{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 4 : Flow Of Fluids" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.1 page number 125" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\n", "delta_p=70.; #in bar\n", "Et=20680. #in bar\n", "\n", "compressibility = delta_p/Et;\n", "\n", "print \"compressibilty of water = %f\"%(compressibility)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "compressibilty of water = 0.003385\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.3 page number 128\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "F=0.5*9.8; #in N\n", "A=3.14*0.05*0.15; #in m2\n", "\n", "shear_stress=F/A; #in Pa\n", "print \"shear_stress = %f Pa\"%(shear_stress)\n", "\n", "velocity_distribution =0.1/(0.05*10**-3);\n", "viscosity=shear_stress/velocity_distribution;\n", "print \"viscosity = %f Pa-s\"%(viscosity) \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "shear_stress = 208.067941 Pa\n", "viscosity = 0.104034 Pa-s\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.5 page number 133\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "loss_ratio=3.6; #delta_P2/delta_P1=3.6\n", "velocity_ratio=2.; #u2/u1=2\n", "\n", "n=math.log(loss_ratio,2); #delta_P2/delta_P1=(u2/u1)**n\n", "\n", "print \"power constant = %f flow is turbulent\"%(n)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "power constant = 1.847997 flow is turbulent\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.8 page number 137\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "print ('part 1')\n", "\n", "x=0.05 #in m\n", "density=1000. #in kg/m3\n", "\n", "viscosity=1.*10**-3 #in Pa-s\n", "u=1. #in m/s\n", "Re=(density*u*x)/viscosity;\n", "\n", "print \"Reynolds Number = %f\"%(Re)\n", "\n", "thickness=4.65*x*(Re)**-0.5;\n", "print \"boundary layer thickness = %f m\"%(thickness)\n", "\n", "print ('part 2')\n", "Re_x=3.2*10**5;\n", "x_cr=(Re_x*viscosity)/(density*u);\n", "print \"transition takes place at x = %f m\"%(x_cr) \n", "\n", "print ('part 3')\n", "x=0.5 #in m\n", "Re=(density*u*x)/viscosity;\n", "thickness=0.367*x*(Re)**-0.2;\n", "print \"boundary layer thickness= %f m\"%(thickness)\n", "\n", "t_sublayer=71.5*x*(Re)**-0.9;\n", "print \"sub layer thickness= %f m\"%(t_sublayer)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "part 1\n", "Reynolds Number = 50000.000000\n", "boundary layer thickness = 0.001040 m\n", "part 2\n", "transition takes place at x = 0.320000 m\n", "part 3\n", "boundary layer thickness= 0.013300 m\n", "sub layer thickness= 0.000266 m\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.9 page number 138\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "d1=0.05 #in m\n", "A1=(3.14*d1**2)/4.;\n", "density_1=2.1 #in kg/m3\n", "u1=15. #in m/s\n", "P1=1.8; #in bar\n", "P2=1.3; #in bar\n", "\n", "w=density_1*A1*u1;\n", "density_2=density_1*(P2/P1);\n", "print \"density at section 2 = %f kg/cubic meter\"%(density_2)\n", "\n", "u2=u1*(density_1/density_2)*(0.05/0.075)**2;\n", "print \"velocity at section 2 = %f m/s\"%(u2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "density at section 2 = 1.516667 kg/cubic meter\n", "velocity at section 2 = 9.230769 m/s\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.10 page number 139\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "Q=0.001*10**5 #in J/s\n", "w=0.001*1000 #in kg/s\n", "density=1000. #in kg/m3\n", "cp=4.19*10**3 #in J/kg K\n", "\n", "delta_T=Q/(w*cp);\n", "\n", "print \"Temperature increase = %f degree celcius\"%(delta_T)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature increase = 0.023866 degree celcius\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.11 page number 142\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "u1=0; #in m/s\n", "ws=0;\n", "P1=0.7*10**5 #in Pa\n", "P3=0\n", "density=1000 #in kg/m3\n", "\n", "u3=((2*(P1-P3))/density)**0.5;\n", "print \"u3 = %f m/s\"%(u3)\n", "\n", "ratio_area=0.5;\n", "u2=u3/ratio_area;\n", "print \"u2 = %f m/s\"%(u2)\n", "\n", "P2=1.7*10**5-((density*u2**2)/2)\n", "print \"P2 = %f Pa\"%(P2)\n", "print \"this flow is physically unreal\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "u3 = 11.832160 m/s\n", "u2 = 23.664319 m/s\n", "P2 = -110000.000000 Pa\n", "this flow is physically unreal\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.12 page number 143\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\n", "Q=3800./(24*3600) #in m3/s\n", "d=0.202 #in m\n", "\n", "u=Q/((3.14/4)*d**2); #in m/s\n", "delta_P=5.3*10**6 #in Pa\n", "density=897. #in kg/m3\n", "F=delta_P/density; #in J/kg\n", "ws=9.8*30+F;\n", "mass_flow_rate= Q*density;\n", "power=(ws*mass_flow_rate)/0.6;\n", "\n", "print \"power required = %f kW\"%(power/1000)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "power required = 407.834267 kW\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.13 page number 146\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "density=1000 #in kg/m3\n", "viscosity=1*10**-3 #in Pa s\n", "P=100*1000 #in Pa\n", "\n", "vdP=P/density;\n", "\n", "Q=2.5*10**-3/(24*3600)\n", "A=3.14*(0.0005)**2/4;\n", "u=Q/A;\n", "print \"u = %f m/s\"%(u)\n", "\n", "Re=density*u*0.0005/viscosity;\n", "print \"Re = %f\"%(Re)\n", "\n", "L=(-u**2+vdP)/18.86;\n", "print \"L = %f m\"%(L)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "u = 0.147440 m/s\n", "Re = 73.720217\n", "L = 5.301074 m\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.14 page number 151\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "d=0.025 #in m\n", "u=3. #in m/s\n", "density=894. #in kg/m3\n", "viscosity=6.2*10**4 #in Pa-s\n", "\n", "Re=(u*d*density)/viscosity;\n", "f=0.0045;\n", "L=50.;\n", "\n", "delta_P=2*f*density*u**2*(L/d)\n", "print \"frictional head loss = %f kPa\"%(delta_P/1000)\n", "\n", "required_P=25*density*9.8;\n", "total_head=delta_P+required_P;\n", "print \"total pressure head = %f bar\"%(total_head/10**5)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "frictional head loss = 144.828000 kPa\n", "total pressure head = 3.638580 bar\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.15 page number 152\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "Q=0.8*10**-3; #in m3/s\n", "d=0.026 #in m\n", "A=(3.14*(d**2))/4 #in m2\n", "\n", "u=Q/A; #in m/s\n", "density=800 #in kg/m3\n", "viscosity=0.0005 #in Pa-s\n", "\n", "Re=(u*density*d)/viscosity;\n", "f=0.079*(Re)**-0.25;\n", "L=60\n", "h_f=2*f*((u**2)/9.8)*(L/d);\n", "\n", "print \"level difference = %f m\"%(h_f)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "level difference = 5.343360 m\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.16 page number 153\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "delta_z=50; #in m\n", "L=290.36 #in m\n", "d=0.18 #in m\n", "Q=0.05 #in m3/s\n", "\n", "A=(3.14*d**2)/4; #in m2\n", "u=Q/A; #in m/s\n", "density=1180; #in kg/m3\n", "viscosity=0.0012 #in Pa-s\n", "Re=u*density*d/viscosity;\n", "\n", "f=0.004;\n", "sigma_F=2*f*u**2*L/d;\n", "ws=((9.8*50)+sigma_F)/0.6;\n", "mass_flow_rate=Q*density; #in Kg/s\n", "power=mass_flow_rate*ws/1000; #in KW\n", "energy_cost=power*24*0.8;\n", "\n", "print \"Energy cost = Rs %f\"%(energy_cost)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Energy cost = Rs 1019.280105\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.17 page number 154\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "density=998 #in kg/m3\n", "viscosity=0.0008 #in Pa-s\n", "d=0.03 #in m\n", "u=1.2 #in m/s\n", "\n", "Re=density*d*u/viscosity;\n", "\n", "f=0.0088;\n", "D=1 #in m\n", "N=10\n", "L=3.14*D*N;\n", "delta_P=(2*f*u**2*L)/d; #in Pa\n", "delta_P_coil=delta_P*(1+(3.54*(d/D)));\n", "\n", "print \"frictional pressure drop = %f kPa\"%(delta_P_coil)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "frictional pressure drop = 29.343858 kPa\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.18 page number 154\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\n", "b=0.050 #in m\n", "a=0.025 #in m\n", "d_eq=b-a #in m\n", "density=1000 #in kg/m3\n", "u=3 #in m/s\n", "viscosity = 0.001\n", "\n", "Re=d_eq*u*density/viscosity;\n", "\n", "e=40*10**6 #in m\n", "f=0.0062;\n", "P_perunit_length=2*f*density*u**2/d_eq; #in Pa/m\n", "\n", "print \"pressure per unit length = %f Pa/m\"%(P_perunit_length)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "pressure per unit length = 4464.000000 Pa/m\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.19 page number 155\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "d = 0.3 #in m\n", "u = 17.63 #avg velocity in m/s\n", "\n", "q = (3.14/4)*d**2*u;\n", "\n", "print \"volumetric flow rate = %f cubic meter per second\"%(q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "volumetric flow rate = 1.245559 cubic meter per second\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.20 page number 156\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "\n", "d = 0.15 #in m\n", "\n", "u = (0.0191/0.15**2); #in m/s\n", "q = (3.14/4)*d**2*u;\n", "\n", "print \"volumetric flow rate = %f cubic meter/s\"%(q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "volumetric flow rate = 0.014994 cubic meter/s\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.21 page number 160\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "Q=0.0003 #in m3/s\n", "d=0.05 #in m\n", "A=(3.14*d**2)/4;\n", "\n", "u=Q/A;\n", "\n", "density=1000; #in kg/m3\n", "viscosity=0.001; #in Pa-s\n", "e=0.3;\n", "dp=0.00125; #particle diameter in m\n", "\n", "Re=(dp*u*density)/(viscosity*(1-e));\n", "fm=(150/Re)+1.75;\n", "L=0.5 #in m\n", "delta_Pf=fm*((density*L*u**2)/dp)*((1-e)/e**3); #in Pa\n", "\n", "delta_P=delta_Pf-(density*9.8*L);\n", "pressure_gradient=delta_P/(L*1000); #in kPa/m\n", "\n", "print \"required pressure gradient = %f kPa/m of packed height\"%(pressure_gradient)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "required pressure gradient = 1104.702008 kPa/m of packed height\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.22 page number 163\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from scipy.optimize import fsolve \n", "import math \n", "\n", "d=120*10**-6 #in m\n", "density=2500 #particle density in kg/m3\n", "e_min=0.45;\n", "density_water=1000 #in kg/m3\n", "\n", "viscosity=0.9*10**-3; #in Pa-s\n", "umf=(d**2*(density-density_water)*9.8*e_min**3)/(150*viscosity*(1-e_min));\n", "print \"minimum fludization velocity = %f m/s\"%(umf)\n", "\n", "Re_mf=(d*umf*density_water)/(viscosity*(1-e_min));\n", "\n", "\n", "def F(e):\n", " return e**3+1.657*e-1.675;\n", "\n", "x = 10.;\n", "e = fsolve(F,x)\n", "\n", "print \"e = %f\"%(e)\n", "length_ratio=(1-e_min)/(1-e);\n", "print \"ratio of heights = %f\"%(length_ratio)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "minimum fludization velocity = 0.000260 m/s\n", "e = 0.753096\n", "ratio of heights = 2.227583\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 4.23 page number 167\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math \n", "P=9807. #in Pa\n", "density=1000. #in kg/m3\n", "Q=250./(60.*density)\n", "head=25. #in m\n", "\n", "w= head*Q*P; #in kW\n", "power_delivered=w/0.65;\n", "power_taken=power_delivered/0.9;\n", "\n", "print \"power_delivered = %f kW\"%(power_delivered/1000)\n", "print \"power taken by motor = %f kW\"%(power_taken/1000)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "power_delivered = 1.571635 kW\n", "power taken by motor = 1.746261 kW\n" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }