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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:4641f495fb637b43843e8fcd55506866f439259b641b4627c67482beed84d471"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4 : Conservation Principle of Momentum"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.1 Page No : 111"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "Q = 0.2 \t\t\t#m**3/s\n",
+ "v = 30. \t\t\t#m/s\n",
+ "angle = 120. \t\t\t#degrees\n",
+ "rho = 1000. \t\t\t#kg/m**3\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "Rx = rho*Q*(v-v*math.cos(math.radians(angle)))\n",
+ "Ry = rho*Q*v*math.sin(math.radians(angle))\n",
+ "R = math.sqrt(Rx**2 +Ry**2)\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"Resultant force = %.2f kN\"%(R/1000)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant force = 10.39 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3 Page No : 112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "angle = 45. \t\t#degrees\n",
+ "p1 = 150.*10**3 \t#pressure at inlet - N/m**2\n",
+ "Q = 0.5 \t\t\t#rate of flow - m**3/s\n",
+ "d1 = 60. \t\t\t#cm\n",
+ "d2 = 30. \t\t\t#cm\n",
+ "rho = 1000. \t\t#kg/m**3\n",
+ "g = 9.81 \t\t\t#m/s**2\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "V1 = Q/(math.pi/4 *(d1/100)**2)\n",
+ "V2 = V1*(d1/d2)**2\n",
+ "P2 = rho*g*(p1/(rho*g) + V1**2 /(2*g) -V2**2 /(2*g))\n",
+ "Rx = p1*math.pi/4*(d1/100)**2 - P2*math.pi/4 *(d2/100)**2 *math.cos(math.radians(angle)) -rho*Q*(V2*math.cos(math.radians(angle)) -V1)\n",
+ "Ry = P2*math.pi/4 *(d2/100)**2 *math.sin(math.radians(angle)) + rho*Q*(V2*math.sin(math.radians(angle)))\n",
+ "R = math.sqrt(Rx**2 + Ry**2)\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"resultant force = %.2f kN\"%(R/1000)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resultant force = 35.58 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4 Page No : 113"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "Q = 20.*10**3 \t\t\t#discharge - cc/s\n",
+ "depth = 4. \t\t\t#m\n",
+ "d = 5. \t \t\t#cm\n",
+ "g = 9.81 \t\t \t#m/s**2\n",
+ "rho = 10.**3 \t\t\t#kg/m**3\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "V1 = Q/(math.pi/4 *d**2) /100\n",
+ "V2 = math.sqrt(2*g*(V1**2/(2*g) + depth))\n",
+ "W = rho*Q*(V2-V1)/10**6\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"weight of water = %d N\"%(W)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "weight of water = 66 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No : 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "g = 9.81 \t \t\t#m/s**2\n",
+ "rho = 10.**3 \t\t\t#kg/m**3\n",
+ "V = 50. \t\t \t#velocity - m/s\n",
+ "u = 20. \t\t\t #m/s\n",
+ "A = 6./10**4 \t\t\t#area - m**2\n",
+ "angle = 180. \t\t\t#degrees\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "Vr = V-u\n",
+ "rq = rho*A*Vr\n",
+ "Rx = -rq*(Vr*math.cos(math.radians(angle)) - Vr)\n",
+ "Rx2 = -rho*A*V*(Vr*math.cos(math.radians(angle)) -Vr)\n",
+ "power = Rx2*u\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"Force exetred on fluid = %d N\"%(Rx)\n",
+ "print \" Force transferred in case 2 = %d N\"%(Rx2)\n",
+ "print \" Power transferred in case 2 = %d kW\"%(power/1000)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force exetred on fluid = 1080 N\n",
+ " Force transferred in case 2 = 1800 N\n",
+ " Power transferred in case 2 = 36 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6 Page No : 119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "g = 9.81 \t\t\t#m/s**2\n",
+ "rho = 10.**3 \t\t#kg/m**3\n",
+ "Vr = 10. \t\t\t#m/s\n",
+ "u = 8.5 \t\t\t#m/s\n",
+ "A = 250./10**4 \t\t#m**2\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "V = Vr-u\n",
+ "Q = A*Vr\n",
+ "R = rho*Q*V\n",
+ "P = R*u\n",
+ "eth = 1/(1+ V/(2*u))\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"Power required = %.3f kW\"%(P/1000)\n",
+ "print \" Efficiency of jet propulsion = %.0f percent\"%(eth*100)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power required = 3.188 kW\n",
+ " Efficiency of jet propulsion = 92 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.7 Page No : 123"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "g = 9.81 \t\t\t#m/s**2\n",
+ "rho = 10.**3 \t\t#kg/m**3\n",
+ "v1 = 20. \t\t\t#m/s\n",
+ "v2 = 5. \t\t\t#m/s\n",
+ "r1 = 50./100 \t\t#cm\n",
+ "r2 = 30./100 \t\t#cm\n",
+ "a1 = 20. \t\t\t#degrees\n",
+ "a2 = 80. \t\t\t#degrees\n",
+ "N = 300. \t\t\t#rpm\n",
+ "Q = 5. \t\t\t #m**3/s\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "u1 = round(math.pi*2*r1*N/60,1)\n",
+ "u2 = round(math.pi*2*r2*N/60,2)\n",
+ "T = rho*Q*(r1*v1*math.cos(math.radians(a1)) - r2*v2*math.cos(math.radians(a2)))\n",
+ "H = 1/g *(u1*v1*math.cos(math.radians(a1)) - u2*v2*math.cos(math.radians(a2)))\n",
+ "power = rho*g*Q*H\n",
+ "\t\n",
+ " \n",
+ "#results\n",
+ "print \"torque = %d N m\"%(T)\n",
+ "print \" Heat = %.1f m\"%(H)\n",
+ "print \" Power = %d kW\"%(power/10**3)\n",
+ "\n",
+ "# Note :The answers given in textbook are a bit different due to rounding off error. please check using calculator."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "torque = 45682 N m\n",
+ " Heat = 29.2 m\n",
+ " Power = 1434 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.8 Page No : 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\t\t\t\n",
+ "#Initialization of variables\n",
+ "g = 9.81 \t\t\t#m/s**2\n",
+ "rho = 10.**3 \t\t#kg/m**3\n",
+ "d1 = 0.05 \t\t\t#m\n",
+ "d2 = 0.3 \t\t\t#m\n",
+ "N = 1800. \t\t\t#rpm\n",
+ "Q = 0.425/60 \t\t#m**3/s\n",
+ "\t\t\t\n",
+ "#calculations\n",
+ "u1 = math.pi*d1*N/60\n",
+ "u2 = math.pi*d2*N/60\n",
+ "T = rho*Q*(d2*u2 - d1*u1)/2\n",
+ "\t\t\t\n",
+ "#results\n",
+ "print \"Torque supplied = %.1f Nm\"%(T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Torque supplied = 29.2 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-19 19:08:13 +0000