diff options
Diffstat (limited to 'Fluid_Mechanics-Fundamentals_&_Applications/Chapter08_1.ipynb')
| -rwxr-xr-x | Fluid_Mechanics-Fundamentals_&_Applications/Chapter08_1.ipynb | 475 |
1 files changed, 475 insertions, 0 deletions
diff --git a/Fluid_Mechanics-Fundamentals_&_Applications/Chapter08_1.ipynb b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter08_1.ipynb new file mode 100755 index 00000000..e70edd03 --- /dev/null +++ b/Fluid_Mechanics-Fundamentals_&_Applications/Chapter08_1.ipynb @@ -0,0 +1,475 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:11a32dcbb7adff422edff329d33e29629cd83e2f8ab7cf7ac7803e8cbd9385ca" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 08:Internal Flow" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-1, Page No:349" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "u_max=6 #Maximum Velocity in m/s\n", + "R=0.02 #Radius of the Pipe in m\n", + "L=70 #Length of the pipe in m\n", + "rho=1252 #Density of glycerin in kg/m^3\n", + "u=0.3073 #Viscosity of glycerin in kg/m.s\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "C=10**-3 #Conversion factor\n", + "\n", + "#Calculations\n", + "D=R*2 #Diameter of the pipe in m\n", + "V=u_max/2 #Average Velocity in m/s\n", + "V_dot=V*(pi*R**2) #Volumertic Flow rate in m^3/s\n", + "Re=(rho*V*D)/u #Reynolds Number \n", + "f=64/Re #Friction Factor\n", + "h_L=(f*L*V**2)/(2*g*D) #Head loss in m\n", + "theta=(pi*15)/180 #Angle in radians\n", + "\n", + "#Applying the energy balance equation\n", + "#As z2=z1 z2-z1=0 hence we do not consider it in the computation\n", + "delta_P=rho*g*(h_L)*C #Pressure difference in kPa\n", + "W_dot=V_dot*delta_P #Useful pumping Power in kW\n", + "\n", + "#Inclined Case\n", + "delta_z=L*sin(theta) #elevation difference in m\n", + "delta_P_up=(rho*g*delta_z*C)+(rho*g*h_L*C) #Pressure difference up in kPa\n", + "V_dot_upward=W_dot/delta_P_up #Flow rate through the upward pipe in m^3/s\n", + "\n", + "#Percentage Calculations\n", + "per_V=((V_dot-V_dot_upward)/V_dot)*100 #Percentage change in the flow rate\n", + "\n", + "#Result\n", + "print \"The velocity of the flow is\",round(V),\"m/s\"\n", + "print \"The pressure difference across 70m long pipe is\",round(delta_P),\"kPa\"\n", + "print \"The power required to maintain the flow is\",round(W_dot,2),\"kW\"\n", + "print \"The percentage change in the flow rate is\",round(per_V,1),\"%\"\n", + "#Answer for percentage change and flow rate through the pipe upward direction are incorrect" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity of the flow is 3.0 m/s\n", + "The pressure difference across 70m long pipe is 1291.0 kPa\n", + "The power required to maintain the flow is 4.87 kW\n", + "The percentage change in the flow rate is 14.7 %\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-2, Page No:350" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "rho=1000 #Density of water in kg/m^3\n", + "u=1.519*10**-3 #Viscosity of water in kg/m.s\n", + "L=9 #Length of the pipe in m\n", + "D=0.003 #Diameter of the pipe in m\n", + "V=0.9 #Average velocity inside the pipe of water in m/s\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "\n", + "#Calculations\n", + "#Part(a)\n", + "\n", + "Re=(rho*V*D)/u #Reynolds Number\n", + "f=64/Re #Friction Factor\n", + "h_L=(f*L*V**2)/(2*g*D) #Head Loss in m\n", + "\n", + "#Part(b)\n", + "delta_P=(f*L*V**2)/(2*D) #Pressure difference in kPa\n", + "\n", + "#Part(c)\n", + "V_dot=(V*pi*D**2)/4 #Volumetric Flow rate in m^3/s\n", + "W_dot=V_dot*delta_P*1000 #Pumping power required in W\n", + "\n", + "#Result\n", + "print \"The Head Loss is\",round(h_L,2),\"m\"\n", + "print \"The pressure drop is\",round(delta_P,1),\"kPa\"\n", + "print \"The pumping power required is\",round(W_dot,2),\"W\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Head Loss is 4.46 m\n", + "The pressure drop is 43.7 kPa\n", + "The pumping power required is 0.28 W\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-3, Page No:360" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "rho=999 #Density of water in kg/m^3\n", + "u=1.138*10**-3 #Viscosity in kg/m.s\n", + "D=0.05 #Diameter of the pipe in m\n", + "V_dot= 0.006 #Volumetric Flow rate in m^3/s\n", + "L=60 #Length of the pipe in m\n", + "e=0.002 #Relative roughness value from table\n", + "f=0.0172 #Value from Moody Chart\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "\n", + "#Calculations\n", + "V=round((V_dot*4)/(pi*D**2),2) #Velocity of the flow in the pipe in m/s\n", + "Re=(rho*V*D)/u #Reynolds Number\n", + "e_D=e/(D*1000) #Relative roughness\n", + "\n", + "#Taking the value for root f from Moody Chart as f=0.0172\n", + "delta_P=(f*L*rho*V**2)/(D*2) #Pressure Drop in N/m^2\n", + "h_L=delta_P/(rho*g) #Head Loss in m\n", + "W_pump=V_dot*delta_P #Required Power in W\n", + "\n", + "#Result\n", + "print \"The Pressure Drop is\",round(delta_P),\"N/m^2\"\n", + "print \"The head loss is\",round(h_L,2),\"m\"\n", + "print \"The Power required is\",round(W_pump),\"W\" \n", + "\n", + "#The answer for delta_P is off by 4 due to decimal accuracy in the formula\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Pressure Drop is 96536.0 N/m^2\n", + "The head loss is 9.85 m\n", + "The Power required is 579.0 W\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-4, Page No:361" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V_dot=0.35 #Volumertic flow rate in m^3/s\n", + "L=150 #Length of the pipe in m\n", + "rho=1.145 #Density of the fluid in kg/m^3\n", + "u=1.895*10**-5 #Dynamic viscosity of the fluid in kg/m.s\n", + "v=1.655*10**-5 #Kinematic Viscosity of the fluid in m^2/s\n", + "h_l=20 #Allowable head loss in m\n", + "g= 9.81 #Acceleration due to gravity in m/s^2\n", + "\n", + "#The following three equations are solved using EES hence we will be taking the values directly here\n", + "D=0.267 #Diameter of the pipe in m\n", + "f=0.0180\n", + "V=6.24 #Velocity of low in m/s\n", + "Re=100800 #Reynolds Number\n", + "\n", + "#Calculations\n", + "#Simplfying the calculations\n", + "c=V_dot**9.4\n", + "d=L/(g*h_l)\n", + "f=d**5.2\n", + "#Using Swamee-Jain Formula\n", + "D=0.66*((v*c*f)**0.04) #Diameter of the pipe in m\n", + "\n", + "#Result\n", + "print \"The diameter of the pipe is\",round(D,3),\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The diameter of the pipe is 0.271 m\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-5, Page No:362" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Deceleration\n", + "#Using the computationally simple method given in the discussion\n", + "\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "D=0.267 #Diameter in m\n", + "h_l=20 #Head loss in m\n", + "L=300 #Length of the pipe in m\n", + "v=1.655*10**-5 #Kinematic Voscosity in m^2/s\n", + "V_dot_old=0.35 #Volumetric Flow rate in m^3/s\n", + "\n", + "#Calculations\n", + "a=((3.17*v**2*L)/(g*D**3*h_l))**0.5\n", + "b=log(a)\n", + "c=((g*D**5*h_l)/L)**0.5\n", + "\n", + "V_dot_new=-0.965*b*c #Volumetric Flow rate in m^3/s\n", + "V_dot=V_dot_old-V_dot_new #Drop in the flow rate in m^/s\n", + "\n", + "print \"The drop in the flow rate is\",round(V_dot,2),\"m^3/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The drop in the flow rate is 0.11 m^3/s\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-6, Page No:370" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "D1=0.06 #Diameter of the pipe at section 1 in m\n", + "D2=0.09 #Diameter of the pipe at section 2 in m\n", + "V1=7 #Average Velocity at section 1 in m/s\n", + "K_l=0.133 # interpolating from table\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "P1=150 #Pressure head at section one in kPa\n", + "rho=1000 #Density of the fluid in kg/m^3\n", + "alpha1=1.06 #momentum correction factor\n", + "alpha2=alpha1 #momentum correction factor\n", + "C=10**-3 #Conversion factor\n", + "\n", + "#Calculations\n", + "#Applying the one dimensional continuity equation\n", + "V2=(D1**2/D2**2)*V1 #Velocity of the fluid at section 2 in m/s\n", + "\n", + "#Irreversible head loss\n", + "h_l=K_l*(V1**2/(2*g)) #Irreversible head loss in m\n", + "\n", + "#Using the energy equation\n", + "P2=P1+rho*(((alpha1*V1**2-alpha2*V2**2)*0.5)-g*h_l)*C #Pressure head at section 2 in kPa\n", + "\n", + "#Result\n", + "print \"The head loss is\",round(h_l,4),\"m\"\n", + "print \"The pressure head at section two is\",round(P2),\"kPa\"\n", + "#The answer differs due to decimal point accuracy\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The head loss is 0.3322 m\n", + "The pressure head at section two is 168.0 kPa\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-8, Page No:377" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable decleration\n", + "rho=999.7 #Density of the fluid in kg/m^3\n", + "u=1.307*10**-3 # Dynamic Viscosity in kg/m.s \n", + "e=0.00026 #Roughness of cast iron in m\n", + "V_dot=0.006 #Volumetric Flow rate in m^3/s\n", + "z2=4 #static head at section 2 in m\n", + "D=0.05 #Diameter of the pipe in m\n", + "#Kl declerations\n", + "Kl_entrance=0.5\n", + "Kl_elbow=0.3\n", + "Kl_valve=0.2\n", + "Kl_exit=1.06\n", + "f=0.0315 #Using Moody Chart and Colebrook Equation friction factor\n", + "L=89 #Length of the pipe in m \n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "\n", + "#Calculations\n", + "V=(V_dot*4)/(pi*D**2) #Average Velocity in the pipe in m/s\n", + "Re=(rho*V*D)/u #Reynolds Number\n", + "e_D=e/D\n", + "sum_Kl=Kl_entrance+2*Kl_elbow+Kl_valve+Kl_exit #Summation of all Kl\n", + "#Total Head Loss\n", + "h_l=(((f*L)/D)+sum_Kl)*(V**2/(2*g)) #Total head loss in m\n", + "\n", + "#Using Energy equation\n", + "z1=z2+h_l #Free surface of the first reservoir in m\n", + "\n", + "#Result\n", + "print \"The elevation of the free surface of the first reservoir is\",round(z1,1),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The elevation of the free surface of the first reservoir is 31.8 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8-10, Page No:385" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "rho_met=788.4 #Density of the fluid in kg/m^3\n", + "u=5.857*10**-4 #Dynamic Viscosity in kg/m.s\n", + "rho_hg=13600 #Density of mercury in kg/m^3\n", + "d=0.03 #diameter of the orifice meter in m\n", + "D=0.04 #Diameter of the pipe in m\n", + "h=0.11 #differential height of the manometer in m\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "Cd=0.61 #Coefficient of discharge\n", + "\n", + "#Calculations\n", + "beta=d/D #Diameter ratio\n", + "Ao=(pi*d**2)/4 #Area of throat in m^2\n", + "\n", + "#Pressure Drop\n", + "delta_P=(rho_hg-rho_met)*g*h #Pressure drop in m\n", + "\n", + "#Flow rate\n", + "V_dot=Ao*Cd*(((2*delta_P)/(rho_met*(1-beta**4)))**0.5) #Volumetric Flow rate in m^3/s\n", + "V=(V_dot*4)/(pi*D**2) #Average Velocity in m/s\n", + "\n", + "#Reynolds Number\n", + "Re=(rho_met*V*D)/u #Reynolds Number\n", + "\n", + "#Coefficient of Discharge\n", + "Cd_calculations=0.5959+0.0312*beta**2.1-0.184*beta**8+((91.71*beta**2.50)/Re**0.75)\n", + "\n", + "#Result\n", + "print \"The flow rate of methanol in the pipe is\",round(V_dot,5),\"m^3/s\"\n", + "print \"The average velocity of low in the pipe is\",round(V,2),\"m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The flow rate of methanol in the pipe is 0.00309 m^3/s\n", + "The average velocity of low in the pipe is 2.46 m/s\n" + ] + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |