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diff --git a/Fluid_Mechanics_and_Hydraulic_Machines/ch8.ipynb b/Fluid_Mechanics_and_Hydraulic_Machines/ch8.ipynb new file mode 100755 index 00000000..829a5e5d --- /dev/null +++ b/Fluid_Mechanics_and_Hydraulic_Machines/ch8.ipynb @@ -0,0 +1,759 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:a6125783e5c667dece42915a12b250cb19816611a67eefd7aa139b1763963ae5" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 8 : Impact of Jets" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.1 Page No : 164" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "V = 25. #m/s velocity\n", + "F = 300. # N\n", + "g = 9.81 \n", + "p = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p\n", + "A = (F*g)/(w*V*V)\n", + "V1 = 35\n", + "F1 = (w*A*V1*V1)/(g)\n", + "\n", + "# Results \n", + "print \"force in N on the plate if the velocity of the jet is increased to 35 m/sec\",F1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force in N on the plate if the velocity of the jet is increased to 35 m/sec 588.0\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.2 Page No : 164" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Variables\n", + "d = 0.05 # mm water \n", + "V = 15. #m/s velocity\n", + "g = 9.81 \n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "a = math.pi*d*d/4\n", + "F = (w*a*V*V)/g\n", + "u = 5\n", + "F1 = (w*a*((V-u)**2))/g\n", + "\n", + "# Results \n", + "print \"force in N on plate if plate is stationary\",round(F,3),\"N\"\n", + "print \"force in N on plate if plate is moving in the direction of the jet\",round(F1,2),\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force in N on plate if plate is stationary 441.786 N\n", + "force in N on plate if plate is moving in the direction of the jet 196.35 N\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.3 page no : 165" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "d = 0.03 #m diameter\n", + "Fx = 900 # N \n", + "x = 30. #degree angle \n", + "g = 9.81 \n", + "w = g*1000\n", + "a = 3.142*d*d/4\n", + "\n", + "# Calculations \n", + "V = ((Fx*g)/(w*a*math.sin(math.radians(x))*math.sin(math.radians(x))))**0.5\n", + "Q = a*V\n", + "\n", + "# Results \n", + "print \"rate of flow in m3/sec\",round((Q*1000),2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "rate of flow in m3/sec 50.45\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.4 Page No : 166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "d = 0.02 #m diameter\n", + "V = 20. #m/s, velocity \n", + "x = 15. #degree angle\n", + "g = 9.81 \n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "a = math.pi*d*d/4\n", + "W = (w*a*V*V)/(g*math.sin(math.radians(x)))\n", + "F1 = (w*a*V*V)/(2*g)\n", + "\n", + "# Results \n", + "print \"weight of the plate in N\",round(W,3),\"N\"\n", + "print \"force in N required at the lower edge of the plate : %.4f\"%F1,\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "weight of the plate in N 485.527 N\n", + "force in N required at the lower edge of the plate : 62.8319 N\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.5 Page No : 167" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "d = 0.05 #m diameter\n", + "V = 20. #m/s velocity \n", + "y = 120. #degree angle\n", + "x = 180.-y \n", + "g = 9.81\n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "a = math.pi*d*d/4\n", + "F = (w*a*V*V*(1+math.cos(math.radians(x))))/(g)\n", + "\n", + "# Results \n", + "print \"force in N exerted by the water jet %.4f\"%F,\"N\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force in N exerted by the water jet 1178.0972 N\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.6 Page No : 167" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "# Variables\n", + "d = 0.05 #m diameter\n", + "V = 20. #m velocity\n", + "u = 7. #m/s \n", + "a = math.pi*d*d/4 \n", + "g = 9.81\n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "F = (w*a*V*V)/g\n", + "F1 = (w*a*((V-u)**2))/g\n", + "work = F1*u\n", + "\n", + "# Results \n", + "print \"force in N if plate is fixed \",F\n", + "print \"force in N if plate is moving with a velocity of 7 m/sec\",round(F1,2)\n", + "print \"work done per sec by the jet\",round(work,3)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force in N if plate is fixed 785.398163397\n", + "force in N if plate is moving with a velocity of 7 m/sec 331.83\n", + "work done per sec by the jet 2322.815\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.7 Page No : 168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "W = 58.86 #N weighing\n", + "d = 0.02 #m diameter \n", + "V = 5. #m/s velocity\n", + "z = 0.15 #m axis \n", + "g = 9.81 \n", + "p1 = 1000. \n", + "w = g*p1\n", + "\n", + "# Calculations \n", + "a = math.pi*d*d/4\n", + "F = (w*a*V*V)/g\n", + "cog = 0.1\n", + "x = 30\n", + "P = (F*z)/cog\n", + "F1 = ((P*cog*(math.cos(math.radians(x))))+(W*cog*(math.sin(math.radians(x)))))\n", + "V1 = ((F1*g)/(w*a))**0.5\n", + "\n", + "# Results \n", + "print \"velocity in m/sec of the jet if the plate is deflected through 30 degree\",round(V1,2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "velocity in m/sec of the jet if the plate is deflected through 30 degree 3.55\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8 Page No : 169" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V = 25. #m velocity\n", + "u = 10. #m velocity \n", + "q = 0.001 #m**3/s\n", + "g = 9.81\n", + "p1 = 1000.\n", + "w = g*p1\n", + "x = 180. #degree \n", + "u1 = 8. #m velocity\n", + "\n", + "# Calculations \n", + "F1 = (w*q/g)*V*(1-math.cos(math.radians(x)))\n", + "F2 = (w*q*((V-u)**2)*(1-math.cos(math.radians(x))))/(g*V)\n", + "F3 = (w*q*(V-u1)*(1-math.cos(math.radians(x))))/g\n", + "\n", + "# Results \n", + "print \"force of jet in N when,the cup is stationary,the cup is moving with velocity of 10m/sec,series of cup with velocity of 8m/sec\" ,\\\n", + "F1,F2,F3\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force of jet in N when,the cup is stationary,the cup is moving with velocity of 10m/sec,series of cup with velocity of 8m/sec 50.0 18.0 34.0\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.9 Page No : 170" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "x1 = 30. #m/s velocity\n", + "V1 = 30. #degree \n", + "Q = 0.001 \n", + "g = 9.81\n", + "w = g*1000.\n", + "Vf1 = V1*math.sin(math.radians(x1))\n", + "Vw1 = V1*math.cos(math.radians(x1))\n", + "u = 15.\n", + "x2 = 120.\n", + "y1 = math.degrees(math.atan(Vf1/(Vw1-u)))\n", + "Vr1 = ((Vf1*Vf1)+((Vw1-u)**2))**0.5\n", + "z = u*math.sin(math.radians(x2))/Vr1\n", + "y2 = 60-math.degrees(math.asin(z))\n", + "V2 = Vr1*math.sin(math.radians(y2))/math.sin(math.radians(x2))\n", + "Vw2 = V2*math.cos(math.radians(x2/2))\n", + "W = (w*Q*(Vw1+Vw2)*u)/g\n", + "n = W*2/(V1*V1)\n", + "print \"angle of vane : %.3f degrees \\\n", + "\\nwork done of water entering the vane : %.3f Nm/s \\\n", + "\\nefficiency : %.2f %%\"%(y2,W,n*100)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle of vane : 15.670 degrees \n", + "work done of water entering the vane : 433.194 Nm/s \n", + "efficiency : 96.27 %\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.10 Page No : 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Q = 0.283 #m**3/s, flow of water \n", + "d = 0.05 #m diameter\n", + "x = 170. #angle \n", + "u = 48. #m/s velocity \n", + "g = 9.81 \n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "a = math.pi*d*d/4\n", + "V1 = Q/a\n", + "Vw1 = V1\n", + "Vr1 = V1-u\n", + "x1 = 0\n", + "Vr2 = Vr1\n", + "Vw2 = (Vr2*math.cos(math.radians(180-x)))-u\n", + "Fx = (w*a*(V1-u)*(Vw1+Vw2))/g\n", + "P = Fx*u/1000\n", + "n = (P*1000*g*2)/(w*Q*V1*V1)\n", + "\n", + "# Results \n", + "print \"force exerted by the jet : %.3f N \\\n", + "\\npower developed by the vane : %.4f kW \\\n", + "\\nefficiency : %.1f %%\"%(Fx,P,(n*100))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "force exerted by the jet : 36014.111 N \n", + "power developed by the vane : 1728.6773 kW \n", + "efficiency : 58.8 %\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.11 Page No : 174" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "y1 = 30. #angle\n", + "y2 = 15. #angle \n", + "a = 13.*(10**-4) #cm**2 \n", + "x1 = 15. #incline\n", + "V1 = 60. #m/s area moving \n", + "\n", + "# Calculations \n", + "Vf1 = V1*math.sin(math.radians(y2))\n", + "Vw1 = V1*math.cos(math.radians(y2))\n", + "u = Vw1-(Vf1/math.tan(math.radians(y1)))\n", + "Vw2 = u-(Vf1*math.cos(math.radians(y2))/math.sin(math.radians(y1)))\n", + "Vf2 = (u-Vw2)*math.tan(math.radians(y2))\n", + "V2 = (Vf2*Vf2+Vw2*Vw2)**0.5\n", + "x2 = math.degrees(math.atan(Vf2/Vw2))\n", + "g = 9.81\n", + "p1 = 1000\n", + "w = g*p1\n", + "Fx = (w*a*V1*(Vw1-Vw2))/g\n", + "Fy = (w*a*V1*(V1*math.sin(math.radians(y2))-V2*math.sin(math.radians(x2))))/g\n", + "Fr = (Fx*Fx+Fy*Fy)**0.5\n", + "o = math.degrees(math.atan(Fy/Fx))\n", + "\n", + "# Results \n", + "print \"velocity of the vane : %.4f m/s \\\n", + "\\ndirection of velocity at exit : %.4f m/s \\\n", + "\\nresultant force : %.4f N \\\n", + "\\nangle between forces : %.1f degrees\"%(u,V2,Fr,o)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "velocity of the vane : 31.0583 m/s \n", + "direction of velocity at exit : 8.1078 m/s \n", + "resultant force : 4476.2818 N \n", + "angle between forces : 7.5 degrees\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.12 Page No : 177" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V1 = 13. # m/s\n", + "y1 = 30. \n", + "y2 = y1\n", + "u = 4.5 # m/s\n", + "g = 9.81\n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "w = g*p1\n", + "Q = 0.001\n", + "x1 = math.degrees(math.acos(0.9394))\n", + "Vw1 = V1*math.cos(math.radians(x1))\n", + "Vr1 = (Vw1-u)/math.cos(math.radians(y1))\n", + "Vw2 = Vr1*math.cos(math.radians(y1))-u\n", + "Vf2 = Vr1*math.sin(math.radians(y1))\n", + "V2 = (Vf2*Vf2+Vw2*Vw2)**0.5\n", + "x2 = math.degrees(math.atan(Vf2/Vw2))\n", + "W = (w*Q*(Vw1+Vw2)*u)/g\n", + "\n", + "# Results \n", + "print \"direction of velocity : %.3f \\\n", + "\\nvelocity of water at exit : %.3f m/s \\\n", + "\\ndirection of work : %.3f \\\n", + "\\nmagnitude of work done per kg of water : %.3f\"%(x1,V2,x2,W)\n", + "\n", + "# note : rounding off errors." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "direction of velocity : 20.049 \n", + "velocity of water at exit : 5.490 m/s \n", + "direction of work : 54.193 \n", + "magnitude of work done per kg of water : 69.410\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.13 Page No : 179" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V1 = 40. #m/s velocity\n", + "u = 12. #m/s \n", + "x1 = 20. #angle\n", + "x2 = 90. #velocity \n", + "\n", + "# Calculations \n", + "Vw1 = V1*math.cos(math.radians(x1))\n", + "Vf1 = V1*math.sin(math.radians(x1))\n", + "y1 = math.degrees(math.atan(Vf1/(Vw1-u)))\n", + "Vr1 = Vf1/math.sin(math.radians(y1))\n", + "Vr2 = 0.9*Vr1\n", + "y2 = math.degrees(math.acos(u/Vr2))\n", + "W = 1*Vw1*u\n", + "n = W/(V1*V1*0.5*1)\n", + "\n", + "# Results \n", + "print \"vane angle at the exit : %.4f and %.4f \\\n", + "\\nwork done on the vane per kg of water : %.4f N m/s\\\n", + "\\nefficiency : %.2f %%\"%(y1,y2,W,(n*100))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "vane angle at the exit : 28.1318 and 62.6435 \n", + "work done on the vane per kg of water : 451.0525 N m/s\n", + "efficiency : 56.38 %\n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.14 Page No : 180" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "d = 0.05 #m diameter\n", + "V1 = 25. #m/s velocity \n", + "x1 = 30. #angle\n", + "x = 50. #angle\n", + "x2 = x1+x\n", + "g = 10. #m/s**2\n", + "p1 = 1000.\n", + "\n", + "# Calculations \n", + "a = 3.142*d*d/4\n", + "w = g*p1\n", + "Fx = (w*a*V1*V1*(math.cos(math.radians(x1))-math.cos(math.radians(x2))))/g\n", + "Fy = (w*a*V1*V1*(math.sin(math.radians(x1))-math.sin(math.radians(x2))))/g\n", + "F = (Fx*Fx+Fy*Fy)**0.5\n", + "z = math.degrees(math.atan(-Fy/Fx))\n", + "\n", + "# Results \n", + "print \"resultant force %.3f and %.3f \\\n", + "\\nangle made by the resultant force with the horizontal : %.4f\"%(round(Fy,3),round(Fx,3),round(z,4))\n", + "\n", + "# note : It seems book answers are wrong. Kindly check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "resultant force -595.026 and 849.785 \n", + "angle made by the resultant force with the horizontal : 35.0000\n" + ] + } + ], + "prompt_number": 44 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.15 Page No : 182" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "x1 = 0. \n", + "x2 = 60. # angle\n", + "V1 = 30. #m/s velocity\n", + "V2 = 25. #m/s velocity \n", + "m = 0.8 #Kg/s nozzle \n", + "\n", + "# Calculations \n", + "Fx = m*((V1*math.cos(math.radians(x1)))-(V2*math.cos(math.radians(x2))))\n", + "Fy = m*((V1*math.sin(math.radians(x1)))-(V2*math.sin(math.radians(x2))))\n", + "R = (Fx*Fx+Fy*Fy)**0.5\n", + "z = math.degrees(math.atan(-Fy/Fx))\n", + "\n", + "# Results \n", + "print \"magnitude and direction of resultant force :\",round(R,3),round(z,4)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "magnitude and direction of resultant force : 22.271 51.0517\n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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