{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 4: Flow Of Fluids" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.10: Temperature_rise.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.10 page number 139\n\n')\n", "\n", "//to find the temperature increase\n", "\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", "printf('Temperature increase = %f degree celcius',delta_T)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.11: Bernoulli_equation.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.11 page number 142\n\n')\n", "\n", "//to find the pressure\n", "\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", "printf('u3 = %f m/s',u3)\n", "\n", "ratio_area=0.5;\n", "u2=u3/ratio_area;\n", "printf('\n\nu2 = %f m/s',u2)\n", "\n", "//applying bernoulli's equation\n", "P2=1.7*10^5-((density*u2^2)/2)\n", "printf('\n\nP2 = %f Pa',P2)\n", "printf('\nthis flow is physically unreal')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.12: Power_requirements.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.12 page number 143\n\n')\n", "\n", "//to find the power requirements\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", "printf('power required = %f kW',power/1000)\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.13: Hagen_Poiseulle_equation.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.13 page number 146\n\n')\n", "\n", "//to find the tube length\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", "printf('u = %f m/s',u)\n", "\n", "Re=density*u*0.0005/viscosity;\n", "printf('\n\nRe = %f',Re)\n", "\n", "//F=18.86*L\n", "L=(-u^2+vdP)/18.86;\n", "printf('\n\nL = %f m',L)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.14: Pressure_Head_calculatio.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.14 page number 151\n\n')\n", "\n", "//to find the discharge pressure\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", "printf('frictional head loss = %f kPa',delta_P/1000)\n", "\n", "required_P=25*density*9.8;\n", "total_head=delta_P+required_P;\n", "printf('\n\ntotal pressure head = %f bar',total_head/10^5)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.15: Level_difference_calculation.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.15 page number 152\n\n')\n", "\n", "//to find the level difference\n", "\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", "printf('level difference = %f m',h_f)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16: Energy_cost_calculation.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.16 page number 153\n\n')\n", "\n", "//to find the engery cost\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", "printf('Energy cost = Rs %f',energy_cost)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.17: Pressure_loss.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.17 page number 154\n\n')\n", "\n", "//to find the pressure loss\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", "printf('frictional pressure drop = %f kPa',delta_P_coil)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.18: Pressure_gradient.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.18 page number 154\n\n')\n", "\n", "//to find pressure drop per unit length\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", "printf('pressure per unit length = %f Pa/m',P_perunit_length)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.19: Flow_rate.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.19 page number 155\n\n')\n", "\n", "//to find the flow rate\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", "printf('volumetric flow rate = %f cubic meter per second',q)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.1: Water_compressibility.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.1 page number 125\n\n')\n", "\n", "//to find water compressibility\n", "delta_p=70; //in bar\n", "Et=20680 //in bar\n", "compressibility = delta_p/Et;\n", "printf('compressibilty of water = %f',compressibility)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.20: Pipe_dimensions.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.20 page number 156\n\n')\n", "\n", "//to find the size of pipe required\n", "d = 0.15 //in m\n", "u = (0.0191/0.15^2); //in m/s\n", "\n", "q = (3.14/4)*d^2*u;\n", "printf('volumetric flow rate = %f cubic meter/s',q)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.21: Pressure_gradient.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.21 page number 160\n\n')\n", "\n", "//to find the pressure gradient\n", "\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", "//applying bernoulli's equation, we get\n", "delta_P=delta_Pf-(density*9.8*L);\n", "pressure_gradient=delta_P/(L*1000); //in kPa/m\n", "printf('required pressure gradient = %f kPa/m of packed height',pressure_gradient)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.22: Minimum_fluidization_velocity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.22 page number 163\n\n')\n", "\n", "//to find minimum fluidization velocity\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", "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", "printf('minimum fludization velocity = %f m/s',umf)\n", "\n", "Re_mf=(d*umf*density_water)/(viscosity*(1-e_min));\n", "\n", "\n", "//given that uo/umf=10\n", "function[f] = F(e)\n", " f = e^3+1.657*e-1.675;\n", "endfunction\n", "\n", "//initial guess\n", "x = 10;\n", "e = fsolve(x,F);\n", "\n", "printf('\n\ne = %f',e)\n", "length_ratio=(1-e_min)/(1-e);\n", "printf('\n\nratio of heights = %f',length_ratio)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.23: Pumping_of_fluids.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.23 page number 167\n\n')\n", "\n", "//to find the power requirements\n", "\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", "printf('power_delivered = %f kW',power_delivered/1000)\n", "printf('\n\npower taken by motor = %f kW',power_taken/1000)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.2: Isothermal_Compressibility.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.2 page number 125\n\n')\n", "\n", "disp('this is a theoritical problem,book shall be referred for solution')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.3: Viscosity.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.3 page number 128\n\n')\n", "\n", "//to find the viscosity of oil\n", "\n", "F=0.5*9.8; //in N\n", "A=3.14*0.05*0.15; //in m2\n", "shear_stress=F/A; //in Pa\n", "printf('shear_stress = %f Pa',shear_stress)\n", "\n", "velocity_distribution =0.1/(0.05*10^-3);\n", "viscosity=shear_stress/velocity_distribution;\n", "printf('\n\nviscosity = %f Pa-s',viscosity) " ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.4: Streamline_flow.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.4 page number 130\n\n')\n", "printf('this is a theoritical problem,book shall be referred for solution')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.5: Frictional_losses.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.5 page number 133\n\n')\n", "\n", "//to find variation of losses with velocity\n", "loss_ratio=3.6; //delta_P2/delta_P1=3.6\n", "velocity_ratio=2; //u2/u1=2\n", "n=log2(loss_ratio); //delta_P2/delta_P1=(u2/u1)^n\n", "printf('power constant = %f flow is turbulent',n)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.6: Velocity_profile.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.6 page number 133\n\n')\n", "printf('this is a theoritical problem,book shall be referred for solution')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.7: Velocity_profile.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.7 page number 134')\n", "disp('this is a theoritical problem,book shall be referred for solution')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.8: Boundary_layer.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.8 page number 137\n\n')\n", "\n", "//to find the boundary layer properties\n", "\n", "disp('part 1')\n", "x=0.05 //in m\n", "density=1000 //in kg/m3\n", "viscosity=1*10^-3 //in Pa-s\n", "u=1 //in m/s\n", "Re=(density*u*x)/viscosity;\n", "\n", "printf('Reynolds Number = %f',Re)\n", "\n", "thickness=4.65*x*(Re)^-0.5;\n", "printf('\nboundary layer thickness = %f m\n',thickness)\n", "\n", "disp('part 2')\n", "Re_x=3.2*10^5;\n", "x_cr=(Re_x*viscosity)/(density*u);\n", "printf('transition takes place at x = %f m\n',x_cr) \n", "\n", "disp('part 3')\n", "x=0.5 //in m\n", "Re=(density*u*x)/viscosity;\n", "thickness=0.367*x*(Re)^-0.2;\n", "printf('boundary layer thickness= %f m',thickness)\n", "\n", "t_sublayer=71.5*x*(Re)^-0.9;\n", "printf('\nsub layer thickness= %f m',t_sublayer)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.9: Pipe_flow.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clc\n", "clear \n", "printf('example 4.9 page number 138\n\n')\n", "\n", "//to find the flow properties\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", "printf('density at section 2 = %f kg/cubic meter',density_2)\n", "\n", "u2=u1*(density_1/density_2)*(0.05/0.075)^2;\n", "printf('\n\nvelocity at section 2 = %f m/s',u2)" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }