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Diffstat (limited to 'Fluid_Mechanics_/Chapter4.ipynb')
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diff --git a/Fluid_Mechanics_/Chapter4.ipynb b/Fluid_Mechanics_/Chapter4.ipynb new file mode 100644 index 00000000..20d6f3d5 --- /dev/null +++ b/Fluid_Mechanics_/Chapter4.ipynb @@ -0,0 +1,557 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1587038d9ed42ba6cd2ab38d651a00ef2c4ed8f4723b6c6b72bdf9880d8ef943" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Chapter 4 : Fluid Dynamics" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.1 Page no 159" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Difference in pressure at top and bottom\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "d1 = 0.1 # diameter in m\n", + "\n", + "d2 = 0.05 # diameter in m\n", + "\n", + "Q = 0.1 # discharge in m**3/s\n", + "\n", + "A1 = pi*d1**2/4\n", + "\n", + "A2 = pi*d2**2/4\n", + "\n", + "gma =9810 # specific weight\n", + "\n", + "z= 6 # difference in the height\n", + "\n", + "g = 9.81\n", + "\n", + "# Solution\n", + "\n", + "V1 = Q/A1 # velocity at section 1\n", + "\n", + "V2 = Q/A2 # velocity at section 2\n", + "\n", + "dP = gma*((V2**2/(2*g))-(V1**2/(2*g))-z)/1000\n", + "\n", + "print \"Difference in pressure in section 1 and 2 = \",round(dP,1),\"kN/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Difference in pressure in section 1 and 2 = 1157.0 kN/m**2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.2 Page no 160" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Actual discharge\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "d = 2.5 # diameter in cm\n", + "\n", + "h =200 # head in cm\n", + "\n", + "Cd = 0.65 # coefficient of discharge\n", + "\n", + "A =pi*d**2/4\n", + "\n", + "g = 9.81 # acceleration due to gravity in m/s**2 \n", + "\n", + "# Solution\n", + "\n", + "Q = Cd*A*sqrt(2*g*h)/100\n", + "\n", + "print \"Actual discharge =\",round(Q,2),\"l/s\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Actual discharge = 2.0 l/s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.3 Page no 162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Discharge through the orifice\n", + "\n", + "from __future__ import division\n", + "\n", + "from math import *\n", + "\n", + "from scipy import integrate\n", + "\n", + "import numpy as np\n", + "\n", + "# Given\n", + "\n", + "H1 = 3 # height in m\n", + "\n", + "H2 = 4 # height in m\n", + "\n", + "b = 0.5 # width in m\n", + "\n", + "Cd = 0.65 # co-efficient of discharge \n", + "\n", + "g = 9.81 # acceleration due to grvity in m/s**2\n", + "\n", + "# Solution\n", + "\n", + "q = lambda h: h**(1/2)\n", + " \n", + "Q,err = integrate.quad(q, H1, H2)\n", + "\n", + "Qt = Cd*b*sqrt(2*g)*Q\n", + "\n", + "print \"Discharge through the orifice =\",round(Qt,2),\"m**3/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Discharge through the orifice = 2.69 m**3/s\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.4 Page no 163" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# discharge through orifice\n", + " \n", + "from math import *\n", + "\n", + "from scipy import integrate\n", + "\n", + "from __future__ import division\n", + "\n", + "import numpy as np\n", + "\n", + "# Given\n", + "\n", + "b = 1 # bredth of the tank\n", + "\n", + "d = 0.5 # depth of the tank\n", + "\n", + "h1 = 0.2 # height of the orifice in m\n", + "\n", + "Cd = 0.6 # coefficient of discharge\n", + "\n", + "H1 = 2 # height in m\n", + "\n", + "H2 = 2+h1 # height in m\n", + "\n", + "g = 9.81 # acceleration due to gravity in m/s**2\n", + "\n", + "A = 1*0.3 # area of submerged section in m**2\n", + "\n", + "# Solution\n", + "\n", + "q = lambda h: h**(1/2)\n", + " \n", + "Q,err = integrate.quad(q, H1, H2)\n", + "\n", + "Q1 = Cd*b*sqrt(2*g)*(Q) # Flow through area 1\n", + "\n", + "Q2 = Cd*sqrt(2*g*H2)*A\n", + "\n", + "Td = Q1+Q2\n", + "\n", + "print \"Total Discharge =\",round(Td,2),\"m**3/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total Discharge = 1.95 m**3/s\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.5 Page no 165" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Determine flow rate of water\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "d1 = 2 # radius of pipe\n", + "\n", + "d2 = 1 # radius of throat\n", + "\n", + "D1 = 40\n", + "\n", + "D2 = 20\n", + "\n", + "A1 = pi*D1**2/4\n", + "\n", + "A2 = pi*D2**2/4\n", + "\n", + "Cd = 0.95\n", + "\n", + "# Solution\n", + "\n", + "V2 = sqrt(21582/0.9375)\n", + "\n", + "Q = 1.52*pi*(d1/100)**2/4\n", + "\n", + "Qa = Q*Cd\n", + "\n", + "print \"Actual discharge =\",round(Qa,6),\"m**3/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Actual discharge = 0.000454 m**3/s\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.6 Page no 166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity of stream point at the point of insertion\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "# Given\n", + "\n", + "dx = 0.5 # in ft\n", + "\n", + "K = 1 # constant\n", + "\n", + "g = 32.2 # acceleration due to gravity in ft/s**2\n", + "\n", + "# solution\n", + "\n", + "V = sqrt(2*g*dx)\n", + "\n", + "print \"velocity at the dept of 1 ft =\",round(V,2),\"ft/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "velocity at the dept of 1 ft = 5.67 ft/s\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example no 4.7 Page no 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Discharge throught the system\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "gma= 0.8 # specific weight\n", + "\n", + "V2 = 40 # velocity in m/s\n", + "\n", + "z1 =25 # height at point 1\n", + "\n", + "g = 9.81 # acceleration due to gravity in m/s**2\n", + "\n", + "d = 15 # diameter of the nozzle in cm\n", + "\n", + "# Solution\n", + "\n", + "V2 = sqrt(2*g*z1/4.25)\n", + "\n", + "A = pi*(d/100)**2/4\n", + "\n", + "Q = A*V2*1000\n", + "\n", + "print \"Discharge throught the system =\",round(Q,0),\"l/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Discharge throught the system = 190.0 l/s\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.8 Page no 174" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Power input to the pump\n", + "\n", + "from math import *\n", + "\n", + "from __future__ import division\n", + "\n", + "\n", + "# Given\n", + "\n", + "Eff = 0.8 # pump efficiency\n", + "\n", + "Hl = 30 # head loss in m\n", + "\n", + "D1 =6 # diameter in cm\n", + "\n", + "D2 = 2 # diameter in cm\n", + "\n", + "gma = 9810 # specific weight in N/m**3\n", + "\n", + "V2 = 40 # velocity in m/s\n", + "\n", + "P1 = -50 # pressure at point 1 in N/m**2\n", + "\n", + "z2 = 100 # height at point 2\n", + "\n", + "g = 9.8 # acceleration due to gravity in m/s**2\n", + "\n", + "z1 = 30 # height in m\n", + "\n", + "# Solution\n", + "\n", + "V1=(2/6)**2*V2\n", + "\n", + "Q = (pi*6**2/4)*V1*10**-4\n", + "\n", + "Hs = z2 + (V2**2/(2*g)) + z1 + (50/gma) -(V1**2/(2*g))\n", + "\n", + "P = gma*Q*Hs\n", + "\n", + "Pi = (P/Eff)/1000\n", + "\n", + "print \"Power input = \",round(Pi,1),\"kW\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power input = 32.5 kW\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.9 Page no 176" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Pressure head at A and B\n", + "\n", + "from math import *\n", + "\n", + "# Given\n", + "\n", + "Q = 0.2 # discharge in m**3/s\n", + "\n", + "d1 = 0.25 # diameter of the pipe in m\n", + "\n", + "A = pi*d1**2/4 # area of the pipe\n", + "\n", + "za = 480 # height in m\n", + "\n", + "z1 = 500 # height in m\n", + "\n", + "z3 = 550 # elevation in m\n", + "\n", + "gma =9810 # specific weight in N/m**2\n", + "\n", + "g =9.81 # acceleration due to gravity in m/s**2\n", + "\n", + "# Solution\n", + "\n", + "V=Q/A # Velocity of in m/s\n", + "\n", + "Hl1 = (0.02*100*V**2/(0.25*2*9.81))\n", + "\n", + "# pressure head at A\n", + "\n", + "Pa =(z1-za-(V**2/(2*g))-Hl1)\n", + "\n", + "El = za+Pa\n", + "\n", + "print \"Elevation at height A =\",round(El,2),\"m\"\n", + "\n", + "# pressure head at B\n", + "\n", + "hs = z3 - z1 + (0.02*(500/0.25)*(V**2/(2*g))) \n", + "\n", + "El2 = El+hs\n", + "\n", + "print \"Elevation at height B =\",round(El2,2),\"m\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Elevation at height A = 492.39 m\n", + "Elevation at height B = 576.23 m\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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