{ "metadata": { "name": "", "signature": "sha256:03b40b6d5c44ff714aac13480905f296c46afa917e2740a687e8aa66bb21b428" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 10: Laminar and Turbulent Flows in Bounded System" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.1, Page 329" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "import sympy\n", "from sympy import symbols,diff,solve\n", "\n", " #Initializing the variables\n", "mu = 0.9;\n", "rho = 1260;\n", "g = 9.81;\n", "x = 45; #theta in degrees\n", "P1 = 250 * 10**3;\n", "P2 = 80* 10**3;\n", "Z1 = 1;\n", "Z2 = 0; # datum\n", "U = -1.5;\n", "Y = 0.01;\n", "\n", " #Calculations\n", "gradP1 = P1+ rho*g*Z1;\n", "gradP2 = P2+ rho*g*Z2;\n", "DPstar = (gradP1-gradP2)*math.sin(math.radians(x))/(Z1-Z2);\n", "A = U/Y; # Coefficient U/Y for equation 10.6\n", "B = DPstar/(2*mu) # Coefficient dp*/dx X(1/2mu) for equation 10.6\n", "y = symbols('y')\n", "v = round((A + B*Y),1)*y -round(B)*y**2\n", "duBYdy = diff(v,y);\n", "tau = 0.9*duBYdy;\n", "stagPnts = solve(duBYdy,y)\n", "ymax=stagPnts[0] #value of y where derivative vanishes.;\n", "umax = (A + B*Y)*ymax + B*ymax**2; # Check the value there is slight mistake in books answer\n", "def u(y):\n", " z = (A + B*Y)*y -B*y**2;\n", " return diff(z,y)\n", "def dif(y):\n", " return round((A + B*Y)) -2*round(B)*y\n", "\n", "taumax=abs(mu*dif(Y))\n", "\n", "print \"velocity distribution :\",v\n", "print \"shear stress distribution :\",mu*dif(y)\n", "print \"maximum flow velocity (m/s) :\",round(umax,2)\n", "print \"Maximum Shear Stress (kN/m^2):\",(round(taumax)/1000)\n", " \n", "\n", "print " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "velocity distribution : -71638.0*y**2 + 566.4*y\n", "shear stress distribution : -128948.4*y + 509.4\n", "maximum flow velocity (m/s) : 3.36\n", "Maximum Shear Stress (kN/m^2): 0.78\n", "\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.2, Page 335" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "mu = 0.9;\n", "rho = 1260;\n", "d = 0.01;\n", "Q = 1.8/60*10**-3; #Flow in m**3 per second\n", "l = 6.5;\n", "ReCrit = 2000;\n", " #Calculations\n", "A = (math.pi*d**2)/4;\n", "MeanVel = Q/A;\n", "Re = rho*MeanVel*d/mu/10; # Check properly the answer in book there is something wrong\n", "Dp = 128*mu*l*Q/(math.pi*d**4)\n", "Qcrit = Q*ReCrit/Re*10**3;\n", "\n", "print \"Pressure Loss (kN/m2) :\",round(Dp/1000,0)\n", "print \"Maximum Flow rate (litres/s) :\",round(Qcrit,0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Pressure Loss (kN/m2) : 715.0\n", "Maximum Flow rate (litres/s) : 112.0\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.3, Page 341" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "mu = 1.14*10**-3;\n", "rho = 1000;\n", "d = 0.04;\n", "Q = 4*10**-3/60; #Flow in m**3 per second\n", "l = 750;\n", "ReCrit = 2000;\n", "g = 9.81;\n", "k = 0.00008; # Absolute Roughness\n", "\n", " #Calculations\n", "A = (math.pi*d**2)/4;\n", "MeanVel = Q/A;\n", "Re = rho*MeanVel*d/mu;\n", "Dp = 128*mu*l*Q/(math.pi*d**4);\n", "hL = Dp/(rho*g);\n", "f = 16/Re;\n", "hlDa = 4*f*l*MeanVel**2/(2*d*g); # By Darcy Equation\n", "Pa = rho*g*hlDa*Q;\n", "\n", " #Part(b)\n", "Q = 30*10**-3/60; #Flow in m**3 per second\n", "MeanVel = Q/A;\n", "Re = rho*MeanVel*d/mu;\n", "RR = k/d; # relative roughness\n", "f = 0.008 #by Moody diagram for Re = 1.4 x 10**4 and relative roughness = 0.002\n", "hlDb = 4*f*l*MeanVel**2/(2*d*g); # By Darcy Equation\n", "Pb = rho*g*hlDb*Q;\n", "\n", "\n", "print \"!---- Case (a) ----!\\n\",\"Head Loss(mm) :\",round(hlDa*1000,1)\n", "print \"Power Required (W) :\",round(Pa,4)\n", "print \"\\n!---- Case (b) ----!\\n\",\"Head Loss(m) :\",round(hlDb,2)\n", "print \"Power Required (W) :\",round(Pb,0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "!---- Case (a) ----!\n", "Head Loss(mm) : 92.5\n", "Power Required (W) : 0.0605\n", "\n", "!---- Case (b) ----!\n", "Head Loss(m) : 4.84\n", "Power Required (W) : 24.0\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.4, Page 343" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "w = 4.5;\n", "d = 1.2 ;\n", "C = 49;\n", "i = 1/800;\n", "\n", " #Calculations\n", "A = d*w;\n", "P = 2*d + w;\n", "m = A/P;\n", "v = C*(m*i)**0.5;\n", "Q = v*A;\n", "\n", "print \"Mean Velocity (m/s):\",round(v,2)\n", "print \"Discharge (m3/s) :\",round(Q,2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mean Velocity (m/s): 1.53\n", "Discharge (m3/s) : 8.28\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.5, Page 348" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import sympy\n", "from sympy import symbols\n", "\n", " #Initializing the variables\n", "r,R = symbols('r R')\n", "\n", "#Calculations\n", "rbyR=round((1-(49/60)**7),3)\n", "r = (rbyR)*R \n", "\n", "#Result\n", "print \"radius at which actual velocity is equal to mean velocity is\",r" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "radius at which actual velocity is equal to mean velocity is 0.758*R\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.7, Page 355" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "d1 = 0.140;\n", "d2 = 0.250;\n", "DpF_DpR = 0.6; #Difference in head loss when in forward and in reverse direction\n", "K = 0.33 #From table\n", "g = 9.81;\n", " #Calculations\n", "ratA = (d1/d2)**2;\n", "v =(DpF_DpR*2*g/((1-ratA)**2-K))**0.5;\n", "\n", "print \"Velocity (m/s):\",round(v,2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Velocity (m/s): 9.13\n" ] } ], "prompt_number": 8 } ], "metadata": {} } ] }