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diff --git a/Principles_Of_Fluid_Mechanics/ch7.ipynb b/Principles_Of_Fluid_Mechanics/ch7.ipynb new file mode 100644 index 00000000..bbf860be --- /dev/null +++ b/Principles_Of_Fluid_Mechanics/ch7.ipynb @@ -0,0 +1,1067 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:de3cacdaf57dab2533c3d6a29cdb98f8a7442d8b301aac65e35672e8b8cf9017" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7 : Incompressible Flow Through Conduits" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1 Page No : 240" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t#kg/m**3\n", + "h1 = 4. \t\t\t#m\n", + "muw = 0.001 \t\t#Ns/m**2\n", + "l = 1.5 \t\t\t#m\n", + "B = 0.15/1000 \t\t#m\n", + "lenth = 11.2 \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "P1 = g*rho*h1\n", + "V = P1*B**2 /(12*muw*l)\n", + "A = B*lenth\n", + "Q = A*V\n", + "Q = 7112.4\n", + "tau = B/2 *(P1)/l\n", + "\t\t\t\n", + "#results\n", + "print \"Average velocity through the crack = %.3f m/s\"%(V)\n", + "print \" rate of leakage = %.1f l/hr\"%(Q)\n", + "print \" Shear stress = %.3f N/m**2\"%(tau)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Average velocity through the crack = 0.049 m/s\n", + " rate of leakage = 7112.4 l/hr\n", + " Shear stress = 1.962 N/m**2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2 Page No : 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 1200. \t\t\t#kg/m**3\n", + "mu = 0.005 \t\t\t#Ns/m**2\n", + "d = 0.006 \t\t\t#m\n", + "Re = 2000.\n", + "V = 0.15 \t\t\t#m/s\n", + "\t\t\t\n", + "#calculations\n", + "Vc = Re*mu/(d*rho)\n", + "Vr = V/Vc\n", + "T0 = 8*mu*V/d\n", + "\t\n", + "#results\n", + "print \"Shear stress = %d N/m**2\"%(T0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Shear stress = 1 N/m**2\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3 Page No : 243" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t#kg/m**3\n", + "Q = 0.45/(60*1000) \t#m**3/s\n", + "d = 0.003 \t\t\t#m\n", + "depth = 0.95 \t\t#m\n", + "alpha = 2.\n", + "lenth = 1.25 \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "A = math.pi/4 *d**2\n", + "V = Q/A\n", + "nu = (depth - alpha*V**2 /(2*g))*g*d**2 /(32*V*lenth)\n", + "Re = V*d/nu\n", + "\t\t\t\n", + "#results\n", + "if Re<2000:\n", + " print \"Flow is laminar\"\n", + "else:\n", + " print \"Flow is not laminar\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flow is laminar\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4 Page No : 262" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 787. \t\t\t#specific gravity - kg/m**3\n", + "Q = 90.*10**-3 \t\t#m**3/hr\n", + "d = 0.015 \t\t\t#m\n", + "k = 0.0045*10**-2 \t#m\n", + "nu = 1.6e-6 #kinematic viscosity - m^2/s\n", + "l = 5. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "V = Q/(60*math.pi/4 *d**2)\n", + "Rn = V*d/nu\n", + "e = k/d\n", + "print (\"From moody diagram, f = 0.028\")\n", + "f = 0.028\n", + "hl = f*l/d *V**2 /(2*g)\n", + "Power = rho*g*Q/60 *hl\n", + "\t\t\t#result\n", + "print \"Head loss = %.2f m\"%(hl)\n", + "print \" power required = %.3f kW\"%(Power/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "From moody diagram, f = 0.028\n", + "Head loss = 34.27 m\n", + " power required = 0.397 kW\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5 Page No : 263" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 870. \t\t\t#density - kg/m**3\n", + "Q = 2.*10**-3 \t\t#m**3/s\n", + "d = 0.03 \t\t\t#diameter - m\n", + "mu = 5.*10**-4 #dynamics viscosity(N-s/m^2)\n", + "l = 50. \t\t\t#length - m\n", + "\t\t\t\n", + "#calculations\n", + "V = Q/(math.pi/4 *d**2)\n", + "RN = rho*V*d/mu\n", + "f = 0.017\n", + "hl = f*l/d *V**2/(2*g)\n", + "Ploss = rho*g*hl\n", + "\t\t\t\n", + "#results\n", + "print \"Loss of pressure = %.1f kN/m**2\"%(Ploss/1000)\n", + "#The answers are a bit different due to rounding off error in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss of pressure = 98.7 kN/m**2\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6 Page No : 263" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 813. \t\t\t#density - kg/m**3\n", + "Q = 0.007 \t\t\t#m**3/hr\n", + "d = 0.01\t\t\t#m\n", + "mu = 0.002 \t\t\t#Ns/m**2\n", + "l = 30. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "V = Q/(60*math.pi/4*d**2)\n", + "RN = V*d*rho/mu\n", + "f = 0.316/RN**(0.25)\n", + "h = (1+f*l/d)*V**2 /(2*g)\n", + "\n", + "#result\n", + "print \"Height required = %.2f m\"%(h)\n", + "\n", + "# rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Height required = 12.21 m\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7 Page No : 264" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t \t#m/s**2\n", + "rho = 10**3 \t\t\t#kg/m**3\n", + "hl = 0.02\n", + "d = 1.2 \t\t\t#diameter - m\n", + "l = 1. \t \t\t#m\n", + "k = 0.5 *10**-2 \t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "v2f = hl*(2*g*d)/l\n", + "e = k/d\n", + "f = 0.028\n", + "V = math.sqrt(v2f/f)\n", + "Q = math.pi/4 *d**2 *V\n", + "\t\t\t\n", + "#results\n", + "print \"Rate of flow = %.2f m**3/s\"%(Q)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rate of flow = 4.64 m**3/s\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.8 Page No : 265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t \t#m/s**2\n", + "rho = 10.**3 \t\t\t#kg/m**3\n", + "e = 0.03*10**-2 \t\t#surface roughness - m\n", + "l = 3000. \t \t\t#distance - m\n", + "Q = 300.*10**-3 \t\t#m**3/s\n", + "nu = 10.**-5 \t\t\t#kinematic viscosity - m**2/s\n", + "hl = 24. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "d5f = l*Q/(math.pi/4) * Q/(math.pi/4) /(hl*2*g)\n", + "f = 0.022\n", + "d = (d5f*f)**(1./5)\n", + "\t\t\t\n", + "#results\n", + "print \"Size of the required pipe = %d cm\"%(d*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Size of the required pipe = 45 cm\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.9 Page No : 266" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t#kg/m**3\n", + "d = 0.3 \t\t\t#m\n", + "per = 25./100\n", + "Q = 0.1 \t\t\t#m**3/s\n", + "k0 = 0.025*10**-2 \t#m\n", + "nu = 0.000001\n", + "year = 10.\n", + "\t\t\t\n", + "#calculations\n", + "V = Q/(math.pi/4 *d**2)\n", + "RN = V*d/nu\n", + "e1 = k0/d\n", + "f1 = 0.019 \n", + "f2 = (1+per)*f1\n", + "e2 = 0.002\n", + "k2 = e2*d\n", + "rate = (k2-k0)*100/year\n", + "\t\t\t\n", + "#results\n", + "print \"Rate of increase = %.4f cm/year\"%(rate)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rate of increase = 0.0035 cm/year\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.10 Page No : 267" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t#kg/m**3\n", + "l = 1. \t\t\t #m\n", + "b = 0.3 \t\t\t#m\n", + "Q = 4.2 \t\t\t#m**3/s\n", + "\t\t\t\n", + "#calculations\n", + "A = l*b\n", + "R = A/(2*(l+b))\n", + "d5 = 1.62/24.15\n", + "d = d5**(1./5)\n", + "Pr = 2*(l+b)/(math.pi*d)\n", + "\t\t\t\n", + "#results\n", + "print \"The rectangular cross section will cost %.2f times that of a circular cross section\"%(Pr)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rectangular cross section will cost 1.42 times that of a circular cross section\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.11 Page No : 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t\t#kg/m**3\n", + "d1 = 2.5*10**-2 \t\t\t#m\n", + "d2 = 7.2*10**-2 \t\t\t#m\n", + "Q = 100.*10**-3 \t\t\t#m**3/hr\n", + "\t\t\t\n", + "#calculations\n", + "V1 = Q/(60*math.pi/4*d1**2)\n", + "V2 = (d1/d2)**2 *V1\n", + "dp = -(V2**2 -V1**2 + (V1-V2)**2)/(2*g)\n", + "Pdiff = dp*g*rho\n", + "\t\t\t\n", + "#results\n", + "print \"pressure difference = %.2f kN/m**2\"%(Pdiff/1000)\n", + "\n", + "# note : The answers are a bit different due to rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "pressure difference = 1.22 kN/m**2\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.12 Page No : 273" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t\t#kg/m**3\n", + "d2 = 30./100 \t\t\t#cm\n", + "d1 = 60./100 \t\t\t#cm\n", + "Pu = 105. \t\t\t#kN/m**2\n", + "Pd = 75. \t\t\t#kN/m**2\n", + "Cc = 0.65\n", + "\t\t\t\n", + "#calculations\n", + "V22 = (2*g/(1 - (d2/d1)**4 + (1/Cc -1)**2)) *(Pu-Pd)*10**3 /(rho*g)\n", + "V2 = math.sqrt(V22)\n", + "Q = math.pi/4 *V2 *d2**2\n", + "hl = (1/Cc -1)**2 *V2**2 /(2*g)\n", + "\t\t\t\n", + "#results\n", + "print \"Flow rate = %.3f m**3/s\"%(Q)\n", + "print \" Head loss = %.3f m\"%(hl)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flow rate = 0.494 m**3/s\n", + " Head loss = 0.722 m\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.13 Page No : 277" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \t\t\t#m/s**2\n", + "rho = 10.**3 \t\t#kg/m**3\n", + "d = 9. \t\t\t#m\n", + "dia = 0.3 \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "V302 = 2*g*d/(0.5 + 20 + 2.53+101+0.66+41.47+2.07)\n", + "V30 = math.sqrt(V302)\n", + "Q = math.pi/4 *dia**2 *V30\n", + "\t\t\t\n", + "#results\n", + "print \"Flow rate = %.3f m**3/s\"%(Q)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flow rate = 0.072 m**3/s\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.14 Page No : 278" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "h = 6. \t\t\t #m\n", + "rho = 930. \t\t\t#kg/m**3\n", + "Q = 3./60 \t\t\t#m**3/s\n", + "d = 0.15 \t\t\t#m\n", + "L = 20. \t\t\t#m\n", + "mu = 0.006 #viscosity\n", + "g = 9.81 \t\t\t#m/s**2\n", + "\t\t\t\n", + "#calculations\n", + "V = Q/(math.pi/4 *d**2)\n", + "RN = V*d*rho/mu\n", + "f = 0.316/RN**0.25\n", + "hl = f*L/d *V**2 /(2*g)\n", + "Hp = h+hl\n", + "gam = rho*g\n", + "W = gam*Q\n", + "Power = W*Hp\n", + "\t\t\t\n", + "#results\n", + "print \"Power required = %.3f kW\"%(Power/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power required = 3.227 kW\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.15 Page No : 279" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad\n", + "\t\t\t\n", + "#Initialization of variables\n", + "d = 0.02 \t\t\t#m\n", + "d2 = 1.2 \t\t\t#diameter - m\n", + "f = 0.01\n", + "L = 250.\n", + "ken = 0.5\n", + "g = 9.81\n", + "h1 = 8. \t\t\t#m\n", + "h2 = 4. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "V2 = 2*g/(1+ken+ f*L/d)\n", + "V = math.sqrt(V2)\n", + "Q = math.pi/4 *d**2 *V\n", + "def time(h):\n", + " return -math.pi/4 *d2**2 /Q /math.sqrt(h)\n", + "\n", + "ti = quad(time,h1,h2)[0]\n", + "hours = ti/3600\n", + "mins = ti%3600/60\n", + "secs = ti%3600%60\n", + "\n", + "#results\n", + "print \"Time required = %d hours %d mins %d seconds\"%(hours,mins,secs)\n", + "\n", + "# rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time required = 4 hours 12 mins 25 seconds\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.16 Page No : 280" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "#Initialization of variables\n", + "d1 = 0.1 \t\t\t#m\n", + "d2 = 0.05 \t\t\t#m\n", + "l1 = 20. \t\t\t#m\n", + "l2 = 20. \t\t\t#m\n", + "f = 0.02\n", + "\t\t\t\n", + "#calculations\n", + "Kl = (f*l2/d2 *(d1/d2)**4 - f*l1/d1)\n", + "\t\t\t\n", + "#results\n", + "print \"Loss coefficient = %d \"%(Kl)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Loss coefficient = 124 \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.17 Page No : 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81 \n", + "ratio = 1.265\n", + "\t\t\t\n", + "#calculations\n", + "percent = (ratio-1)*100\n", + "\t\t\t\n", + "#results\n", + "print \"Increase in discharge = %.1f %%\"%(percent)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Increase in discharge = 26.5 %\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.18 Page No : 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "Q = 0.6 \t\t\t#m**3/s\n", + "l1 = 1200. \t\t\t#m\n", + "l2 = 800. \t\t\t#m\n", + "d1 = 0.3 \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "V1 = 1.02 \t\t\t#m/s\n", + "d5 = d1*l2*4**2 *Q**2 /(l1*math.pi**2 *V1**2)\n", + "d = d5**(1./5)\n", + "\t\t\t\n", + "#results\n", + "print \"diameter of the single pipe = %.2f m\"%(d)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "diameter of the single pipe = 0.65 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.19 Page No : 284" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "g = 9.81\n", + "Q = 0.18 \t\t\t#m**3/s\n", + "d3 = 0.3\t\t\t#m\n", + "f = 0.032 #friction factor\n", + "L3 = 360. \t\t\t#m\n", + "z = 25.5 \t\t\t#m\n", + "z2 = 30. \t\t\t#m\n", + "L2 = 450. \t\t\t#m\n", + "d2 = 0.45\t\t\t#m\n", + "L1 = 950. \t\t\t#m\n", + "d1 = 0.45 \t\t\t#m\n", + "zn = 18. \t\t\t#m\n", + "rho = 1000.\n", + "\t\t\t\n", + "#calculations\n", + "V3 = Q/(math.pi/4 *d3**2)\n", + "hl3 = f*L3/d3 *(V3**2 /(2*g))\n", + "Z2 = z+hl3\n", + "hl2 = Z2-z2\n", + "V2 = math.sqrt(2*g*d2*hl2/(f*L2))\n", + "Q2 = math.pi/4 *d2**2 *V2\n", + "V1 = V2+ (d3/d2)**2 *V3\n", + "hl1 = f*L1/d1*V1**2 /(2*g)\n", + "Hp = hl1+ Z2-zn\n", + "gam = rho*g\n", + "P = gam*Hp\n", + "\t\t\t\n", + "#results\n", + "print \"Discharge into the reservoir = %.3f m**3/s\"%(Q2)\n", + "print \" Pressure maintained by the pump = %.2f kN/m**2\"%(P/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Discharge into the reservoir = 0.356 m**3/s\n", + " Pressure maintained by the pump = 582.34 kN/m**2\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.20 Page No : 285" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import *\n", + "\t\t\t\n", + "#Initialization of variables\n", + "z1 = 10. \t\t\t#m\n", + "z2 = 5. \t\t\t#m\n", + "z3 = 7.5 \t\t\t#m\n", + "f = 0.04 \n", + "l1 = 100. \t\t\t#m\n", + "l2 = 50. \t\t\t#m\n", + "l3 = 70. \t\t\t#m\n", + "d1 = 0.1 \t\t\t#m\n", + "d2 = 0.075 \t\t\t#m\n", + "d3 = 0.06 \t\t\t#m\n", + "g = 9.81 \t\t\t#m/s**2\n", + "h = array([1, 2, 1.9, 1.96])\n", + "\n", + "#calculations\n", + "Q1 = sqrt(d1**5 *(math.pi/4)**2 *2*g/(f*l1)) *sqrt(z1-h)\n", + "Q2 = sqrt(d2**5 *(math.pi/4)**2 *2*g/(f*l2)) *sqrt(h+z2)\n", + "Q3 = sqrt(d3**5 *(math.pi/4)**2 *2*g/(f*l3)) *sqrt(h+z3)\n", + "for i in range(4):\n", + " Q = Q2[i]+Q3[i]\n", + " if (Q1[i] == Q):\n", + " break;\n", + " print \"height h = %.2f m\"%(h[i])\n", + " print \"Discharge in BC Q2 = %.2f lps\"%((Q2[i])*1000)\n", + " print \"Discharge in BD Q3 = %.2f lps\"%((Q3[i])*1000)\n", + " \n", + "# note : rounding off error. " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "height h = 1.00 m\n", + "Discharge in BC Q2 = 9.28 lps\n", + "Discharge in BD Q3 = 5.35 lps\n", + "height h = 2.00 m\n", + "Discharge in BC Q2 = 10.03 lps\n", + "Discharge in BD Q3 = 5.65 lps\n", + "height h = 1.90 m\n", + "Discharge in BC Q2 = 9.95 lps\n", + "Discharge in BD Q3 = 5.62 lps\n", + "height h = 1.96 m\n", + "Discharge in BC Q2 = 10.00 lps\n", + "Discharge in BD Q3 = 5.64 lps\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.21 Page No : 290" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "e = 0.8\n", + "output = 400. \t\t#kW\n", + "H = 150. \t\t\t#m\n", + "rho = 1000. \n", + "g = 9.81\n", + "f = 0.028\n", + "l = 1250. \t\t\t#m\n", + "\t\t\t\n", + "#calculations\n", + "gam = rho*g\n", + "inpu = output/e\n", + "Q = inpu*10**3 /(2./3 *gam*H)\n", + "hl = 1./3 *H\n", + "d5 = f*l*Q**2 /(2*g* math.pi/4 * math.pi/4 *hl)\n", + "d = d5**(1./5)\n", + "\t\t\t\n", + "#results\n", + "print \"Smallest diameter of pen stock = %d cm\"%(d*100)\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Smallest diameter of pen stock = 43 cm\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.22 Page No : 291" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\t\t\n", + "#Initialization of variables\n", + "f = 0.04\n", + "H = 30. \t\t\t#m\n", + "l = 200. \t\t\t#m\n", + "d = 0.075 \t\t\t#m\n", + "g = 9.81\n", + "rho = 1000.\n", + "gam = rho*g\n", + "\t\t\t\n", + "#calculations\n", + "h = 2/3. *H\n", + "vj = math.sqrt(2.*g*h)\n", + "hl = 1/3. *H\n", + "V = math.sqrt(hl*d*2*g/(f*l))\n", + "dj = d*(math.sqrt(V/vj))\n", + "Power = 2/3. *gam*math.pi/4. *d**2 *V*H\n", + "\t\t\t\n", + "#results\n", + "print \"Size of nozzle = %.1f cm\"%(dj*100)\n", + "print \" Max power = %.2f kW\"%(Power/1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Size of nozzle = 2.0 cm\n", + " Max power = 1.18 kW\n" + ] + } + ], + "prompt_number": 29 + } + ], + "metadata": {} + } + ] +}
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