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+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 4 : Flow Of Fluids"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.1 page number 125"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find water compressibility\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "delta_p=70.;   #in bar\n",
+      "Et=20680.     #in bar\n",
+      "\n",
+      "# Calculations\n",
+      "compressibility = delta_p/Et;\n",
+      "\n",
+      "# Results\n",
+      "print \"compressibilty of water = %f\"%(compressibility)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "compressibilty of water = 0.003385\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.3 page number 128\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the viscosity of oil\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "F=0.5*9.8;   #in N\n",
+      "A=3.14*0.05*0.15;   #in m2\n",
+      "\n",
+      "# Calculations and Results\n",
+      "shear_stress=F/A;   #in Pa\n",
+      "print \"shear_stress = %f Pa\"%(shear_stress)\n",
+      "\n",
+      "velocity_distribution =0.1/(0.05*10**-3);\n",
+      "viscosity=shear_stress/velocity_distribution;\n",
+      "print \"viscosity = %f Pa-s\"%(viscosity) \n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "shear_stress = 208.067941 Pa\n",
+        "viscosity = 0.104034 Pa-s\n"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.5 page number 133\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find variation of losses with velocity\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "loss_ratio=3.6;     #delta_P2/delta_P1=3.6\n",
+      "velocity_ratio=2.;   #u2/u1=2\n",
+      "\n",
+      "# Calculations\n",
+      "n=math.log(loss_ratio,2);  #delta_P2/delta_P1=(u2/u1)**n\n",
+      "\n",
+      "# Results\n",
+      "print \"power constant = %f flow is turbulent\"%(n)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "power constant = 1.847997 flow is turbulent\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.8 page number 137\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the boundary layer properties\n",
+      "\n",
+      "import math \n",
+      "print ('part 1')\n",
+      "\n",
+      "# Variables\n",
+      "x=0.05   #in m\n",
+      "density=1000.   #in kg/m3\n",
+      "\n",
+      "# Calculations and Results\n",
+      "viscosity=1.*10**-3    #in Pa-s\n",
+      "u=1.   #in m/s\n",
+      "Re=(density*u*x)/viscosity;\n",
+      "\n",
+      "print \"Reynolds Number = %f\"%(Re)\n",
+      "\n",
+      "thickness=4.65*x*(Re)**-0.5;\n",
+      "print \"boundary layer thickness = %f m\"%(thickness)\n",
+      "\n",
+      "print ('part 2')\n",
+      "Re_x=3.2*10**5;\n",
+      "x_cr=(Re_x*viscosity)/(density*u);\n",
+      "print \"transition takes place at x = %f m\"%(x_cr) \n",
+      "\n",
+      "print ('part 3')\n",
+      "x=0.5   #in m\n",
+      "Re=(density*u*x)/viscosity;\n",
+      "thickness=0.367*x*(Re)**-0.2;\n",
+      "print \"boundary layer thickness= %f m\"%(thickness)\n",
+      "\n",
+      "t_sublayer=71.5*x*(Re)**-0.9;\n",
+      "print \"sub layer thickness= %f m\"%(t_sublayer)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "part 1\n",
+        "Reynolds Number = 50000.000000\n",
+        "boundary layer thickness = 0.001040 m\n",
+        "part 2\n",
+        "transition takes place at x = 0.320000 m\n",
+        "part 3\n",
+        "boundary layer thickness= 0.013300 m\n",
+        "sub layer thickness= 0.000266 m\n"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.9 page number 138\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the flow properties\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "d1=0.05   #in m\n",
+      "A1=(3.14*d1**2)/4.;\n",
+      "density_1=2.1   #in kg/m3\n",
+      "u1=15.     #in m/s\n",
+      "P1=1.8;   #in bar\n",
+      "P2=1.3;   #in bar\n",
+      "\n",
+      "# Calculations and Results\n",
+      "w=density_1*A1*u1;\n",
+      "density_2=density_1*(P2/P1);\n",
+      "print \"density at section 2 = %f kg/cubic meter\"%(density_2)\n",
+      "\n",
+      "u2=u1*(density_1/density_2)*(0.05/0.075)**2;\n",
+      "print \"velocity at section 2 = %f m/s\"%(u2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "density at section 2 = 1.516667 kg/cubic meter\n",
+        "velocity at section 2 = 9.230769 m/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.10 page number 139\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the temperature increase\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "Q=0.001*10**5   #in J/s\n",
+      "w=0.001*1000   #in kg/s\n",
+      "density=1000.   #in kg/m3\n",
+      "cp=4.19*10**3   #in J/kg K\n",
+      "\n",
+      "# Calculations\n",
+      "delta_T=Q/(w*cp);\n",
+      "\n",
+      "# Results\n",
+      "print \"Temperature increase = %f degree celcius\"%(delta_T)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Temperature increase = 0.023866 degree celcius\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.11 page number 142\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the pressure\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "u1=0;   #in m/s\n",
+      "ws=0;\n",
+      "P1=0.7*10**5    #in Pa\n",
+      "P3=0\n",
+      "density=1000   #in kg/m3\n",
+      "\n",
+      "# Calculations and Results\n",
+      "u3=((2*(P1-P3))/density)**0.5;\n",
+      "print \"u3 = %f m/s\"%(u3)\n",
+      "\n",
+      "ratio_area=0.5;\n",
+      "u2=u3/ratio_area;\n",
+      "print \"u2 = %f m/s\"%(u2)\n",
+      "\n",
+      "#applying bernoulli's equation\n",
+      "P2=1.7*10**5-((density*u2**2)/2)\n",
+      "print \"P2 = %f Pa\"%(P2)\n",
+      "print \"this flow is physically unreal\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "u3 = 11.832160 m/s\n",
+        "u2 = 23.664319 m/s\n",
+        "P2 = -110000.000000 Pa\n",
+        "this flow is physically unreal\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.12 page number 143\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the power requirements\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "Q=3800./(24*3600)    #in m3/s\n",
+      "d=0.202    #in m\n",
+      "\n",
+      "# Calculations\n",
+      "u=Q/((3.14/4)*d**2);    #in m/s\n",
+      "delta_P=5.3*10**6    #in Pa\n",
+      "density=897.    #in kg/m3\n",
+      "F=delta_P/density;    #in J/kg\n",
+      "ws=9.8*30+F;\n",
+      "mass_flow_rate= Q*density;\n",
+      "power=(ws*mass_flow_rate)/0.6;\n",
+      "\n",
+      "# Results\n",
+      "print \"power required = %f kW\"%(power/1000)\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "power required = 407.834267 kW\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.13 page number 146\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the tube length\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "density=1000    #in kg/m3\n",
+      "viscosity=1*10**-3   #in Pa s\n",
+      "P=100*1000    #in Pa\n",
+      "\n",
+      "# Calculations and Results\n",
+      "vdP=P/density;\n",
+      "\n",
+      "Q=2.5*10**-3/(24*3600)\n",
+      "A=3.14*(0.0005)**2/4;\n",
+      "u=Q/A;\n",
+      "print \"u = %f m/s\"%(u)\n",
+      "\n",
+      "Re=density*u*0.0005/viscosity;\n",
+      "print \"Re = %f\"%(Re)\n",
+      "\n",
+      "#F=18.86*L\n",
+      "L=(-u**2+vdP)/18.86;\n",
+      "print \"L = %f m\"%(L)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "u = 0.147440 m/s\n",
+        "Re = 73.720217\n",
+        "L = 5.301074 m\n"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.14 page number 151\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the discharge pressure\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "d=0.025     #in m\n",
+      "u=3.        #in m/s\n",
+      "density=894.   #in kg/m3\n",
+      "viscosity=6.2*10**4     #in Pa-s\n",
+      "\n",
+      "# Calculations and Results\n",
+      "Re=(u*d*density)/viscosity;\n",
+      "f=0.0045;\n",
+      "L=50.;\n",
+      "\n",
+      "delta_P=2*f*density*u**2*(L/d)\n",
+      "print \"frictional head loss = %f kPa\"%(delta_P/1000)\n",
+      "\n",
+      "required_P=25*density*9.8;\n",
+      "total_head=delta_P+required_P;\n",
+      "print \"total pressure head = %f bar\"%(total_head/10**5)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "frictional head loss = 144.828000 kPa\n",
+        "total pressure head = 3.638580 bar\n"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.15 page number 152\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the level difference\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "Q=0.8*10**-3;   #in m3/s\n",
+      "d=0.026    #in m\n",
+      "A=(3.14*(d**2))/4   #in m2\n",
+      "\n",
+      "# Calculations\n",
+      "u=Q/A;    #in m/s\n",
+      "density=800    #in kg/m3\n",
+      "viscosity=0.0005   #in Pa-s\n",
+      "\n",
+      "Re=(u*density*d)/viscosity;\n",
+      "f=0.079*(Re)**-0.25;\n",
+      "L=60\n",
+      "h_f=2*f*((u**2)/9.8)*(L/d);\n",
+      "\n",
+      "# Results\n",
+      "print \"level difference = %f m\"%(h_f)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "level difference = 5.343360 m\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.16 page number 153\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the engery cost\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "delta_z=50;    #in m\n",
+      "L=290.36    #in m\n",
+      "d=0.18    #in m\n",
+      "Q=0.05    #in m3/s\n",
+      "\n",
+      "# Calculations\n",
+      "A=(3.14*d**2)/4;    #in m2\n",
+      "u=Q/A;    #in m/s\n",
+      "density=1180;   #in kg/m3\n",
+      "viscosity=0.0012   #in Pa-s\n",
+      "Re=u*density*d/viscosity;\n",
+      "\n",
+      "f=0.004;\n",
+      "sigma_F=2*f*u**2*L/d;\n",
+      "ws=((9.8*50)+sigma_F)/0.6;\n",
+      "mass_flow_rate=Q*density;    #in Kg/s\n",
+      "power=mass_flow_rate*ws/1000;   #in KW\n",
+      "energy_cost=power*24*0.8;\n",
+      "\n",
+      "# Results\n",
+      "print \"Energy cost = Rs %f\"%(energy_cost)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Energy cost = Rs 1019.280105\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.17 page number 154\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the pressure loss\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "density=998   #in kg/m3\n",
+      "viscosity=0.0008  #in Pa-s\n",
+      "d=0.03   #in m\n",
+      "u=1.2   #in m/s\n",
+      "\n",
+      "# Calculations\n",
+      "Re=density*d*u/viscosity;\n",
+      "\n",
+      "f=0.0088;\n",
+      "D=1   #in m\n",
+      "N=10\n",
+      "L=3.14*D*N;\n",
+      "delta_P=(2*f*u**2*L)/d;   #in Pa\n",
+      "delta_P_coil=delta_P*(1+(3.54*(d/D)));\n",
+      "\n",
+      "# Results\n",
+      "print \"frictional pressure drop = %f kPa\"%(delta_P_coil)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "frictional pressure drop = 29.343858 kPa\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.18 page number 154\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find pressure drop per unit length\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "b=0.050    #in m\n",
+      "a=0.025    #in m\n",
+      "d_eq=b-a  #in m\n",
+      "density=1000  #in kg/m3\n",
+      "u=3    #in m/s\n",
+      "viscosity = 0.001\n",
+      "\n",
+      "# Calculations\n",
+      "Re=d_eq*u*density/viscosity;\n",
+      "\n",
+      "e=40*10**6   #in m\n",
+      "f=0.0062;\n",
+      "P_perunit_length=2*f*density*u**2/d_eq;   #in Pa/m\n",
+      "\n",
+      "# Results\n",
+      "print \"pressure per unit length = %f Pa/m\"%(P_perunit_length)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "pressure per unit length = 4464.000000 Pa/m\n"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.19 page number 155\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the flow rate\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "d = 0.3   #in m\n",
+      "u = 17.63   #avg velocity in m/s\n",
+      "\n",
+      "# Calculations\n",
+      "q = (3.14/4)*d**2*u;\n",
+      "\n",
+      "# Results\n",
+      "print \"volumetric flow rate = %f cubic meter per second\"%(q)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "volumetric flow rate = 1.245559 cubic meter per second\n"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.20 page number 156\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the size of pipe required\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "d = 0.15   #in m\n",
+      "\n",
+      "# Calculations\n",
+      "u = (0.0191/0.15**2);   #in m/s\n",
+      "q = (3.14/4)*d**2*u;\n",
+      "\n",
+      "# Results\n",
+      "print \"volumetric flow rate = %f cubic meter/s\"%(q)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "volumetric flow rate = 0.014994 cubic meter/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.21 page number 160\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the pressure gradient\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "Q=0.0003    #in m3/s\n",
+      "d=0.05    #in m\n",
+      "A=(3.14*d**2)/4;\n",
+      "\n",
+      "# Calculations\n",
+      "u=Q/A;\n",
+      "\n",
+      "density=1000;   #in kg/m3\n",
+      "viscosity=0.001;  #in Pa-s\n",
+      "e=0.3;\n",
+      "dp=0.00125;   #particle diameter in m\n",
+      "\n",
+      "Re=(dp*u*density)/(viscosity*(1-e));\n",
+      "fm=(150/Re)+1.75;\n",
+      "L=0.5   #in m\n",
+      "delta_Pf=fm*((density*L*u**2)/dp)*((1-e)/e**3);   #in Pa\n",
+      "\n",
+      "#applying bernoulli's equation, we get\n",
+      "delta_P=delta_Pf-(density*9.8*L);\n",
+      "pressure_gradient=delta_P/(L*1000);   #in kPa/m\n",
+      "\n",
+      "# Results\n",
+      "print \"required pressure gradient = %f kPa/m of packed height\"%(pressure_gradient)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "required pressure gradient = 1104.702008 kPa/m of packed height\n"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.22 page number 163\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find minimum fluidization velocity\n",
+      "\n",
+      "from scipy.optimize import fsolve \n",
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "d=120*10**-6    #in m\n",
+      "density=2500   #particle density in kg/m3\n",
+      "e_min=0.45;\n",
+      "density_water=1000   #in kg/m3\n",
+      "\n",
+      "# Calculations and Results\n",
+      "viscosity=0.9*10**-3;   #in Pa-s\n",
+      "umf=(d**2*(density-density_water)*9.8*e_min**3)/(150*viscosity*(1-e_min));\n",
+      "print \"minimum fludization velocity = %f m/s\"%(umf)\n",
+      "\n",
+      "Re_mf=(d*umf*density_water)/(viscosity*(1-e_min));\n",
+      "\n",
+      "\n",
+      "#given that uo/umf=10\n",
+      "def F(e):\n",
+      "    return e**3+1.657*e-1.675;\n",
+      "\n",
+      "#initial guess\n",
+      "x = 10.;\n",
+      "e = fsolve(F,x)\n",
+      "\n",
+      "print \"e = %f\"%(e)\n",
+      "length_ratio=(1-e_min)/(1-e);\n",
+      "print \"ratio of heights = %f\"%(length_ratio)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "minimum fludization velocity = 0.000260 m/s\n",
+        "e = 0.753096\n",
+        "ratio of heights = 2.227583\n"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "example 4.23 page number 167\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#to find the power requirements\n",
+      "\n",
+      "import math \n",
+      "# Variables\n",
+      "P=9807.   #in Pa\n",
+      "density=1000.   #in kg/m3\n",
+      "Q=250./(60.*density)\n",
+      "head=25.   #in m\n",
+      "\n",
+      "# Calculations\n",
+      "w= head*Q*P;     #in kW\n",
+      "power_delivered=w/0.65;\n",
+      "power_taken=power_delivered/0.9;\n",
+      "\n",
+      "# Results\n",
+      "print \"power_delivered = %f kW\"%(power_delivered/1000)\n",
+      "print \"power taken by motor = %f kW\"%(power_taken/1000)\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "power_delivered = 1.571635 kW\n",
+        "power taken by motor = 1.746261 kW\n"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file