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diff --git a/Fluid_Mechanics_by_John_F_Douglas/Chapter_6.ipynb b/Fluid_Mechanics_by_John_F_Douglas/Chapter_6.ipynb new file mode 100755 index 00000000..5cde4008 --- /dev/null +++ b/Fluid_Mechanics_by_John_F_Douglas/Chapter_6.ipynb @@ -0,0 +1,504 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:df3153eb902c7efba51ed445ceefd3e3c02fa6ed938e4ef53fe06333d531bf11" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6: The Energy Equation and its Applications" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.1, Page 170" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "Pc = 0; # Atmospheric Pressure\n", + "Z3 = 30+2; #height of nozzle\n", + "Ep = 50 ; #Energy per unit weight supplied by pump\n", + "d1 = 0.150; #Diameter of sump\n", + "d2 = 0.100; #Diameter of delivery pipe\n", + "d3 = 0.075 ; #Diameter of nozzle\n", + "g = 9.81; # Acceleration due to gravity\n", + "Z2 = 2; #Height of pump\n", + "rho = 1000; # Density of water\n", + "\n", + " #Calculations\n", + "U3 = (2*g*(Ep-Z3)/(1+5*(d3/d1)**4 + 12*(d3/d2)**4))**0.5;\n", + "U1 = U3/4;\n", + "Pb = rho*g*Z2 + 3*rho*U1**2;\n", + "print \"Velocity of Jet through nozzle (m/s) :\",round(U3,3)\n", + "print \"Pressure in the suction pipe at the inlet to the pump at B (kN/m^2) :\",round(Pb/1000,3) " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of Jet through nozzle (m/s) : 8.314\n", + "Pressure in the suction pipe at the inlet to the pump at B (kN/m^2) : 32.58\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.2, Page 183" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + " #Initializing the variables \n", + "x = 45; # Inclination of pipe\n", + "l = 2; #Length of pipe under consideration\n", + "Ep = 50 ; #Energy per unit weight supplied by pump\n", + "d1 = 0.2; #Diameter of sump\n", + "d2 = 0.1; #Diameter of delivery pipe\n", + "g = 9.81; # Acceleration due to gravity\n", + "rho = 1000; # Density of water\n", + "V1 = 2;\n", + "RD_oil = 0.9; # relative density of oil\n", + "RD_Merc = 13.6; # Relative density of Mercury\n", + "\n", + " #Calculations\n", + "V2 = V1*(d1/d2)**2;\n", + "dZ = round(l*math.sin(math.radians(x)),3); # it is used in book as 1.414,by rounding so here also\n", + "rho_Oil = RD_oil*rho;\n", + "rho_Man = RD_Merc*rho;\n", + "dP = 0.5*rho_Oil*(V2**2-V1**2) + rho_Oil*g*dZ;\n", + "h = rho_Oil *( dP/(rho_Oil*g)- dZ)/(rho_Man - rho_Oil);\n", + "\n", + "print \"Pressure Difference(N/m2) : \",round(dP,0)\n", + "print \"Difference in the level of mercury (m):\",round(h,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure Difference(N/m2) : 39484.0\n", + "Difference in the level of mercury (m): 0.217\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.3, Page 187" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "d1 = 0.25; #Pipeline diameter\n", + "d2 = 0.10; #Throat diameter\n", + "h =0.63; #Difference in height\n", + "rho = 1000; #Density of water\n", + "g = 9.81 #Acceleration due to gravity\n", + "\n", + " #Calculations\n", + "rho_Hg = 13.6*rho;\n", + "rho_Oil = 0.9*rho;\n", + "A1 = (math.pi*d1**2)/4; # Area at entry\n", + "m = (d1/d2)**2; #Area ratio\n", + "Q = (A1/(m**2-1)**0.5)*(2*g*h*(rho_Hg/rho_Oil -1))**0.5;\n", + "\n", + "print \"Thepretical Volume flow rate (m3/s ):\",round(Q,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thepretical Volume flow rate (m3/s ): 0.105\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4, Page 190" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "\n", + "x = 1.5;\n", + "y =0.5;\n", + "H = 1.2;\n", + "A = 650*10**-6;\n", + "Q =0.117;\n", + "g = 9.81;\n", + "\n", + " #Calculations\n", + "Cv =(x**2/(4*y*H))**0.5;\n", + "Cd = Q / (60*A*(2*g*H)**0.5);\n", + "Cc = Cd/Cv;\n", + "\n", + "\n", + "print \"Coefficient of velocity :\",round(Cv,3)\n", + "print \"Coefficient of Discharge :\",round(Cd,3)\n", + "print \"Coefficient of contraction :\",round(Cc,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coefficient of velocity : 0.968\n", + "Coefficient of Discharge : 0.618\n", + "Coefficient of contraction : 0.639\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5, Page 192" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "B = 0.7;\n", + "H1 = 0.4;\n", + "H2 = 1.9;\n", + "g =9.81;\n", + "z = 1.5 ; # height of opening\n", + "\n", + " #Calculations\n", + "Q_Th = 2/3 *B*(2*g)**0.5*(H2**1.5 - H1**1.5);\n", + "A = z*B;\n", + "h = 0.5*(H1+H2);\n", + "Q = A*(2*g*h)**0.5;\n", + "\n", + "print \"Percentage error in discharge (%):\",round((Q-Q_Th)*100/Q_Th,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage error in discharge (%): 1.98\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.6, Page 195" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "Cd = 0.6; #Coefficient of discharge\n", + "Q = 0.28;\n", + "x = 90; #Theta\n", + "g = 9.81;\n", + "dH = 0.0015;\n", + "\n", + " #Calculations\n", + "H = (Q*(15/8)/(Cd*(2*g)**0.5*math.tan(math.radians(x/2))))**(2/5)\n", + "Frac_Q = 5/2 *( dH/H);\n", + "\n", + "print \"Percentage error in discharge(%)\",round(Frac_Q*100,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage error in discharge(%) 0.72\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.7, Page 196" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "B = 0.9;\n", + "H = 0.25;\n", + "alpha = 1.1;\n", + "g = 9.81; \n", + "\n", + " #Calculations\n", + "Q = 1.84 * B * H**(3/2);\n", + "print \"Q(m3/s) :\",Q\n", + "\n", + "i = 1;\n", + "while(i <= 3):\n", + " v = Q /(1.2* (H+0.2));\n", + " print \"V(m/s) :\",round(v,4)\n", + " k = ((1 + alpha*v**2/(2*g*H))**1.5 -(alpha*v**2/(2*g*H))**1.5 );\n", + " Q = k* 1.84 * B * H**(3/2);\n", + " print \"Q(m3/s) :\",round(Q,4)\n", + " i = i+1;\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Q(m3/s) : 0.207\n", + "V(m/s) : 0.3833\n", + "Q(m3/s) : 0.2161\n", + "V(m/s) : 0.4001\n", + "Q(m3/s) : 0.2168\n", + "V(m/s) : 0.4016\n", + "Q(m3/s) : 0.2169\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8, Page 197" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "rho = 1000;\n", + "v = 66 ;\n", + "Q = 0.13;\n", + "g = 9.81; \n", + "z =240;\n", + "\n", + " #Calculations\n", + "P_Jet = 0.5*rho*v**2*Q;\n", + "P_Supp = rho*g*Q*z;\n", + "P_Lost = P_Supp -P_Jet;\n", + "h = P_Lost/(rho*g*Q);\n", + "eff = P_Jet/P_Supp;\n", + "\n", + "print \"Part(a) - power of the jet(kW): \",round(P_Jet/1000,2)\n", + "print \"Part(b) - power supplied from the reservoir (kW):\",round(P_Supp/1000,2) \n", + "print \"Part(C) - head used to overcome losses (m): \",round(h,2)\n", + "print \"Part(d) - Efficiency(%) : \",round(eff*100,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Part(a) - power of the jet(kW): 283.14\n", + "Part(b) - power supplied from the reservoir (kW): 306.07\n", + "Part(C) - head used to overcome losses (m): 17.98\n", + "Part(d) - Efficiency(%) : 92.5\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.9, Page 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "from scipy import integrate\n", + "\n", + " #Initializing the variables \n", + "r1 = 0.2;\n", + "Z1 = 0.500;\n", + "Z2 = 0.340;\n", + "g = 9.81;\n", + "rho = 0.9*1000 ;\n", + "\n", + " #Calculations\n", + "r0 = r1*((2-2*Z2/Z1)**0.5);\n", + "omega = round((2*g*Z1/r0**2)**0.5,1)\n", + "\n", + "def G(r):\n", + " out =r**3 - r*r0**2;\n", + " return out\n", + " \n", + "results = integrate.quad(G, r0, r1)\n", + "\n", + "F = rho*omega**2*math.pi*results[0];\n", + "\n", + "print r0,r1\n", + "print \"Part(a) Speed of rotation (rad/s ):\",round(omega,1)\n", + "print \"Part(b) Upward force on the cover (N): \",round(F,1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.16 0.2\n", + "Part(a) Speed of rotation (rad/s ): 19.6\n", + "Part(b) Upward force on the cover (N): 56.3\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.10, Page 206" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + " #Initializing the variables \n", + "Ra = 0.2;\n", + "Rb = 0.1;\n", + "H = 0.18;\n", + "Za = 0.125;\n", + "\n", + " #Calculations\n", + "Y = Ra**2*(H-Za);\n", + "Zb = H - Y/Rb**2;\n", + "\n", + "print \"Height above datum of a point B on the free surface at a radius of 100 mm (mm):\",Zb*1000" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Height above datum of a point B on the free surface at a radius of 100 mm (mm): -40.0\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
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