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diff --git a/Problems_In_Fluid_Flow/ch3.ipynb b/Problems_In_Fluid_Flow/ch3.ipynb new file mode 100644 index 00000000..092a98ed --- /dev/null +++ b/Problems_In_Fluid_Flow/ch3.ipynb @@ -0,0 +1,325 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3 : velocity boundary layers\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 3.1 page no : 50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "fluid in boundary layer would be entirely\n", + "reynolds \n", + "boundary layer width\n", + "velocity of water\n", + "shear stress \n", + "mean shear stress experienced\n", + "total force experienced\n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "rho=998.\n", + "mu=1.002/1000\n", + "x=48/100.\n", + "u=19.6/100\n", + "x1=30/100.\n", + "b=2.6\n", + "\n", + "#calculation\n", + "\n", + "print \"fluid in boundary layer would be entirely in streamline motion \"\n", + "Re=rho*x*u/mu\n", + "print \"reynolds no is %.2e\"%(Re)\n", + "\n", + "#part 2\n", + "Re1=rho*x1*u/mu\n", + "delta=x1*4.64*Re1**-.5\n", + "print \"boundary layer width in (mm): %.4f\"%(delta*1000)\n", + "\n", + "#part3\n", + "y=0.5*delta #middle of boundary layer\n", + "ux=3/2*u*y/delta-.5*u*(y/delta)**3\n", + "print \"velocity of water in (cm/s): %.4f\"%(ux*100)\n", + "\n", + "#part4\n", + "R=0.323*rho*u**2*Re1**-0.5\n", + "print \"shear stress at 30cm in (N/m**2): %.4f\"%R\n", + "\n", + "#part5\n", + "Rms=0.646*rho*u**2*Re**-0.5\n", + "print \"mean shear stress experienced over whole plate in (N/m**2) %.4f\"%Rms\n", + "\n", + "#part6\n", + "F=Rms*x*b\n", + "print \"total force experienced by the plate in (N) %.4f\"%F\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "fluid in boundary layer would be entirely in streamline motion \n", + "reynolds no is 9.37e+04\n", + "boundary layer width in (mm): 5.7520\n", + "velocity of water in (cm/s): 8.5750\n", + "shear stress at 30cm in (N/m**2): 0.0512\n", + "mean shear stress experienced over whole plate in (N/m**2) 0.0809\n", + "total force experienced by the plate in (N) 0.1010\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 3.2 page no : 52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "% of surface over which turbulent boundary layer \n", + "thickness of boundary layer \n", + "velocity of air at mid point \n", + "thickness of laminar boundary layer\n", + "velocity at outer edge of laminar sublayer\n", + "shearforce expericienced\n", + "mean shearforce \n", + "total drag force expericienced by the plate \n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "P=102.7*1000\n", + "M=28.8/1000\n", + "R=8.314\n", + "temp=273+18\n", + "Recrit=10.**5\n", + "u=18.4\n", + "b=4.7#width\n", + "x=1.3\n", + "mu=1.827/100000\n", + "\n", + "#calculation\n", + "#part1\n", + "rho=P*M/R/temp\n", + "xcrit=Recrit*mu/rho/u\n", + "a=1-xcrit/1.65\n", + "print \"%% of surface over which turbulent boundary layer exist is : %.4f\"%(a*100)\n", + "\n", + "#part2\n", + "Rex=rho*u*x/mu\n", + "thik=0.375*Rex**-.2*x\n", + "print \"thickness of boundary layer in (cm): %.4f\"%(thik*100)\n", + "\n", + "y=0.5*thik\n", + "ux=u*(y/thik)**(1./7)\n", + "print \"velocity of air at mid point is (m/s): %.4f\"%ux\n", + "\n", + "#part4\n", + "lthik=74.6*Rex**-.9*x\n", + "print \"thickness of laminar boundary layer in (mm): %.4f\"%(lthik*1000)\n", + "\n", + "#part5\n", + "ub=u*(lthik/thik)**(1./7)\n", + "print \"velocity at outer edge of laminar sublayer in (m/s): %.4f\"%ub\n", + "\n", + "#part6\n", + "R=0.0286*rho*u**2*Rex**-0.2\n", + "print \"shearforce expericienced in (N/m**2) : %.4f\"%R\n", + "\n", + "#part7\n", + "x1=1.65 #length of plate\n", + "Rex1=rho*u*x1/mu\n", + "Rms=0.0358*rho*u**2*Rex1**-0.2\n", + "print \"mean shearforce in (N/m**2): %.4f\"%Rms\n", + "\n", + "#part8\n", + "F=x1*Rms*b\n", + "print \"total drag force expericienced by the plate is (N): %.4f\"%F\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "% of surface over which turbulent boundary layer exist is : 95.0776\n", + "thickness of boundary layer in (cm): 2.7997\n", + "velocity of air at mid point is (m/s): 16.6653\n", + "thickness of laminar boundary layer in (mm): 0.2528\n", + "velocity at outer edge of laminar sublayer in (m/s): 9.3924\n", + "shearforce expericienced in (N/m**2) : 0.6798\n", + "mean shearforce in (N/m**2): 0.8114\n", + "total drag force expericienced by the plate is (N): 6.2921\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "example 3.3 page no : 55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "'''\n", + "find\n", + "pipe flow reynolds\n", + "Water will be in streamline motion in the pipe\n", + "velocity gradient at the pipe wall\n", + "Sherastress at pipe wall\n", + "new av. fluid velocity \n", + "thickness of laminar sublayer\n", + "thickness of buffer layer \n", + "percentage of pipe-s core occupied by turbulent core\n", + "velocity where sublayer and buffer layer meet \n", + "velocity where turbulent core and buffer layer meet\n", + "fluid velocity \n", + "shearstress \n", + "'''\n", + "\n", + "import math \n", + "\n", + "# Initialization of Variable\n", + "Q=37.6/1000000\n", + "d=3.2/100\n", + "mu=1.002/1000\n", + "rho=998.\n", + "pi=3.14\n", + "\n", + "#calculation\n", + "#part1\n", + "u=4.*Q/pi/d**2.\n", + "Re=rho*u*d/mu\n", + "print \"pipe flow reynolds no : %.4f\"%Re\n", + "print \"Water will be in streamline motion in the pipe\"\n", + "\n", + "#part2\n", + "a=-8.*u/d\n", + "print \"velocity gradient at the pipe wall is (s**-1): %.4f\"%a\n", + "\n", + "#part3\n", + "Ro=-mu*a\n", + "print \"Sherastress at pipe wall is N/m**2) %.2e\"%(Ro)\n", + "\n", + "#part4\n", + "Q=2.10/1000\n", + "u=4.*Q/pi/d**2\n", + "u=round(u*1000.)/1000.\n", + "print \"new av. fluid velocity is (m/s): %.4f\"%u\n", + "\n", + "Re=rho*u*d/mu\n", + "phi=0.0396*Re**-0.25 #friction factor\n", + "phi=round(phi*10**5)/10.**5\n", + "delb=5*d*Re**-1*phi**-.5\n", + "print \"thickness of laminar sublayer in (10**-6m): %.4f\"%(delb*10**6)\n", + "\n", + "#part5\n", + "y=30.*d/phi**0.5/Re #thickness\n", + "tbl=y-delb\n", + "print \"thickness of buffer layer in (mm): %.4f\"%(tbl*1000)\n", + "\n", + "#part6\n", + "A=pi*d**2./4 #cross sectional area of pipe\n", + "dc=d-2*y #dia of turbulent core\n", + "Ac=pi*dc**2/4.\n", + "p=(1-A/Ac)*100.\n", + "print \"percentage of pipe-s core occupied by turbulent core is (%%): %.4f\"%p\n", + "\n", + "#part7\n", + "uplus=5. #from reference\n", + "ux=uplus*u*phi**0.5\n", + "print \"velocity where sublayer and buffer layer meet is (m/s): %.4f\"%ux\n", + "\n", + "#part8\n", + "yplus=30. #from reference\n", + "ux2=u*phi**0.5*(2.5*math.log(yplus)+5.5)\n", + "print \"velocity where turbulent core and buffer layer meet is (m/s): %.4f\"%ux2\n", + "\n", + "#part9\n", + "us=u/0.81\n", + "print \"fluid velocity along the pipe axis (m/s): %.4f\"%us\n", + "\n", + "#part10\n", + "Ro=phi*rho*u**2\n", + "print \"shearstress at pipe wall (N/m**2): %.4f\"%Ro\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "pipe flow reynolds no : 1490.8400\n", + "Water will be in streamline motion in the pipe\n", + "velocity gradient at the pipe wall is (s**-1): -11.6939\n", + "Sherastress at pipe wall is N/m**2) 1.17e-02\n", + "new av. fluid velocity is (m/s): 2.6120\n", + "thickness of laminar sublayer in (10**-6m): 39.8159\n", + "thickness of buffer layer in (mm): 0.1991\n", + "percentage of pipe-s core occupied by turbulent core is (%): -3.0544\n", + "velocity where sublayer and buffer layer meet is (m/s): 0.6304\n", + "velocity where turbulent core and buffer layer meet is (m/s): 1.7655\n", + "fluid velocity along the pipe axis (m/s): 3.2247\n", + "shearstress at pipe wall (N/m**2): 15.8647\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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