*pi/180))-Vb)))#Blade angle in degrees\n",
    "b2=b1#Blade angle in degrees\n",
    "Vr1=(V1*sin(a*pi/180))/sin(b1*pi/180)#Velocity in m/s\n",
    "Vr2=f*Vr1#Velocity in m/s\n",
    "w=(T/((Vr1*sin(b1*pi/180))-(Vr2*sin(b2*pi/180))))#Mass flow rate in kg/s\n",
    "dVw=(Vr2*cos(b2*pi/180))+(Vr1*cos(b1*pi/180))#Velocity in m/s\n",
    "P=(w*dVw*Vb*10**-3)#Power developed in kW\n",
    "\n",
    "#Output\n",
    "print \"Power deveoped in the blading is %3.2f kW\"%(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.12 Pg: 525"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) Axial thrust is 11.56 N \n",
      "  Tangential thrust is 146.85 N \n",
      "\n",
      " (b) Diagram Power is 29.437 kW \n",
      "\n",
      " (c) Diagram Efficiency is 86.3 percent\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt, cos, pi, atan,sin, degrees\n",
    "#Input data\n",
    "p1=15#Pressure in bar\n",
    "T1=300+273#Temperature in K\n",
    "p2=10#Pressure in bar\n",
    "nn=95#Nozzle efficiency in percent\n",
    "a=20#Nozzle angle in degrees\n",
    "x=5#The blade exit angle is 5 degrees less than the inlet angle\n",
    "f=0.9#Friction factor\n",
    "m=1350#Steam flow rate in kg/h\n",
    "\n",
    "#Calculations\n",
    "h1=3038.9#Enthalpy in kJ/kg\n",
    "s1=6.9224#Entropy in kJ/kg.K\n",
    "s2=s1#Entropy in kJ/kg.K\n",
    "t2s=250#Temperature in degree C\n",
    "h2s=2943.1#Enthalpy in kJ/kg\n",
    "V1=44.72*sqrt((nn/100)*(h1-h2s))#Velocity in m/s\n",
    "Vb=V1*(cos(a*pi/180)/2)#Velocity in m/s\n",
    "b1=degrees(atan((V1*sin(a*pi/180))/((V1*cos(a*pi/180))-Vb)))#Blade angle in degrees\n",
    "b2=b1-x#Blade angle in degrees\n",
    "Vr1=((V1*sin(a*pi/180))/sin(b1*pi/180))#Velocity in m/s\n",
    "Vr2=(f*Vr1)#Velocity in m/s\n",
    "dVw=(Vr1*cos(b1*pi/180))+(Vr2*cos(b2*pi/180))#Velocity in m/s\n",
    "dVa=(Vr1*sin(b1*pi/180))-(Vr2*sin(b2*pi/180))#Velocity in m/s\n",
    "Pa=(m/3600)*dVa#Axial thrust in N\n",
    "Pt=(m/3600)*dVw#Tangential thrust in N\n",
    "WD=(Pt*Vb*10**-3)#Diagram Power in kW\n",
    "dn=((WD*1000)/((1/2)*(m/3600)*V1**2))*100#Diagram efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \" (a) Axial thrust is %3.2f N \\n  Tangential thrust is %3.2f N \\n\\n (b) Diagram Power is %3.3f kW \\n\\n (c) Diagram Efficiency is %3.1f percent\"%(Pa,Pt,WD,dn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.13 Pg: 527"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) the tangential thrust is 5.355 kW \n",
      " (b) Axial thrust is 0.29 kN \n",
      " (c) Power developed is 642.54 kW \n",
      " (d) Diagram efficiency is 71.39 percent\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt, cos, pi, atan,sin, degrees\n",
    "\n",
    "#Input data\n",
    "V1=600#Velocity in m/s\n",
    "a=16#Nozzle angle in degrees\n",
    "Vb=120#Mean blade angle in degrees\n",
    "b2=18#Exit angle in degrees\n",
    "aa1=22#Exit angle in degrees\n",
    "b4=36#Exit angle in degrees\n",
    "m=5#Steam flow rate in kg/s\n",
    "f=0.85#Friction coefficient\n",
    "\n",
    "#Calculations\n",
    "b1=degrees(atan((V1*sin(a*pi/180))/((V1*cos(a*pi/180))-Vb)))#Exit angle in degrees\n",
    "Vr1=((V1*sin(a*pi/180))/sin(b1*pi/180))#Velocity in m/s\n",
    "Vr2=(f*Vr1)#Velocity in m/s\n",
    "a1=degrees(atan((Vr2*sin(pi/180*b2))/((Vr2*cos(pi/180*b2))-Vb)))#Angle in degrees\n",
    "V2=((Vr2*sin(pi/180*b2))/sin(pi/180*a1))#Velocity in m/s\n",
    "V3=(f*V2)#Velocity in m/s\n",
    "dVw1=(Vr1*cos(pi/180*b1))+(Vr2*cos(pi/180*b2))#Velocity in m/s\n",
    "dVa1=(V1*sin(pi/180*a))-(V2*sin(pi/180*a1))#Velocity in m/s\n",
    "b3=degrees(atan((V3*sin(pi/180*aa1))/((V3*cos(pi/180*aa1))-Vb)))#Angle in degrees\n",
    "Vr3=((V3*sin(pi/180*aa1))/sin(pi/180*b3))#Velocity in m/s\n",
    "Vr4=(f*Vr3)#velocity in m/s\n",
    "dVw2=(Vr3*cos(pi/180*b3))+(Vr4*cos(pi/180*b4))#Velocity in m/s\n",
    "dVa2=(V3*sin(pi/180*aa1))-(Vr4*sin(pi/180*b4))#Velocity in m/s\n",
    "udVw=(dVw1+dVw2)#Total velocity in m/s\n",
    "udVa=(dVa1+dVa2)#Total velocity in m/s\n",
    "Pt=(m*udVw*10**-3)#tangential thrust in kN\n",
    "Pa=(m*udVa*10**-3)#Axial thrust in kN\n",
    "WD=(Pt*Vb)#Power developed in kW\n",
    "nd=((2*udVw*Vb)/V1**2)*100#Diagram efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \" (a) the tangential thrust is %3.3f kW \\n (b) Axial thrust is %3.2f kN \\n (c) Power developed is %3.2f kW \\n (d) Diagram efficiency is %3.2f percent\"%(Pt,Pa,WD,nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.14 Pg: 529"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) Absolute velocity of steam leaving the stage is  75 m/s \n",
      " (b) the diagram work is 130 kJ/kg \n",
      " (c) the diagram efficiency is 78.64 percent\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "#Input data\n",
    "a=17#Nozzle angle in degrees\n",
    "Vb=125#Blade velocity in m/s\n",
    "b2=22#Blade angle n degrees\n",
    "a1=26#Blade angle n degrees\n",
    "b4=30#Blade angle n degrees\n",
    "f=0.9#Friction factor\n",
    "a2=90#Axial angle in degrees\n",
    "\n",
    "#Calculations\n",
    "dVw=1040#Velocity in m/s from Velocity triangles Fig. E.7.14\n",
    "V1=575#Velocity in m/s from Velocity triangles Fig. E.7.14\n",
    "V4=75#Velocity of steam exiting stage in m/s from Velocity triangles Fig. E.7.14\n",
    "WD=(dVw*Vb)/1000#Diagram work in kJ/kg\n",
    "nd=((WD*1000)/((1/2)*V1**2))*100#Diagram efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \" (a) Absolute velocity of steam leaving the stage is %3.0f m/s \\n (b) the diagram work is %3.0f kJ/kg \\n (c) the diagram efficiency is %3.2f percent\"%(V4,WD,nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.15 Pg: 530"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Efficiency of first stage is 66.67 percent \n",
      " Percentage of the total power developed by the turbine is 22.22 percent\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "p1=35#Pressure in bar\n",
    "T1=350+273#Temperature in K\n",
    "p2=0.07#Pressure in bar\n",
    "x=1/4#Fraction of drop in isentropic enthalpy\n",
    "a=20#Nozzle angle in degrees\n",
    "nn=88#Nozzle efficiency in percent\n",
    "y=0.2#Velocity ratio\n",
    "b2=30#Exit blade angle in degrees\n",
    "b4=30#Exit blade angle in degrees\n",
    "f=0.9#Friction coefficienct\n",
    "In=75#Internal efficiency of the turbine in percent\n",
    "\n",
    "#Calculations\n",
    "h1=3106.4#Enthalpy in kJ/kg\n",
    "s1=6.6643#Entropy in kJ/kg.K\n",
    "x2s=(s1-0.5582)/7.7198#dryness fraction\n",
    "h2s=(163.16+x2s*2409.54)#Enthalpy in kJ/kg\n",
    "dh=(h1-h2s)#Change in enthalpy in kJ/kg\n",
    "h13s=x*dh#Change in enthalpy in kJ/kg\n",
    "h13=(nn/100)*h13s#Change in enthalpy in kJ/kg\n",
    "V1=(44.72*sqrt(h13))#Velocity in m/s\n",
    "Vb=(y*V1)#Velocity in m/s\n",
    "b1=degrees(atan((V1*sin(pi/180*a))/((V1*cos(pi/180*a))-Vb)))#Angle in degrees\n",
    "Vr1=((V1*sin(pi/180*a))/sin(pi/180*b1))#Velocity in m/s\n",
    "Vr2=(f*Vr1)#Velocity in m/s\n",
    "dVw1=(Vr1*cos(pi/180*b1))+(Vr2*cos(pi/180*b2))#Velocity in m/s\n",
    "V2=sqrt((Vr2*sin(pi/180*b2))**2+((Vr2*cos(pi/180*b2))-Vb)**2)#Velocity in m/s\n",
    "V3=f*V2#Velocity in m/s\n",
    "b3=degrees(atan((V3*sin(pi/180*b2))/((V3*cos(pi/180*b2))-Vb)))#Angle in degrees\n",
    "Vr3=((V3*sin(pi/180*b2))/sin(pi/180*b3))#Velocity in m/s\n",
    "Vr4=f*Vr3#Velocity in m/s\n",
    "dVw2=(Vr3*cos(pi/180*b3))+(Vr4*cos(pi/180*b4))#Velocity in m/s\n",
    "dVw=(dVw1+dVw2)#Velocity in m/s\n",
    "nb1=((2*dVw*Vb)/V1**2)*100#Efficiency in percent\n",
    "ns=(nn*nb1)/100#Efficiency in percent\n",
    "ht=(In/100)*dh#Total change in enthalpy in kJ/kg\n",
    "hc=(ns/100)*h13s#Total change in enthalpy in kJ/kg\n",
    "pp=(hc/ht)*100#Percentage of enthalpy\n",
    "\n",
    "#Output\n",
    "print \" Efficiency of first stage is %3.2f percent \\n Percentage of the total power developed by the turbine is %3.2f percent\"%(ns,pp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.16 Pg: 532 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) the required height of blading is 127.2 mm \n",
      " (b) the power developed by the ring is 2.368 kW\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "R=50#Percentage of reaction\n",
    "b1=35#Angle in degrees\n",
    "q=b1#Angle in degrees\n",
    "b2=20#Angle in degrees\n",
    "a=b2#Angle in degrees\n",
    "N=1500#Speed in rpm\n",
    "d=0.67#Mean diameter in m\n",
    "p=1.5#Pressure in bar\n",
    "x=0.96#Dryness fraction\n",
    "w=3.6#Flow rate in kg/s\n",
    "\n",
    "\n",
    "#Calculations\n",
    "Vb=(3.14*d*N)/60#Velocity in m/s\n",
    "V1=(Vb*(sin(pi/180*180-b1)/sin(pi/180*b1-b2)))#Veocity in m/s\n",
    "Vr1=(Vb*(sin(pi/180*b2)/sin(pi/180*b1-b2)))#Velocity in m/s\n",
    "dVw=(V1*cos(pi/180*a))+(Vr1*cos(pi/180*q))#Velocity in m/s\n",
    "v1=(0.001052+x*1.15937)#Specific volume in m**3/kg\n",
    "hb=((w*v1)/(3.14*d*V1*sin(pi/180*a)))*1000#Required height in mm\n",
    "P=(w*dVw*Vb)/1000#Power developed in kW\n",
    "\n",
    "#Output\n",
    "print \" (a) the required height of blading is %3.1f mm \\n (b) the power developed by the ring is %3.3f kW\"%(hb,P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.17 Pg: 533"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) Blade height is 138 mm \n",
      " (b) the diagram power is 15.42 kW\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "N=400#Speed in rpm\n",
    "P=5#Power in MW\n",
    "m=6#Flow rate in kg/kWh\n",
    "b2=20#Blade angle in degrees\n",
    "a=b2#Angle in degrees\n",
    "x=1.35#Velocity ratio\n",
    "p=1.2#Pressure in bar\n",
    "x1=0.95#Steam quality \n",
    "Dh=12#Ratio of Dm and hb\n",
    "\n",
    "#Calculations\n",
    "w=(m*P*1000)/3600#Mass flow rate in kg/s\n",
    "v1=(0.0010468+x1*1.454)#Specific volume in m**3/kg\n",
    "hb=((w*v1)/(Dh*3.14*x*((Dh*N)/60)*3.14*sin(pi/180*a)))**(1/3)*1000#Blade height in mm\n",
    "Vb=((3.14*Dh*(hb/1000)*N)/60)#velocity in m/s\n",
    "V1=(x*Vb)#Velocity in m/s\n",
    "dVw=((2*V1*cos(pi/180*a))-Vb)#velocity in m/s\n",
    "WD=(w*dVw*Vb*10**-3)#Diagram power in kW\n",
    "\n",
    "#Output\n",
    "print \" (a) Blade height is %3.0f mm \\n (b) the diagram power is %3.2f kW\"%(hb,WD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.18 Pg: 534"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Mass flow rate of steam is 4.698 kg/s \n",
      " Useful enthalpy drop is 117.80 kJ/kg \n",
      " The diagram power is 553.4 kW\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "N=3000#Speed in rpm\n",
    "Vb=100#Mean blade speed in m/s\n",
    "x=0.56#Velocity ratio\n",
    "a=20#Blade angle in degrees\n",
    "b2=a#Blade angle in degrees\n",
    "v=0.65#Specific volume in m**3/kg\n",
    "h=25#Mean height in mm\n",
    "n=5#Number of pairs of blades\n",
    "\n",
    "#Calculations\n",
    "V1=(Vb/x)#Velocity in m/s\n",
    "Vr2=V1#Velocity in m/s\n",
    "Dm=(Vb*60)/(3.14*N)#Diameter in m\n",
    "w=((3.14*Dm*h*V1*sin(pi/180*a))/v)/1000#Mass flow rate in kg/s\n",
    "ws=(w*3600)#Mass flow rate in kg/hr\n",
    "b1=degrees(atan((V1*sin(pi/180*a))/((V1*cos(pi/180*a))-Vb)))#Blade angle in degrees\n",
    "Vr1=((V1*sin(pi/180*a))/sin(pi/180*b1))#Velocity in m/s\n",
    "dhmb=(1/2)*(Vr2**2-Vr1**2)/1000#Change in enthalpy in kJ/kg\n",
    "dsta=(2*dhmb)#Change in enthalpy of stage in kJ/kg\n",
    "dsta5=(n*dsta)#Total Change in enthalpy of stage in kJ/kg\n",
    "Dp=(w*dsta5)#Diagram power in kW\n",
    "\n",
    "#Output\n",
    "print \" Mass flow rate of steam is %3.3f kg/s \\n Useful enthalpy drop is %3.2f kJ/kg \\n The diagram power is %3.1f kW\"%(w,dsta5,Dp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.19 Pg: 535"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) the number of impulse stages are  6 \n",
      " (b) the nozzle height is 2.4 mm\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "P=8#Power in MW\n",
    "N=5000#Speed in rpm\n",
    "p=40#pressure in bar\n",
    "T=500#Temperature in degree C\n",
    "p2=0.1#Pressure in bar\n",
    "In=0.85#Internal efficiency of turbine\n",
    "nm=0.96#Mechanical efficiency\n",
    "nn=0.92#Nozzle efficiency\n",
    "a=15#Nozzle angle in degrees\n",
    "Vb=300#Blade velocity in m/s\n",
    "\n",
    "#Calculations\n",
    "V1=(2*Vb)/cos(pi/180*a)#Velocity in m/s\n",
    "dh=((V1/44.72)**2/nn)#Change in enthalpy in kJ/kg\n",
    "h1=3445.3#Enthalpy in kJ/kg\n",
    "s1=7.0901#Entropy in kJ/kg.K\n",
    "s2=s1#Entropy in kJ/kg.K\n",
    "x2=(s2-0.6493)/7.5009#Dryness fraction\n",
    "h2s=(191.83+x2*2392.8)#Enthalpy in kJ/kg\n",
    "h12s=(h1-h2s)#Change in enthalpy in kJ/kg\n",
    "n=(h12s/dh)#Number of stages\n",
    "w=((P*1000)/(In*nm))/h12s#Mass flow rate in kg/s\n",
    "h13=(nn*dh)#Change in enthalpy in kJ/kg\n",
    "h3=h1-h13#Enthalpy in kJ/kg\n",
    "v3=0.17#Specific volume in m**3/kg\n",
    "A=(w*v3)/V1#Area in m**2\n",
    "hm=(A/(((Vb*60)/N)*sin(pi/180*a)))*1000#Height in mm\n",
    "\n",
    "#Output\n",
    "print \" (a) the number of impulse stages are%3.0f \\n (b) the nozzle height is %3.1f mm\"%(n,hm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.20 Pg: 537"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Height of the moving blades at exit is 58.3 mm \n",
      " Power developed in the blade row is 166.70 kW\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "from __future__ import division\n",
    "#Input data\n",
    "p=1.5#Pressure in bar\n",
    "x1=0.9#Dryness fraction\n",
    "m=7#Steam flow rate in kg/s\n",
    "N=3000#Turbine speed in rpm\n",
    "x=0.7#Velocity ratio\n",
    "y=0.75#Velocity ratio\n",
    "a=20#Exit angle in degrees\n",
    "b2=a#Angle in degrees\n",
    "hx=1/10#Fraction of height\n",
    "\n",
    "#Calculations\n",
    "v=0.001052+x1*1.15937#Specific volume in m**3/kg\n",
    "Dm=((m*v*60)/(3.14*hx*y*3.14*N))**(1/3)#Diameter in m\n",
    "hb=Dm*1000*hx#Height in mm\n",
    "Vb=(3.14*Dm*N)/60#Velocity in m/s\n",
    "dVw=((2*x*Vb*cos(pi/180*a)/sin(pi/180*a))-Vb)#Velocity in m/s\n",
    "P=(m*dVw*Vb)/1000#Power developed in kW\n",
    "\n",
    "#Output\n",
    "print \" Height of the moving blades at exit is %3.1f mm \\n Power developed in the blade row is %3.2f kW\"%(hb,P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.21 Pg: 538"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean diameter of the wheel if the turbine were of \n",
      " (a) single impulse stage is 4.74 m \n",
      " (b) single 50 percent reaction stage is 6.7 m \n",
      " (c) four pressure (or Rateau) stages is 2.37 m \n",
      " (d) one two-row Curtis stage is 2.370 m \n",
      " (e) four stage 50 percent reaction stages is 3.35 m\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "p=40#Pressure in bar\n",
    "T=500#Temperature in degree C\n",
    "p1=0.1#Pressure in bar\n",
    "a=16#Nozzle angle in degrees\n",
    "N=3000#Speed in rpm\n",
    "\n",
    "#Calculations\n",
    "h1=3445.3#Enthalpy in kJ/kg\n",
    "s1=7.0901#Entropy in kJ/kg.K\n",
    "s2=s1#Entropy in kJ/kg.K\n",
    "x2s=(s2-0.6493)/7.5009#Dryness fraction\n",
    "h2s=(191.83+x2s*2392.8)#Enthalpy in kJ/kg\n",
    "V1=44.72*sqrt(h1-h2s)#Velocity in m/s\n",
    "Vb=V1*(cos(pi/180*a)/2)#Velocity in m/s\n",
    "Dm=(Vb*60)/(3.14*N)#Diameter in m\n",
    "V2=44.72*sqrt((h1-h2s)/2)#Velocity in m/s\n",
    "Vb2=V2*cos(pi/180*a)#Velocity in m/s\n",
    "Dm2=(Vb2*60)/(3.14*N)#Diameter in m\n",
    "V3=44.72*sqrt((h1-h2s)/4)#Velocity in m/s\n",
    "Vb3=V3*(cos(pi/180*a)/2)#Velocity in m/s\n",
    "Dm3=(Vb3*60)/(3.14*N)#Diameter in m\n",
    "V4=44.72*sqrt(h1-h2s)#Velocity in m/s\n",
    "Vb4=V4*(cos(pi/180*a)/4)#Velocity in m/s\n",
    "Dm4=(Vb4*60)/(3.14*N)#Diameter in m\n",
    "V5=44.72*sqrt((h1-h2s)/(2*4))#Velocity in m/s\n",
    "Vb5=V5*cos(pi/180*a)#Velocity in m/s\n",
    "Dm5=(Vb5*60)/(3.14*N)#Diameter in m\n",
    "\n",
    "#Output\n",
    "print \"The mean diameter of the wheel if the turbine were of \\n (a) single impulse stage is %3.2f m \\n (b) single 50 percent reaction stage is %3.1f m \\n (c) four pressure (or Rateau) stages is %3.2f m \\n (d) one two-row Curtis stage is %3.3f m \\n (e) four stage 50 percent reaction stages is %3.2f m\"%(Dm,Dm2,Dm3,Dm4,Dm5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.22 Pg: 539"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of stages required in \n",
      " (a) all simple impulse stages are   8 \n",
      " (b) all 50 percent reaction stages are  13 \n",
      " (c) a 2-row Cutris stage follwed by simple impulse stages are   3 \n",
      " (d) a 2-row Cutris stage followed by 50 percent reaction stages are   6\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees,ceil\n",
    "from __future__ import division\n",
    "#Input data\n",
    "p=150#Pressure in bar\n",
    "T=600#Temperature in degree C\n",
    "Vb=300#Velocity in m/s\n",
    "nn=95#Nozzle efficiency in percent\n",
    "a=15#Nozzle angle in degrees\n",
    "a1=25#Angle in degrees\n",
    "\n",
    "#Calculations\n",
    "h1=3582.3#Enthalpy in kJ/Kg\n",
    "s1=6.6776#Entropy in kJ/kg.K\n",
    "s2=s1#Entropy in kJ/kg.K\n",
    "x2s=(s2-0.6493)/7.5009#Dryness fraction\n",
    "h2s=(191.83+x2s*2392.8)#Enthalpy in kJ/kg\n",
    "h12s=(h1-h2s)#Difference in enthalpy in kJ/kg\n",
    "V1=(Vb*2)/cos(pi/180*a)#Velocity in m/s\n",
    "dhs=(V1/44.72)**2/(nn/100)#Change in enthalpy in kJ/kg\n",
    "n1=ceil(h12s/dhs)#Number of stages\n",
    "V2=(Vb/cos(pi/180*a1))#Velocity in m/s\n",
    "dhs2=(V2/44.72)**2/(nn/(2*100))#Change in enthalpy in kJ/kg\n",
    "n2=h12s/dhs2#Number of stages\n",
    "V3=(Vb*4)/cos(pi/180*a)#Velocity in m/s\n",
    "dhs3=(V3/44.72)**2/(nn/100)#Change in enthalpy in kJ/kg\n",
    "dhhs3=(h12s-dhs3)#Change in enthalpy in kJ/kg\n",
    "n3=dhhs3/dhs#Number of stages\n",
    "n4=dhhs3/dhs2#Number of stages\n",
    "\n",
    "#Output\n",
    "print \"Number of stages required in \\n (a) all simple impulse stages are %3.0f \\n (b) all 50 percent reaction stages are %3.0f \\n (c) a 2-row Cutris stage follwed by simple impulse stages are %3.0f \\n (d) a 2-row Cutris stage followed by 50 percent reaction stages are %3.0f\"%(n1,n2,n3,n4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.23 Pg: 541"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " The interstage pressures are 8 bar, 2.6 bar, 0.6 bar \n",
      " The reheat factor is 1.071 \n",
      " The turbine internal efficiency is 80.3 percent\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "#Input data\n",
    "p1=20#Pressure in bar\n",
    "T=400#Temperature in degree C\n",
    "p2=0.1#Pressure in bar\n",
    "n=4#Number of stages\n",
    "ns=75#Stage efficiency in percent\n",
    "\n",
    "#Calculations\n",
    "h16s=(3250-2282)#Change in enthalpy in kJ/kg\n",
    "h12s=(h16s/n)#Change in enthalpy in kJ/kg\n",
    "p=[0,8,2.6,0.6]#pressures in bar from Mollier chart\n",
    "h12=(ns/100)*h12s#Change in enthalpy in kJ/kg\n",
    "h23s=(3060-2800)#Change in enthalpy in kJ/kg\n",
    "h23=(ns/100)*h23s#Change in enthalpy in kJ/kg\n",
    "h34s=(2870-2605)#Change in enthalpy in kJ/kg\n",
    "h34=(ns/100)*h34s#Change in enthalpy in kJ/kg\n",
    "h45s=(2680-2410)#Change in enthalpy in kJ/kg\n",
    "h45=(ns/100)*h45s#Change in enthalpy in kJ/kg\n",
    "h5=2470#Enthalpy in kJ/kg\n",
    "rf=(h12s+h23s+h34s+h45s)/h16s#Reheat factor\n",
    "nth=((h12+h23+h34+h45)/h16s)*100#Internal efficiency in percent\n",
    "nin=(ns*rf)#Internal efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \" The interstage pressures are %d bar, %3.1f bar, %3.1f bar \\n The reheat factor is %3.3f \\n The turbine internal efficiency is %3.1f percent\"%(p[(1)],p[(2)],p[(3)],rf,nin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.25 Pg: 544"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " (a) the flow rate of steam required is 17.99 kg/s \n",
      " (b) the mean blade diameter is 1.302 m \n",
      " (c) the speed of the rotor is 2065 rpm\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "n=20#Number of stages\n",
    "P=12#Power in MW\n",
    "p=15#Pressure in bar\n",
    "T=350#Temperature in degree C\n",
    "p1=0.14#Pressure in bar\n",
    "ns=75#Stage efficiency in percent\n",
    "rf=1.04#Reheat factor\n",
    "p2=1#Pressure in bar\n",
    "a=20#Angle in degrees\n",
    "v=0.7#Velocity ratio\n",
    "h=1/12#Blade height in terms of mean blade diameter\n",
    "\n",
    "#Calculations\n",
    "nint=(ns/100)*rf#Internal efficiency \n",
    "dhs=855#Enthalpy in kJ/kg\n",
    "dha=ceil(nint*dhs)#Actual enthalpy change in kJ/kg\n",
    "w=(P*1000)/dha#Mass flow rate in kg/s\n",
    "Vb=(sqrt((dha/n)/((((2/v)*cos(pi/180*a))-1)*10**-3)))#Velocity in m/s#\n",
    "vg=1.694#Specific volume in m**3/kg\n",
    "Dm=sqrt((w*vg)/(3.14*h*(Vb/v)*sin(pi/180*a)))#Diameter in m\n",
    "N=((Vb*60)/(3.14*Dm))#Speed in rpm\n",
    "\n",
    "#Output\n",
    "print \" (a) the flow rate of steam required is %3.2f kg/s \\n (b) the mean blade diameter is %3.3f m \\n (c) the speed of the rotor is %3.0f rpm\"%(w,Dm,N)\n",
    "#In textbook, Vb is given wrong as 141.4 m/s instead of 140.6 m/s. Hence the answers are different."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.26 Pg: 546"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Blade heights at the exit of each row: \n",
      " First row of moving blades is 29.4 mm \n",
      " Fixed row of guide blades is 37.8 mm \n",
      " Second row of moving blades is 40.6 mm\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from math import sqrt, atan,sin,cos,pi,degrees\n",
    "#Input data\n",
    "V1=600#Velocity in m/s\n",
    "Vb=120#Mean blade velocity in m/s\n",
    "a=16#Nozzle angle in degrees\n",
    "b=[0,18,21,35]#Exit angles in degrees\n",
    "m=5#Steam flow rate in kg/s\n",
    "h=25#Nozzle height in mm\n",
    "v=0.375#Specific volume in m**3/kg\n",
    "p=25#Pitch in mm\n",
    "t=0.5#Thickness in mm\n",
    "kb=0.9#Constant\n",
    "\n",
    "#Calculations\n",
    "l=((m*v)/(sin(pi/180*a)*V1*(h/1000)*kb))#Length of the nozzle arc in m #Length of the nozzle arc is calculated wrong as 0.454m instead of 0.5 m\n",
    "b1= degrees(atan((V1*sin(pi/180*a))/((V1*cos(pi/180*a))-Vb)))#Angle in degrees\n",
    "Vr1=((V1*sin(pi/180*a))/sin(pi/180*b1))#Velocity in m/s\n",
    "Vr2=kb*Vr1#Velocity in m/s\n",
    "V2=sqrt(Vr2**2+Vb**2-2*Vr2*Vb*cos(pi/180*b[(1)]))#Velocity in m/s\n",
    "V3=291#Velocity in m/s\n",
    "b3=degrees(atan((V3*sin(pi/180*b[(2)]))/((V3*cos(pi/180*b[(2)]))-Vb)))#Angle in degrees\n",
    "Vr3=((V3*sin(pi/180*b[(2)]))/sin(pi/180*b3))#Velocity in m/s\n",
    "Vr4=(Vr3*kb)#Velocity in m/s\n",
    "hb1=((m*v*(h/1000))/(l*((p/1000)*sin(pi/180*b[(1)])-(t/1000))*Vr2))*1000#Height in mm\n",
    "hn=((m*v*(h/1000))/(l*((p/1000)*sin(pi/180*b[(2)])-(t/1000))*V3))*1000#Height in mm\n",
    "hb2=((m*v*(h/1000))/(l*((h/1000)*sin(pi/180*b[(3)])-(t/1000))*Vr4))*1000#Height in mm\n",
    "\n",
    "#Output\n",
    "print \" Blade heights at the exit of each row: \\n First row of moving blades is %3.1f mm \\n Fixed row of guide blades is %3.1f mm \\n Second row of moving blades is %3.1f mm\"%(hb1,hn,hb2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.27 Pg: 548"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of parallel exhausts in : \n",
      " (a)condition a are 4 \n",
      " (b)condition b are 8\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt, atan,sin,cos,pi,degrees, ceil\n",
    "#Input data\n",
    "P=200#Power in MW\n",
    "p=180#Pressure in bar\n",
    "T=550#Temperature in degree C\n",
    "P1=600#Power in MW\n",
    "p1=300#Pressure in bar\n",
    "T1=580#Temperature in degree C\n",
    "nt=90#Turbine efficiency in percent\n",
    "\n",
    "#Calculations\n",
    "h1=3430#Enthalpy in kJ/kg\n",
    "h2s=3040#Enthalpy in kJ/kg\n",
    "h12s=(h1-h2s)#Enthalpy in kJ/kg\n",
    "h12=(nt/100)*h12s#Enthalpy in kJ/kg\n",
    "h2=3070#Enthalpy in kJ/kg\n",
    "v2=0.06#Specific volume in m**3/kg\n",
    "h4=3560#Enthalpy in kJ/kg\n",
    "h3s=2000#Enthalpy in kJ/kg\n",
    "h13s=(h1-h3s)#Enthalpy in kJ/kg\n",
    "h13=(nt/100)*h13s#Enthalpy in kJ/kg\n",
    "w=(P*10**3)/h13#Mass flow rate in kg/s\n",
    "Vbm=350#Velocity in m/s\n",
    "N=3000#Speed in rpm\n",
    "a=25#Angle in degrees\n",
    "Dm=(Vbm*60)/(3.14*N)#Diameter in m\n",
    "hD=0.3#Assuming (hb/Dm)max \n",
    "hb=(hD*Dm)#Height in m\n",
    "Ab=(3.14*Dm*hb*0.9*sin(pi/180*a))#Flow area in m**2\n",
    "V1=(Vbm/cos(pi/180*a))#Velocity in m/s\n",
    "Vo=(Ab*V1)#Volume flow rate in m**3/s\n",
    "v=(Vo/w)#Specific volume in m**3/kg\n",
    "h5s=2456#Enthalpy in kJ/kg\n",
    "p5=0.36#Pressure in bar\n",
    "h45s=(h4-h5s)#Enthalpy in kJ/kg\n",
    "h45=(nt/100)*h45s#Enthalpy in kJ/kg\n",
    "h5=h4-h45#Enthalpy in kJ/kg\n",
    "x5=0.952#Dryness fraction\n",
    "h56s=(h5-2340)#Enthalpy in kJ/kg\n",
    "h56=(nt/100)*h56s#Enthalpy in kJ/kg\n",
    "h6=h5-h56#Enthalpy in kJ/kg\n",
    "v6=18#Specific volume in m**3/kg\n",
    "mm=(Vo/v6)#Maximum mass flow that one stage can accommodate in kg/s\n",
    "np=(w/mm)#Number of parallel exhausts\n",
    "rp=(p1/4)#Reheat pressure in bar\n",
    "xh1=3410#Enthalpy in kJ/kg\n",
    "xh2s=3015#Enthalpy in kJ/kg\n",
    "xh12s=xh1-xh2s#Enthalpy in kJ/kg\n",
    "xh12=(nt/100)*xh12s#Enthalpy in kJ/kg\n",
    "xv2=0.035#Specific volume in m**3/kg\n",
    "xh4=3060#Enthalpy in kJ/kg\n",
    "xh3s=1960#Enthalpy in kJ/kg\n",
    "xh13s=xh1-xh3s#Enthalpy in kJ/kg\n",
    "xh3=(xh1-xh13s)#Enthalpy in kJ/kg\n",
    "xw=(P1*10**3)/xh13s#Mass flow rate in kg/s\n",
    "xvm=(Vo/xw)#Maximum specific volume in m**3/kg\n",
    "Vf=(xw*xv2)#Volume flow rate in m**3/s\n",
    "xh5s=2300#Enthalpy in kJ/kg\n",
    "xh45s=xh4-xh5s#Enthalpy in kJ/kg\n",
    "xh45=(nt/100)*xh45s#Enthalpy in kJ/kg\n",
    "xh5=xh4-xh45s#Enthalpy in kJ/kg\n",
    "xv5=1.25#Specific volume in m**3/kg\n",
    "xx5=0.86#Dryness fraction\n",
    "xh6s=2050#Enthalpy in kJ/kg\n",
    "xh56s=xh5-xh6s#Enthalpy in kJ/kg\n",
    "xh56=(nt/100)*xh56s#Enthalpy in kJ/kg\n",
    "xh6=(xh5-xh56)#Enthalpy in kJ/kg\n",
    "xv6=12#Specific volume in m**3/kg\n",
    "xx6=0.792#Dryness fraction\n",
    "xmm=(Vo/xv6)#Maximum mass flow in kJ/kg\n",
    "xnp=ceil(xw/xmm)#Number of parallel exhausts\n",
    "\n",
    "#Output\n",
    "print \"Number of parallel exhausts in : \\n (a)condition a are %d \\n (b)condition b are %d\"%(np,xnp) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex: 7.28 Pg: 552"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) Steam rate at: \n",
      " One-fourth load is 5.75 kg/kWh \n",
      " Half load is 5.25 kg/kWh \n",
      " Three-fourth load is 5.08 kg/kWh \n",
      " Full load is 5.0 kg/kWh \n",
      "\n",
      " (b) Rankine cycle efficiency is 40.7 percent \n",
      " (c) Actual efficiency at full load is 21.7 percent \n",
      " (d) The turbogenerator efficiency at full load is 53.2 percent\n"
     ]
    }
   ],
   "source": [
    "#Input data\n",
    "P=100#Power in MW\n",
    "T=550#temperature in degree C\n",
    "p=0.1#Pressure in bar\n",
    "m=500000#Mass flow rate in kg/h at rated load\n",
    "mo=25000#Mass flow rate in kg/h at zero load\n",
    "x=[0,1/4,1/2,3/4,1]#Fraction of load\n",
    "\n",
    "#Calculations\n",
    "b=(m-mo)/(P*10**3)#Steam rate in kg/kWh\n",
    "y1=(x[(1)]*(P*10**3))#For one-fourth load\n",
    "s1=(mo/y1)+b#Steam rate in kg/kWh\n",
    "y2=(x[(2)]*(P*10**3))#For one-fourth load\n",
    "s2=(mo/y2)+b#Steam rate in kg/kWh\n",
    "y3=(x[(3)]*(P*10**3))#For one-fourth load\n",
    "s3=(mo/y3)+b#Steam rate in kg/kWh\n",
    "y4=(x[(4)]*(P*10**3))#For one-fourth load\n",
    "s4=(mo/y4)+b#Steam rate in kg/kWh\n",
    "h1=3511#Enthalpy in kJ/kg\n",
    "xs1=6.8142#Entropy in kJ/kg.K\n",
    "xs2=xs1#Entropy in kJ/kg.K\n",
    "x2s=(xs2-0.6493)/7.5009#Dryness fraction\n",
    "h2s=191.83+x2s*2392.8#Enthalpy in kJ/kg\n",
    "nR=((h1-h2s)/(h1-191.83))*100#Rankine efficiency in percent\n",
    "nac=((P*10**3*3600)/(m*(h1-191.83)))*100#Actual efficiency in percent\n",
    "nTG=((P*10**3*3600)/(m*(h1-h2s)))*100#Turbogenerator efficiency in percent\n",
    "\n",
    "#Output\n",
    "print \"(a) Steam rate at: \\n One-fourth load is %3.2f kg/kWh \\n Half load is %3.2f kg/kWh \\n Three-fourth load is %3.2f kg/kWh \\n Full load is %3.1f kg/kWh \\n\\n (b) Rankine cycle efficiency is %3.1f percent \\n (c) Actual efficiency at full load is %3.1f percent \\n (d) The turbogenerator efficiency at full load is %3.1f percent\"%(s1,s2,s3,s4,nR,nac,nTG)"
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