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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:e6fd288db6f632d2f9db4681e283b542c5b7c72c7f4eb7e9aa016cd430f69af5"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6 : Fluid Mechanics and Hydraulic Machines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1 Page No : 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "Rn = 1700.\n",
+ "v = 0.744*(10**-4)\n",
+ "d = 0.05\n",
+ "\n",
+ "# Calculations \n",
+ "V = (Rn*v)/d\n",
+ "Vmax = 2*V\n",
+ "x = 0.00625\n",
+ "r = (d/2)-x\n",
+ "V1 = Vmax*(1-(2*r/d)**2)\n",
+ "\n",
+ "# Results \n",
+ "print \"velocity at the point 6.25 mm from the wall in m/sec\",V1\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "velocity at the point 6.25 mm from the wall in m/sec 2.2134\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2 Page No : 117"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "d = 0.3\n",
+ "p = 787.\n",
+ "v = 1.6*(10**-6)\n",
+ "Rn = 2000.\n",
+ "\n",
+ "# Calculations \n",
+ "V = Rn*v/d\n",
+ "a = math.pi*d*d/4\n",
+ "Q = a*V\n",
+ "\n",
+ "# Results \n",
+ "print \"maximum flow rate for which the flow is maximium %.3e\"%Q,\"m**3/s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum flow rate for which the flow is maximium 7.540e-04 m**3/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No : 118"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "vd = 8*(10**-3)*0.1\n",
+ "p = 996.\n",
+ "\n",
+ "# Calculations \n",
+ "vk = vd/p\n",
+ "\n",
+ "# Results \n",
+ "print \"kinematic vismath.cosity in m2/sec %.3e\"%vk\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kinematic vismath.cosity in m2/sec 8.032e-07\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4 Page No : 118"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "u = 1.5/98.1\n",
+ "s = 0.81\n",
+ "d = 0.14\n",
+ "Q = 0.03\n",
+ "g = 9.81\n",
+ "\n",
+ "# Calculations \n",
+ "p = s*1000/g\n",
+ "a = math.pi*d*d/4\n",
+ "V = Q/a\n",
+ "Rn = V*p*d/u\n",
+ "\n",
+ "# Results \n",
+ "print \"Rn less than 2000, flow is laminar\",round(Rn,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Rn less than 2000, flow is laminar 1473.32\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No : 119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "d = 0.2\n",
+ "Q = 0.088\n",
+ "l = 5.\n",
+ "vd = 0.01\n",
+ "p = 1000.\n",
+ "\n",
+ "# Calculations \n",
+ "v = vd/(p*10)\n",
+ "a = 3.142*d*d/4\n",
+ "g = 9.81\n",
+ "V = Q/a\n",
+ "Re = V*d/v\n",
+ "f = 0.0018+(0.092/(3*(Re**0.5)))\n",
+ "Hf = (4*f*l*V*V)/(d*2*g)\n",
+ "\n",
+ "# Results \n",
+ "print \"head lost due to friction in m\",round(Hf,5)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "head lost due to friction in m 0.0736\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No : 120"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "s = 0.75\n",
+ "d = 0.2\n",
+ "l = 1000.\n",
+ "Q = 3/60.\n",
+ "f = 0.01\n",
+ "a = math.pi*d*d/4\n",
+ "V = Q/a\n",
+ "g = 9.81\n",
+ "\n",
+ "# Calculations \n",
+ "Hf = (4*f*l*V*V)/(d*2*g)\n",
+ "w = g*s*1000\n",
+ "dp = w*Hf\n",
+ "\n",
+ "# Results \n",
+ "print \"pressure drop along its entire lenght in N/m2 %.2f\"%dp\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pressure drop along its entire lenght in N/m2 189977.22\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7 Page No : 121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "d = 0.3\n",
+ "g = 9.81\n",
+ "l = 400\n",
+ "Q = 0.3\n",
+ "f = 0.032\n",
+ "\n",
+ "# Calculations \n",
+ "a = 3.142*d*d/4\n",
+ "V = Q/a\n",
+ "Lentrance = (0.5*V*V)/(2*g)\n",
+ "Hf = (4*f*l*V*V)/(d*2*g)\n",
+ "Lexit = (V*V)/(2*g)\n",
+ "Totalloss = Lentrance+Hf+Lexit\n",
+ "\n",
+ "# Results \n",
+ "print \"diffrenc in elevation in m\",round(Totalloss,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " diffrenc in elevation in m 158.02\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.8 Page No : 112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "l = 40.\n",
+ "l1 = 20.\n",
+ "l2 = 20.\n",
+ "d1 = 0.15\n",
+ "d2 = 0.3\n",
+ "H = 8.\n",
+ "f = 0.01\n",
+ "\n",
+ "# Calculations \n",
+ "h1 = (2*d2*d2)/(d1*d1)\n",
+ "h2 = 4*f*l1*16/d1\n",
+ "h3 = 9\n",
+ "h4 = 4*f*l2/d2\n",
+ "g = 9.81\n",
+ "ht = h1+h2+h3+h4+1\n",
+ "V2 = (H*2*g/ht)**0.5\n",
+ "a2 = 3.142*d2*d2/4\n",
+ "Q = V2*a2\n",
+ "\n",
+ "# Results \n",
+ "print \"rate of low in litres/sec\",round((Q*1000),0)\n",
+ "\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rate of low in litres/sec 86.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No : 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "l = 2000.\n",
+ "d = 0.2\n",
+ "V = 0.8\n",
+ "f = 0.01\n",
+ "g = 9.81\n",
+ "\n",
+ "# Calculations \n",
+ "hf = (4*f*l*V*V)/(d*2*g)\n",
+ "\n",
+ "# Results \n",
+ "print \"Head loss due to friction in pipeline\",round(hf,4)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Head loss due to friction in pipeline 13.0479\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No : 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "d1 = 0.15\n",
+ "d2 = 0.1\n",
+ "Q = 0.03\n",
+ "a1 = math.pi*d1*d1/4\n",
+ "a2 = math.pi*d2*d2/4\n",
+ "V1 = Q/a1\n",
+ "V2 = Q/a2\n",
+ "c = 0.6\n",
+ "g = 9.81\n",
+ "\n",
+ "# Calculations \n",
+ "dz = (V2*V2/(2*g))-(V1*V1/(2*g))+(V2*V2/(2*g))*((1/c-1)**2)\n",
+ "w = 9810\n",
+ "dp = dz*w\n",
+ "\n",
+ "# Results \n",
+ "print \"pressure loss across the contraction in N/m2\",round(dp,1)\n",
+ "\n",
+ "# note : rounding off error"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pressure loss across the contraction in N/m2 9096.4\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No : 125"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "d1 = 0.5\n",
+ "d2 = 0.25\n",
+ "p1 = 103005.\n",
+ "p2 = 67689.\n",
+ "p3 = p2\n",
+ "w = 9810.\n",
+ "g = 9.81\n",
+ "c = 0.65\n",
+ "\n",
+ "# Calculations and Results\n",
+ "z = 1-(1./16)+((1/c-1)**2)\n",
+ "dp = p1-p2\n",
+ "v2 = ((dp*2*g)/(w*z))**0.5\n",
+ "a2 = math.pi*d2*d2/4\n",
+ "Q = v2*a2\n",
+ "print \"rate of flow in m3/sec\",round((Q*1000),2)\n",
+ "\n",
+ "v3 = v2\n",
+ "v1 = v3/4\n",
+ "v4 = v1\n",
+ "he = (v3-v4)**2/(2*g)\n",
+ "p4 = w*((p3/w)+((v3*v3-v4*v4)/(2*g))-he)\n",
+ "print \"pressure at the 50 cm enlarge section in N/m2\",round(p4,3)\n",
+ "\n",
+ "# note : rouding off error."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rate of flow in m3/sec 372.37\n",
+ "pressure at the 50 cm enlarge section in N/m2 78478.522\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12 Page No : 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "d = 0.04\n",
+ "v = 2.\n",
+ "dp = 20000.\n",
+ "l = 8.\n",
+ "w = 9810.\n",
+ "\n",
+ "# Calculations \n",
+ "u = (dp*d*d)/(32*l*v)\n",
+ "\n",
+ "# Results \n",
+ "print \"viscosity of the flowing oil\",u,\"N/m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "viscosity of the flowing oil 0.0625 N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13 Page No : 128"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "d = 0.25\n",
+ "l = 12.*1000\n",
+ "w = 9320.\n",
+ "i = 1./300\n",
+ "v = 20.*(10**-4)\n",
+ "a = math.pi*d*d/4\n",
+ "q = 0.015\n",
+ "\n",
+ "# Calculations \n",
+ "V = q/a\n",
+ "g = 9.81\n",
+ "Rn = V*d/v\n",
+ "f = 16/Rn\n",
+ "hf = (4*f*l*V*V)/(2*d*g)\n",
+ "H = hf+(i*l)\n",
+ "p = (w*q*H)/1000\n",
+ "\n",
+ "# Results \n",
+ "print \"power required to pump the oil\",round(p,4),\"kW\"\n",
+ "\n",
+ "# note : rounding off error."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power required to pump the oil 59.1027 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.14 Page No : 129"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "l = 600.\n",
+ "H = 160.\n",
+ "p = 1200.*1000\n",
+ "n = 0.85\n",
+ "f = 0.005\n",
+ "\n",
+ "# Calculations \n",
+ "hf = H/3\n",
+ "w = 9810\n",
+ "H1 = H-hf\n",
+ "q = p/(w*H1*n)\n",
+ "d = ((f*l*q*q)/(3*hf))**0.2\n",
+ "\n",
+ "\n",
+ "# Results \n",
+ "print \"minimium diameter of the pipe in cm\",round((d*100),2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "minimium diameter of the pipe in cm 50.89\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15 Page No : 129"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "d = 0.25\n",
+ "l = 500.\n",
+ "a = math.pi*d*d/4\n",
+ "f = 0.006\n",
+ "q = 0.04\n",
+ "g = 9.81\n",
+ "p2 = 250.*1000\n",
+ "\n",
+ "# Calculations \n",
+ "V = q/a\n",
+ "hf = (4*f*l*V*V)/(d*2*g)\n",
+ "z1 = 0\n",
+ "z2 = 25\n",
+ "w = 9810\n",
+ "p1 = ((p2/w)+z2+hf)*w\n",
+ "\n",
+ "# Results \n",
+ "print \"pressure at point A is N/m2\",round(p1,2),\"N/m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pressure at point A is N/m2 511186.44 N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.16 Page No : 130"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "q = 0.15/(2.5*60)\n",
+ "d = 0.03\n",
+ "p1 = 9810.\n",
+ "p2 = 6867.\n",
+ "l = 2.\n",
+ "w = 9810.\n",
+ "\n",
+ "# Calculations \n",
+ "hf = (p1-p2)/w\n",
+ "a = 3.142*d*d/4\n",
+ "V = q/a\n",
+ "g = 9.81\n",
+ "f = (hf*2*g*d)/(4*l*V*V)\n",
+ "C = V*((4*l)/(d*hf))**0.5\n",
+ "\n",
+ "# Results \n",
+ "print \"darcy co-efficient\",round(f,3)\n",
+ "print \"Chezy formula\",round(C,3)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "darcy co-efficient 0.011\n",
+ "Chezy formula 42.173\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17 Page No : 131"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Variables\n",
+ "a = 90.\n",
+ "H1 = 10.\n",
+ "d = 0.15\n",
+ "l = 400.\n",
+ "H2 = 7.\n",
+ "g = 9.81\n",
+ "f = 0.008\n",
+ "\n",
+ "# Calculations \n",
+ "z = 3.142*d*d*((2*g)**0.5)\n",
+ "z1 = (1.5+(4*f*l/d))**0.5\n",
+ "T = (8*a*z1*(H1**0.5-H2**0.5))/z\n",
+ "\n",
+ "# Results \n",
+ "print \"time to lower the level from 10m to 7m in hr\",round((T/3600),4)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time to lower the level from 10m to 7m in hr 3.0742\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18 Page No : 132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "q = 0.08\n",
+ "d1 = 0.25\n",
+ "d2 = 1.\n",
+ "l1 = 1500.\n",
+ "l2 = 1500.\n",
+ "\n",
+ "# Calculations \n",
+ "a1 = math.pi*d1*d1/4\n",
+ "a2 = math.pi*d2*d2/4\n",
+ "v2 = q*4/(math.pi*((1./32)+1))\n",
+ "v1 = v2*0.5\n",
+ "q1 = v1*a1\n",
+ "q2 = v2*a2\n",
+ "\n",
+ "# Results \n",
+ "print \"disharge through pipe in m3/sec\",round((q2*1000),2),round((q1*1000),4)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "disharge through pipe in m3/sec 77.58 2.4242\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 15:57:04 +0000