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+{
+ "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": {}
+ }
+ ]
+} \ No newline at end of file