{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

# Chapter 12: THE MOMENTUM AND MECHANICAL ENERGY EQUATIONS

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.01, page: 273

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "#Initialization of Variable\n", "V = 10 #ft/s\n", "A = 0.06 #ft2\n", "p = 1.94 #slug/ft3\n", "\n", "#calculations:\n", "Fax = -1*p*A*V**2\n", "Fay = p*A*V**2\n", "\n", "#Results\n", "print \"resultant force in x direction is\", round(Fax,2),\"(1-cos(theta)) lbf\"\n", "print \"resultant force in y direction is\", round(Fay,2),\"sin(theta) lbf\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resultant force in x direction is -11.64 (1-cos(theta)) lbf\n", "resultant force in y direction is 11.64 sin(theta) lbf\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.02, page: 275

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "p = 1.94 #slug/ft3\n", "P1 = 30 #psi\n", "V = 50 #ft/s\n", "P2 = 24 #psi\n", "A = 0.1 #ft2\n", "theta = 180 #deg\n", "\n", "#calcualtions:\n", "#force in x dirn\n", "Fax = 0\n", "#mass flow rate\n", "mdot = p*A*V\n", "#force in y dirn\n", "Fay = -2*mdot*V - (P1 + P2)*144*A\n", "\n", "#Results\n", "print \"resultant force in x direction is\", Fax,\"lbf\"\n", "print \"resultant force in y direction is\", round(Fay,0),\"lbf\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resultant force in x direction is 0 lbf\n", "resultant force in y direction is -1748.0 lbf\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.03, page: 277

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "D1 = 16 #mm\n", "Q = 0.6 #lt/s\n", "Wn = 1 #N\n", "Ww = 0.03 #N\n", "D2 = 5 #mm\n", "P1 = 464 #kPa\n", "P2 = 0 #kPa\n", "p = 999 #kg/m3\n", "\n", "#calculations:\n", "#mass flow rate\n", "mdot = p*Q/1000\n", "#areas\n", "A1 = math.pi*1E-6*(D1**2)/4\n", "A2 = math.pi*1E-6*(D2**2)/4\n", "#volumetric flow rate\n", "V1 = Q*1E-3/A1\n", "V2 = Q*1E-3/A2\n", "Fa = mdot*(V1 - V2) + Wn + Ww + P1*1000*A1 - P2*A2\n", "\n", "#Results\n", "print \"anchoring force is\",round(Fa,1),\"N\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "anchoring force is 77.8 N\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.05, page: 284

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "l = 6 #m\n", "D = 0.1 #m\n", "P1_r = 3 #m\n", "P2_r = 0.5 #m\n", "z1 = 0 #m\n", "z2 = 2 #m\n", "\n", "#calculations:\n", "hL = P1_r - P2_r + z1 - z2\n", "\n", "#Results\n", "print \"head loss in terms of height of water is\", hL, \"m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "head loss in terms of height of water is 0.5 m\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.06, page: 284

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "z1 = 100 #m\n", "V2 = 6 #m/s\n", "g = 9.81 #m/s2\n", "r = 9.8E3 #N/m3\n", "D = 1 #m\n", "\n", "#calculations:\n", "#Volumetric flow rate\n", "Q = math.pi*D**2*V2/4\n", "hL = 0 #no head loss\n", "#turbine head\n", "ht = z1 - (V2**2)/(2*g) - hL\n", "#power output\n", "Wtdot = r*Q*ht/1000\n", "\n", "#Results\n", "print \"max power output is\", round(Wtdot,0),\"kW\" \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "max power output is 4533.0 kW\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.07, page: 285

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "Wpdot = 10 #hp\n", "r = 62.4 #lbf/ft3\n", "Q = 2 #ft3/s\n", "z2 = 30 #ft\n", "z1 = 0\n", "\n", "#calculations:\n", "#pump head\n", "hp = Wpdot*550/(r*Q)\n", "#head Loss\n", "hL = z1 - z2 + hp\n", "#on a power basis, the head loss\n", "hLp = r*Q*hL/550\n", "\n", "#Results\n", "print \"head loss is\", round(hL,1),\"ft or\", round(hLp,2),\"hp\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "head loss is 14.1 ft or 3.19 hp\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.08, page: 286

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "A2 = 0.001 #m2\n", "P1 = 1 #Mpa\n", "P0 = 1 #Mpa\n", "T1 = 360 #K\n", "T0 = 360 #K\n", "k = 1.4\n", "Pb1 = 500 #kPa\n", "Pb2 = 784 #kPa\n", "V1 = 0\n", "R = 8314/28.97 #J/kg-K\n", "\n", "#calculations:\n", "Pcr = 0.528*P0*1000\n", "if Pb1 < Pcr:\n", " M1 = 1\n", "\n", "#exit Temp\n", "T2 = T0/(1 + (k - 1)*M1**2/2)\n", "#exit Velocity\n", "V2 = M1*(k*R*T2)**0.5\n", "#mass flow rate\n", "mdot1 = Pcr*1000*A2*V2/(R*T2)\n", "#Mach at 2\n", "M2 = (2/(k - 1)*((P0*1E6/(Pb2*1E3))**((k-1)/k) - 1))**0.5\n", "#exit Temp\n", "T2 = T0/(1 + (k - 1)*M2**2/2)\n", "#exit Velocity\n", "V2 = M2*(k*R*T2)**0.5\n", "#mass flow rate\n", "mdot2 = Pb2*1000*A2*V2/(R*T2)\n", "\n", "#Results\n", "print \"the mass flow rate and exit mach no at back pressure of 500 kPa are\",round(mdot1,2),\"kg/s and\", M1\n", "print \"the mass flow rate and exit mach no at back pressure of 784 kPa are\",round(mdot2,2),\"kg/s and\", round(M2,1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the mass flow rate and exit mach no at back pressure of 500 kPa are 2.13 kg/s and 1\n", "the mass flow rate and exit mach no at back pressure of 784 kPa are 1.79 kg/s and 0.6\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

## Example 12.09, page: 286

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "\n", "# Initialization of Variable\n", "A2 = 2.4 #in2\n", "P1 = 100 #lbf/in2\n", "P0 = 100 #lbf/in2\n", "T1 = 500 #degR\n", "T0 = 500 #degR\n", "At = 1 #in2\n", "k = 1.4\n", "V1 = 0\n", "R = 1548/28.97 #ft.lbf/lb-degR\n", "\n", "#calculations:\n", "#a)\n", "#mach at throat\n", "Mta = 0.7\n", "#From Table 12.2\n", "#At/A* = At_As\n", "At_Asa = 1.09437\n", "A2_Asa = A2*At_Asa/At\n", "#from Table 12.2\n", "M2a = 0.24\n", "T2_T0a = 0.988\n", "P2_P0a = 0.959\n", "T2a = T0*T2_T0a\n", "P2a = P0*P2_P0a\n", "#velocity at exit\n", "V2a = M2a*(k*R*T2a*32.2)**0.5\n", "#mass flow rate\n", "mdota = P2a*A2*V2a/(R*T2a)\n", "\n", "#b)\n", "#from Table 12.2\n", "M2b = 0.26\n", "T2_T0b = 0.986\n", "P2_P0b = 0.953\n", "T2b = T0*T2_T0b\n", "P2b = P0*P2_P0b\n", "#velocity at exit\n", "V2b = M2b*(k*R*T2b*32.2)**0.5\n", "#mass flow rate\n", "mdotb = P2b*A2*V2b/(R*T2b)\n", "\n", "#c)\n", "#from Table 12.2\n", "M2c = 2.4\n", "P2_P0c = 0.0684\n", "P2c = P0*P2_P0c\n", "#mass flow rate (nozzle is choked same as b)\n", "mdotc = mdotb\n", "\n", "#d)\n", "#from Table 12.2\n", "Mxd = 2.4\n", "Pxd = 6.84 #lbf/in2\n", "Myd = 0.52\n", "M2d = Myd\n", "Pyd = 6.5533*Pxd\n", "P2d = Pyd\n", "#mass flow rate (nozzle is choked same as b)\n", "mdotd = mdotb\n", "\n", "#e)\n", "Ax = 2 #in2\n", "Axs = At\n", "#from table 12.2\n", "Ax_Axs = 2 #Ax/Ax*\n", "Mxe = 2.2\n", "#Poy/Pox\n", "Poy_Pox = 0.62812\n", "#A2/Ay*\n", "A2_Ays = (A2/Axs)*Poy_Pox\n", "M2e = 0.43\n", "#P2/Poy\n", "P2_Poy = 0.88\n", "Pox = P0\n", "P2e = P2_Poy*Poy_Pox*Pox\n", "#mass flow rate (nozzle is choked same as b)\n", "mdote = mdotb\n", "\n", "#Results\n", "print \"a)the mass flow rate is\",round(mdota,2),\"lb/s or\", round(mdota/32.1740,4),\"slug/s, exit pressure is\",round(P2a,1),\"lbf/in2 and exit mach number is\",M2a\n", "print \"b)the mass flow rate is\",round(mdotb,2),\"lb/s or\", round(mdotb/32.1740,4),\"slug/s, exit pressure is\",round(P2b,1),\"lbf/in2 and exit mach number is\",M2b\n", "print \"c)the mass flow rate is\",round(mdotc,2),\"lb/s or\", round(mdotc/32.1740,4),\"slug/s, exit pressure is\",round(P2c,2),\"lbf/in2 and exit mach number is\",M2c\n", "print \"d)the mass flow rate is\",round(mdotd,2),\"lb/s or\", round(mdotd/32.1740,4),\"slug/s, exit pressure is\",round(P2d,2),\"lbf/in2 and exit mach number is\",M2d\n", "print \"e)the mass flow rate is\",round(mdote,2),\"lb/s or\", round(mdote/32.1740,4),\"slug/s, exit pressure is\",round(P2e,1),\"lbf/in2 and exit mach number is\",M2e\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)the mass flow rate is 2.28 lb/s or 0.071 slug/s, exit pressure is 95.9 lbf/in2 and exit mach number is 0.24\n", "b)the mass flow rate is 2.46 lb/s or 0.0765 slug/s, exit pressure is 95.3 lbf/in2 and exit mach number is 0.26\n", "c)the mass flow rate is 2.46 lb/s or 0.0765 slug/s, exit pressure is 6.84 lbf/in2 and exit mach number is 2.4\n", "d)the mass flow rate is 2.46 lb/s or 0.0765 slug/s, exit pressure is 44.82 lbf/in2 and exit mach number is 0.52\n", "e)the mass flow rate is 2.46 lb/s or 0.0765 slug/s, exit pressure is 55.3 lbf/in2 and exit mach number is 0.43\n" ] } ], "prompt_number": 8 } ], "metadata": {} } ] }