{ "metadata": { "name": "", "signature": "sha256:98b9b2cc3c2bb837908ed50b11e73842e607c874a3e8f477bc1209f33ea8918d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 4 : Flow of Water Through Orifices and Mouthpieces" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.1 Page No : 98" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "M = 31*10 \t\t#lbs\n", "P = 3.6 \t\t#lbs\n", "t = 60. \t\t#sec\n", "g = 32.2 \t\t#ft/sec**2\n", "H = 9. \t\t#ft\n", "d = 1. \t\t#in\n", "w = 6.24 \t\t#gallons\n", "\t\t\n", "#CALCULATIONS\n", "v = P*g*t/M\n", "V = math.sqrt(2*g*H)\n", "Cv = v/V\n", "V1 = math.pi*(d/12)**2*V*60*w/4\n", "Cd = M/(10*V1)\n", "Cc = Cd/Cv\n", "Cr = (1/Cv**2)-1\n", "\t\t\n", "#RESULTS\n", "print 'Coefficient of resistance = %.2f '%(Cr)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Coefficient of resistance = 0.15 \n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.2 Page No : 100" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\t\t\n", "#initialisation of variables\n", "M = 1.65 \t\t#lbs\n", "Q = 31. \t\t#gallons per min\n", "d = 1. \t\t#in\n", "h = 4. \t\t#ft\n", "t = 60. \t\t#sec\n", "g = 32.2 \t\t#ft/sec**2\n", "Q1 = 6.24 \t\t#gallons per min\n", "c = 0.36\n", "P = 3.6 # lbs\n", "H = 9. \n", "\n", "#CALCULATIONS\n", "v = P*g*t/(Q*10)\n", "V = math.sqrt(2*g*H)\n", "Cv = (v/V)\n", "vf = V*math.pi*(d/12)**2*60*Q1/4\n", "Cd = Q/vf\n", "Cc = Cd/Cv\n", "Cr = (1/Cv**2)-1\n", "\n", "#RESULTS\n", "print 'velocity of jet = %.2f ft/sec'%(v)\n", "print 'theoretical velocity of jet = %.2f ft/sec'%(V)\n", "print 'Cv = %.2f '%(Cv)\n", "print 'volume flow = %.2f gallons per minute'%(vf)\n", "print 'Cd = %.2f '%(Cd)\n", "print 'Cc = %.2f '%(Cc)\n", "print 'Coefficient of resistance = %.2f '%(Cr)\n", "\n", "# Note : Answer for theoretical velocity is wrong in book. Please check." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "velocity of jet = 22.44 ft/sec\n", "theoretical velocity of jet = 24.07 ft/sec\n", "Cv = 0.93 \n", "volume flow = 49.16 gallons per minute\n", "Cd = 0.63 \n", "Cc = 0.68 \n", "Coefficient of resistance = 0.15 \n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.3 Page No : 101" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "x = 11.5 \t\t#in\n", "y = 1.2 \t\t#in\n", "H = 29. \t\t#in\n", "q = 6.24 \t\t#gallons per minute\n", "d = 1. \t\t#in\n", "g = 32.2 \t\t#ft/sec**2\n", "Q = 16. \t\t#gallons per min\n", "\t\t\n", "#CALCULATIONS\n", "Cv = math.sqrt(x**2/(4*H*y))\n", "Q1 = math.pi*(d/12)**2*math.sqrt(2*g*H/12)*q*60/4\n", "Cd = Q/Q1\n", "Cc = Cd/Cv\n", "Cr = (1/Cv**2)-1\n", "\t\t\n", "#RESULTS\n", "print 'Coefficient of resistance = %.2f '%(Cr)\n", "\n", "# rounding off error." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Coefficient of resistance = 0.05 \n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.4 Page No : 102" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "x = 3.2 \t\t#ft\n", "d = 8. \t\t#ft\n", "W = 5.12 \t\t#lb\n", "A = 1./144\n", "H = 4. \t\t#ft\n", "g = 32.2 \t\t#ft/sec**2\n", "Q = 251.5 \t\t#lbs/min\n", "w = 62.4 \t\t#lbs/ft**2\n", "\t\t\n", "#CALCULATIONS\n", "F = W*x/d\n", "v = W*x*g*60/(d*Q)\n", "V = math.sqrt(2*g*H)\n", "Cv = v/V\n", "Q1 = A*V*60*w\n", "Cd = Q/Q1\n", "Cc = Cd/Cv\n", "\t\t\n", "#RESULTS\n", "print 'Cc = %.2f '%(Cc)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Cc = 0.61 \n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.5 Page No : 106" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "d = 8. \t\t#in\n", "\t\t\n", "#CALCULATIONS\n", "Cd = 1/math.sqrt(1+((1./(8.**2/100)))-1)\n", "area = math.pi/4 * (2./12)**2\n", "Discharge = area * Cd * math.sqrt(2*32.2*4) \t\t\n", "\n", "#RESULTS\n", "print 'Cd = %.2f '%(Cd)\n", "print \"Discharge = %.1f cubic ft./sec.\"%Discharge\n", "\n", "# note : rounding off error. please check." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Cd = 0.80 \n", "Discharge = 0.3 cubic ft./sec.\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.6 Page No : 109" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "d =2. \t\t#in\n", "h = 6. \t \t#ft\n", "H = 26. \t\t#ft\n", "g = 32.2 \t\t#ft/sec**2\n", "R = 6.\n", "\t\t\n", "#CALCULATIONS\n", "v2 = math.sqrt(2*g*(H+h))\n", "Q = math.pi*(d/12)**2*v2/4\n", "v3 = math.sqrt(2*g*h)\n", "r = v2/v3\n", "d3 = math.sqrt(r*d**2)\n", "v4 = math.sqrt(v2**2/R)\n", "d4 = math.sqrt(d**2*(v2/v4))\n", "\t\t\n", "#RESULTS\n", "print 'diameter = %.2f in'%(d4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "diameter = 3.13 in\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.7 Page No : 111" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\t\t\n", "#initialisation of variables\n", "r = 9./16\n", "r1 = 7./16\n", "h = 26. \t\t#ft\n", "\t\t\n", "#CALCULATIONS\n", "r2 = 1/((r**2)+(0.25*r1**2))\n", "H1 = h/(r2-1)\n", "\t\t\n", "#RESULTS\n", "print 'maximu head of the tank = %.3f ft of water'%(H1)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "maximu head of the tank = 14.897 ft of water\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.8 pageno : 114" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# variables\n", "A = 30.*15 # sq ft\n", "a = 2. # sq ft\n", "H1 = 5. # ft\n", "H2 = 0. \n", "\n", "# calculation\n", "T = a*A*H1**(1./2)/(.62*a*8.02)\n", "\n", "# result\n", "print \"Time of emptying pool : T = %.1f seconds\"%T\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time of emptying pool : T = 202.4 seconds\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.9 Page No : 115" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\t\t\n", "#initialisation of variables\n", "H1 = 9. \t\t#ft\n", "A = 2. \t\t#ft**2\n", "H2 = 4. \t\t#ft\n", "d = 2.25 \t\t#in\n", "t = 60. \t\t#sec\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "a = (d/12)**2\n", "Cd = (2*A*(H1-H2)**0.5)/(t*a*math.sqrt(2*g))\n", "\t\t\n", "#RESULTS\n", "print 'coefficient of dicharge = %.3f '%(Cd)\n", "\n", "\n", "#ANSWER GIVEN IN THE TEXTBBOK IS WRONG..VERIFIED WITH CALCULATOR\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "coefficient of dicharge = 0.528 \n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.10 Page No : 115" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\t\t\n", "#initialisation of variables\n", "d = 1. \t\t#ft\n", "h1 = 10. \t\t#ft\n", "h2 = 2. \t\t#ft\n", "Cd = 0.6\n", "g = 32.2 \t\t#ft/sec**2\n", "t = 12.6\n", "\t\t\n", "#CALCULATIONS\n", "A = math.pi*d**2/4\n", "a = 1./144\n", "T1 = (A/(a*Cd*math.sqrt(2*g)))*(1./3)*(h1**1.5-(h1-h2)**1.5-h2**1.5)+t\n", "T2 = 2*A*(h2**0.5)/(Cd*a*math.sqrt(2*g))\n", "T = T1+T2\n", "\t\t\n", "#RESULTS\n", "print 'Total time = %.2f sec'%(T)\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total time = 127.32 sec\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.11 Page No : 117" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from scipy.integrate import quad\n", "\n", "#initialisation of variables\n", "l = 600. \t\t#ft\n", "w = 400. \t\t#ft\n", "s = 1.\n", "h = 20. \t\t#ft\n", "d = 3. \t \t#ft\n", "dh = 10. \t\t#ft\n", "Cd = 0.7\n", "g = 32.2 \t\t#ft/sec**2\n", "k = 240000.\n", "k1 = 2000.\n", "k2 = 4.\n", "\t\t\n", "#CALCULATIONS\n", "def f(x):\n", " return (k/math.sqrt(x) + k1*math.sqrt(x) + k2*x**(3./2))\n", "\n", "T1 = 1./(Cd * math.pi/4 * 9 * 8.02) * quad(f,10,20)[0]\n", "\t\t\n", "#RESULTS\n", "print 'Time taken for 10 feet fall = %.f sec'%(T1)\n", "\n", "# note : quad() gives accurate answer. so answer is slightly different." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time taken for 10 feet fall = 17846 sec\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.12 Page No : 118" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\t\t\n", "#initialisation of variables\n", "Cd = 0.6\n", "H1 = 8. \t\t#ft\n", "H2 = 3. \t\t#ft\n", "l = 90. \t\t#ft\n", "b = 30. \t\t#ft\n", "g = 32.2 \t\t#ft/sec**2\n", "A = 2. \t\t#ft**2\n", "\t\t\n", "#CALCULATIONS\n", "T1 = 2*l*b*(H1**0.5-(H1-H2)**0.5)/(Cd*math.sqrt(2*g)*A)\n", "T2 = (l*b*2/10)*(2./3)*(H1-H2)**1.5/(Cd*math.sqrt(2*g)*A)\n", "T = T1+T2\n", "\t\t\n", "#RESULTS\n", "print 'Time it take to emptify the swimming bath = %.1f sec'%(T)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time it take to emptify the swimming bath = 750.1 sec\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.13 Page No : 120" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "Cd = 0.8\n", "g = 32.2 \t\t#f/sec**2\n", "d = 3. \t\t#in\n", "x = 6. \t \t#ft\n", "l = 25. \t\t#ft\n", "d1 = 8. \t\t#ft\n", "\t\t\n", "#CALCULATIONS\n", "A = math.pi*(d/12)**2/4\n", "T = (2*l/(Cd*A*math.sqrt(2*g)))*(-2./3)*((d1-x)**1.5-d1**1.5)\n", "\t\t\n", "#RESULTS\n", "print 'Time it take to emptify the boiler = %.f sec'%(T+6)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time it take to emptify the boiler = 2100 sec\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.14 Page No : 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "l = 30. \t\t#ft\n", "w = 10. \t\t#ft\n", "d = 4. \t\t#in\n", "h1 = 10. \t\t#ft\n", "h2 = 2. \t\t#ft\n", "Cd = 0.97\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "A1 = w*3*l/4\n", "A2 = l*w/4\n", "A = math.pi*(d/12)**2/4\n", "T = 2*A1*(math.sqrt(h1)-math.sqrt(h2))*10/(Cd*A*math.sqrt(2*g)*(l+w))\n", "\t\t\n", "#RESULTS\n", "print 'Time it take to reduce the height = %.f sec'%(round(T,-1))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time it take to reduce the height = 290 sec\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.15 Page No : 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "A1 = 1000. \t\t#ft**2\n", "A2 = 1000. \t\t#ft**2\n", "a = 2. \t\t#ft**2\n", "H1 = 9. \t\t#ft\n", "H2 = 4. \t\t#ft\n", "Cd =0.8\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "T = a*1000*(math.sqrt(H1)-math.sqrt(H2))/(Cd*a**2*math.sqrt(2*g))\n", "\t\t\n", "#RESULTS\n", "print 'Time it take to reduce the height = %.1f sec'%(T)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time it take to reduce the height = 77.9 sec\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.16 Page No : 128" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "l = 70. \t\t#ft\n", "b = 10. \t\t#ft\n", "Hl = 10. \t\t#ft\n", "H1 = 6. \t\t#ft\n", "h1 = 4. \t\t#ft\n", "h2 = 2. \t\t#ft\n", "w = 2. \t\t#ft\n", "h3 = 3. \t\t#ft\n", "Cd = 0.6\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "t = (l*b)*(Hl+H1)/(Cd*h2*w*h1*math.sqrt(2*g*H1))\n", "t1 = 2*l*b*math.sqrt(Hl)/(Cd*h2*w*h3*math.sqrt(2*g))\n", "\t\t\n", "#RESULTS\n", "# 2nd ans is wrong in book\n", "print 'Time of filling = %.2f sec'%(t)\n", "print ' Time of emptying = %.2f sec'%(t1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time of filling = 59.35 sec\n", " Time of emptying = 76.62 sec\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.17 Page No : 129" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from sympy import Symbol,solve\n", "\t\t\n", "#initialisation of variables\n", "HL = 12.5 \t\t#ft\n", "H1 = 10.5 \t\t#ft\n", "Cd = 0.62\n", "h = 4. \t\t#ft\n", "l = 3. \t \t#ft\n", "n = 2.\n", "t = 5. \t\t #min\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "a1 = n*l*l\n", "A = Symbol('A')\n", "ans = solve( (2*A/(Cd*a1*26)) + 2*A*math.sqrt(H1)/(Cd*a1*8.02) - 300 )\n", "A = ans[0]\n", "\n", "#RESULTS\n", "print 'Area = %.f sq ft'%(A)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Area = 3783 sq ft\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.18 Page No : 130" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "Cd = 0.62\n", "g = 32.2 \t\t#ft/sec**2\n", "l = 200. \t\t#ft\n", "w = 25. \t\t#ft\n", "a1 = 5. \t\t#ft**2\n", "h = 20. \t\t#ft\n", "\t\t\n", "#CALCULATIONS\n", "t = 2*l*w*math.sqrt(h-(h/a1))/(Cd*math.sqrt(2*g)*a1)\n", "\t\t\n", "#RESULTS\n", "print 'tme rquired to fill the lock = %.f sec'%(t)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "tme rquired to fill the lock = 1608 sec\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.19 Page No : 130" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "L = 150. \t\t#ft\n", "w = 20. \t\t#ft\n", "t = 5. \t\t#min\n", "h = 5. \t \t#ft\n", "Cd = 0.6 \n", "Hl = 9. \t\t#ft\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "T = 2*L*w*math.sqrt(Hl)/(Cd*t*60*math.sqrt(2*g))\n", "\t\t\n", "#RESULTS\n", "print 'Area of sumberged slice = %.1f sq ft'%(T)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Area of sumberged slice = 12.5 sq ft\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.20 Page No : 132" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "L = 3. \t\t#ft\n", "H1 = 1.5 \t\t#ft\n", "H2 = 0.75 \t\t#ft\n", "Cd = 0.62\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "Q = 2*Cd*60*L*math.sqrt(2*g)*(H1**1.5-H2**1.5)/3\n", "\t\t\n", "#RESULTS\n", "print 'Discharge per minute = %.1f cubic ft per minute'%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Discharge per minute = 709.1 cubic ft per minute\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.21 Page No : 134" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\n", "#initialisation of variables\n", "Cd = 0.62\n", "H1 = 6. \t\t#ft\n", "H2 = 3. \t\t#ft\n", "H = 4. \t\t#ft\n", "g = 32.2 \t\t#ft/sec**2\n", "\t\t\n", "#CALCULATIONS\n", "Q1 = 2*Cd*H*math.sqrt(2*g)*(H**1.5-H2**1.5)/3\n", "Q2 = Cd*H*(H1-H)*math.sqrt(2*g*H)\n", "Q = Q1+Q2\n", "\t\t\n", "#RESULTS\n", "print 'Total discharge = %.f cuses'%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total discharge = 117 cuses\n" ] } ], "prompt_number": 21 } ], "metadata": {} } ] }