{ "metadata": { "name": "", "signature": "sha256:56204579c9dff23fd133fce17f3b8e6b8ac01dae9f7f133693b953a21d5ed34c" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 2: Pressure and Head" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.1, Page 30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " #Initializing the variables\n", "z1 = 0; #Taking Ground as reference\n", "z2 = -30 #Depth\n", "rho = 1025 #Density\n", "g = 9.81 #Acceleration due to gravity\n", "\n", " #Calculation\n", "pressureIncrease = -rho*g*(z2-z1);\n", "\n", "print \"Increase in Pressure (KN/m2):\",round(pressureIncrease/1000,1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Increase in Pressure (KN/m2): 301.7\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.2, Page 34" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables\n", "p1 = 22.4*10**3 #Initial Pressure\n", "z1 = 11000 #Initial Height\n", "z2 = 15000 #final Height\n", "g = 9.81 #Acceleration due to gravity\n", "R = 287; #Gas Constant\n", "T = 273-56.6 #Temperature \n", "\n", " #Calculations\n", "p2 = p1*math.exp(-g*(z2-z1)/(R*T));\n", "rho2=p2/(R*T);\n", " \n", "print \"Final Pressure (kN/m2):\",round(p2/1000,2)\n", "print \"Final Density (kg/m3):\",round(rho2,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Final Pressure (kN/m2): 11.91\n", "Final Density (kg/m3): 0.192\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.3, Page 37" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "p1 = 101*10**3 #Initial Pressure\n", "z1 = 0 #Initial Height\n", "z2 = 1200 #Final Height\n", "T1 = 15+273 #Initial Temperature\n", "g = 9.81 #Acceleration due to gravity\n", "gamma = 1.4 #Heat capacity ratio\n", "R = 287 #Gas Constant\n", "\n", " #Calculations\n", "p2 = p1*(1-g*(z2-z1)*(gamma-1)/(gamma*R*T1))**(gamma/(gamma-1));\n", "dT_dZ = -(g/R)*((gamma-1)/gamma);\n", "T2 = T1 + dT_dZ*(z2-z1);\n", "rho2 = p2/(R*T2);\n", "\n", "print \"Final Pressure (kN/m2) :\",round(p2/1000,2)\n", "print \"Temprature (in degree celcius):\",round(T2-273,1)\n", "print \"Density (kg/m^3) :\",round(rho2,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Final Pressure (kN/m2) : 87.33\n", "Temprature (in degree celcius): 3.3\n", "Density (kg/m^3) : 1.101\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.4, Page 39" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables\n", "p1 = 101*10**3 #Initial Pressure\n", "z1 = 0 #Initial Height\n", "z2 = 7000 #Final Height\n", "T1 = 15+273 #Initial Temperature\n", "g = 9.81 #Acceleration due to gravity\n", "R = 287 #Gas Constant\n", "dT = 6.5/1000 #Rate of Variation of Temperature\n", "\n", " #Calculations\n", "p2 = p1*(1-dT*(z2-z1)/T1)**(g/(R*dT));\n", "T2 = T1 - dT*(z2-z1);\n", "rho2 = p2/(R*T2);\n", "\n", "\n", "print \"Final Pressure (kN/m^2) :\",round(p2/1000,2)\n", "print \"Final Density (kg/m^3 ):\",round(rho2,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Final Pressure (kN/m^2) : 40.89\n", "Final Density (kg/m^3 ): 0.588\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.5, Page 44" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", " #Initializing the variables\n", "p = 350*10**3; #Gauge Pressure\n", "pAtm = 101.3*10**3; #Atmospheric Pressure \n", "rhoW = 1000; #Density of Water\n", "sigma = 13.6; #Relative Density of Mercury\n", "g = 9.81 #Acceleration due to gravity\n", "\n", " #Calculations\n", "def Head(rho):\n", " head = p/(rho*g);\n", " return head\n", "rhoM = sigma*rhoW;\n", "pAbs = p + pAtm;\n", "\n", "print \"\\nPart(a)- Equivalent head of water (m) :\",round(Head(rhoW),2)\n", "print \"\\nPart(b)- Equivalent head of water (m) :\",round(Head(rhoM),2)\n", "print \"\\nAbsolute pressure (kN/m^2) :\",pAbs/1000" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Part(a)- Equivalent head of water (m) : 35.68\n", "\n", "Part(b)- Equivalent head of water (m) : 2.62\n", "\n", "Absolute pressure (kN/m^2) : 451.3\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.6, Page 45" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " \n", "\n", " #Initializing the variables\n", "rho = 10**3; #Density of water\n", "h = 2; #Height\n", "g = 9.81; #Acceleration due to gravity\n", "\n", " #Calculations\n", "p=rho*h*g; \n", "\n", "print \"Gauge pressure (k/m2) :\",p/1000" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Gauge pressure (k/m2) : 19.62\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.7, Page 46" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables\n", "rho = 0.8*10**3; #Density of fluid\n", "rhoM = 13.6*10**3; #Density of manometer liquid\n", "g = 9.81 #Acceleration due to gravity\n", "\n", " #Calculations\n", "def fluidPressure(h1,h2):\n", " P = rhoM*g*h2-rho*g*h1;\n", " return P\n", "\n", "p1=fluidPressure(0.5,0.9)/1000\n", "p2=fluidPressure(0.1,-0.2)/1000\n", "\n", "print \"!-----Part (a)-----! \\nGauge pressure (kN/m2) :\",round(p1,2)\n", "print \"\\n!-----Part (b)-----! \\nGauge pressure (kN/m2) :\",round(p2,2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "!-----Part (a)-----! \n", "Gauge pressure (kN/m2) : 116.15\n", "\n", "!-----Part (b)-----! \n", "Gauge pressure (kN/m2) : -27.47\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.8, Page 47" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables\n", "rho = 10**3; #Density of fluid\n", "rhoM = 13.6*10**3; #Density of manometer liquid\n", "g = 9.81; #Acceleration due to gravity\n", "H = 0.3; # Differnce in height = b-a as in text\n", "h = 0.7;\n", "\n", " #Calculations\n", "result = rho*g*H + h*g*(rhoM-rho);\n", "\n", "print \"Pressure difference (kN/m^2):\", round(result/1000,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Pressure difference (kN/m^2): 89.467\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.9, Page 50" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "\n", "\n", " #Initializing the variables\n", "rho = 10**3; #Density of fluid\n", "rhoM = 0.8*10**3; #Density of manometer liquid\n", "g = 9.81; #Acceleration due to gravity\n", "a = 0.25;\n", "b = 0.15;\n", "h = 0.3;\n", " #Calculations\n", "def PressureDiff(a,b,h,rho,rhoM):\n", " P = rho*g*(b-a) + h*g*(rho-rhoM);\n", " return P\n", "print \"The presure difference,if the top of the manometer is filled with\"\n", "print \"(a) air :\",PressureDiff(a,b,h,rho,0)/1000, \" N/m^2\"\n", "print \"(b) oil of relative density 0.8. :\",PressureDiff(a,b,h,rho,rhoM), \"N/m^2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The presure difference,if the top of the manometer is filled with\n", "(a) air : 1.962 N/m^2\n", "(b) oil of relative density 0.8. : -392.4 N/m^2\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.10, Page 54" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", " #Initializing the variables\n", "phi = 30; #30 degree\n", "h = 1.2 ; # Height of tank\n", "l = 2; # Length of tank\n", "\n", " #Calculations\n", "def SurfaceAngle(a,phi):\n", " g=9.81; # m/s**2 \n", " Theta = math.atan(-a*math.cos(math.radians(phi))/(g+a*math.sin(math.radians(phi)))); \n", " return Theta\n", "\n", " #case (a) a = 4\n", "\n", "print \"ThetaA (degree) :\",round(180 + 180/math.pi*SurfaceAngle(4,phi),2)\n", "\n", " #Case (b) a = - 4.5\n", "tanThetaR = math.tan((SurfaceAngle(-4.5,phi)));\n", "\n", "print \"\\nThetaR (degree) :\",round(SurfaceAngle(-4.5,phi)*180/math.pi,2)\n", "\n", "Depth = h - l*tanThetaR/2;\n", "print \"\\nMaximum Depth of tank (m) :\",round(Depth,4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "ThetaA (degree) : 163.65\n", "\n", "ThetaR (degree) : 27.27\n", "\n", "Maximum Depth of tank (m) : 0.6845\n" ] } ], "prompt_number": 4 } ], "metadata": {} } ] }