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+{
+ "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": {}
+ }
+ ]
+} \ No newline at end of file