{ "metadata": { "name": "", "signature": "sha256:5a87247e3e7d335ec3f93a6763434ef47db612054d0c0f12922c9d7638e3f184" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 15 : Impulse Turbines" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 15.1 Page No : 486" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from numpy import *\n", "\t\n", "#Initialization of variables\n", "z2 = 500.\t#ft\n", "z1 = 300.\t#ft\n", "D = array([1, 1.5, 2 ,2.5, 3, 4, 6])\n", "g = 32.2\n", "gam = 62.4\n", "\t\n", "#calculations\n", "Dj = D/12\n", "Vj = sqrt((z2-z1)*2*g/(1.04 + 640.*Dj**4))\n", "Aj = math.pi/4 *Dj**2\n", "Q = Aj*Vj\n", "Pjet = gam*Q*Vj**2 /(2*g) /550\n", "Pj = max(Pjet)\n", "for i in range(0,len(Pjet)):\n", " if(Pjet[i] == Pj):\n", " break\n", " \n", "diameter = D[i]\n", "\t\n", "#Results\n", "print \"Dj,in Dj,ft Vj,fps Aj,ft**2 Q=AjVj,cfs Pjet,hp\"\n", "for i in range(len(D)):\n", " print \"%5.1f %5.3f %5.f %7.4f %5.2f %5.1f\"%(D[i],Dj[i],Vj[i],Aj[i],Q[i],Pjet[i])\n", "print \"Thus a pipe of %d in will be the optimum\"%(diameter)\n", "\n", "# answer are slightly different because of rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Dj,in Dj,ft Vj,fps Aj,ft**2 Q=AjVj,cfs Pjet,hp\n", " 1.0 0.083 110 0.0055 0.60 12.7\n", " 1.5 0.125 104 0.0123 1.27 24.2\n", " 2.0 0.167 92 0.0218 2.00 29.6\n", " 2.5 0.208 76 0.0341 2.58 26.1\n", " 3.0 0.250 60 0.0491 2.96 19.0\n", " 4.0 0.333 38 0.0873 3.31 8.4\n", " 6.0 0.500 18 0.1963 3.48 1.9\n", "Thus a pipe of 2 in will be the optimum\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 15.2 Page No : 498" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from sympy.functions.elementary.trigonometric import acot\n", "\t\n", "#Initialization of variables\n", "phi = 0.46\n", "g = 32.2\n", "k = 0.44\n", "cv = 0.98\n", "d = 10. \t#in\n", "A = 0.545 \t #ft**2\n", "beta = 160. \t#degrees\n", "\t\n", "#calculations\n", "u = phi*math.sqrt(2*g)\n", "V1 = cv*math.sqrt(2*g)\n", "gQ = 62.4*A*V1\n", "T = d/2 *gQ/g *(1 - math.cos(math.radians(beta)) /math.sqrt(1+k) )*math.sqrt(2*g)*(cv-phi)\n", "Power = T*2*u/d\n", "\t\n", "#Results\n", "print \"Torque required = %d ft lb\"%(T)\n", "print \" Power transferred = %d ft lb/s\"%(Power)\n", "Pi = gQ\n", "He = Power/Pi\n", "print \" Hydraulic efficiency = %.2f\"%(He)\n", "v1 = V1-u\n", "v2 = v1/(math.sqrt(1+k))\n", "hl = k*v2**2 /(2*g)\n", "print \"Head loss in bucket friction = %.1f %%\"%(hl*100)\n", "Hn = (1/cv**2 -1)*V1**2 /(2*g)\n", "print \" Head loss in nozzle = %.4f\"%(Hn*100)\n", "V2cos = u+v2*math.cos(math.radians(beta))\n", "V2sin = v2*math.sin(math.radians(beta))\n", "#alpha = math.degrees(1/math.atan(V2cos/V2sin))\n", "alpha = math.degrees(acot(V2cos/V2sin))\n", "V2 = V2sin/math.sin(math.radians(alpha))\n", "Hd = V2**2/(2*g)\n", "print \" Head loss at discharge = %.1f %%\"%(Hd*100)\n", "Htotal = Hd+Hn+hl\n", "print \" Total head loss = %.2f %%\"%(Htotal*100)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque required = 309 ft lb\n", " Power transferred = 228 ft lb/s\n", " Hydraulic efficiency = 0.85\n", "Head loss in bucket friction = 8.3 %\n", " Head loss in nozzle = 3.9600\n", " Head loss at discharge = 2.5 %\n", " Total head loss = 14.70 %\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 15.3 Page No : 501" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "cv = 0.98\n", "g = 32.2\n", "h = 1320. \t#ft\n", "A = 0.196 \t#ft**2\n", "eta = 0.85\n", "ne = 400.\n", "phi = 0.45\n", "\t\n", "#calculations\n", "V = cv*math.sqrt(2*g*h)\n", "Q = A*V\n", "bhp = eta*62.4*Q*h/550\n", "ns = ne*math.sqrt(bhp) /h**(5./4)\n", "u = phi*math.sqrt(2*g*h)\n", "D = u*60/math.pi/ne\n", "\t\n", "#Results\n", "print \"Pitch diameter = %.2f ft\"%(D)\n", "\n", "\n", "# part b\n", "#Initialization of variables\n", "cv = 0.98\n", "g = 32.2\n", "h = 1320. \t#ft\n", "A = 0.196 \t#ft**2\n", "eta = 0.85\n", "ne = 400.\n", "phi = 0.45\n", "\t\n", "#calculations\n", "V = cv*math.sqrt(2*g*h)\n", "Q = A*V/3\n", "bhp = eta*62.4*Q*h/550\n", "ne2 = 600.\n", "ns1 = ne2*math.sqrt(bhp) /h**(5./4)\n", "D = 2500./ne2\n", "Dj = math.sqrt(Q*4/V/math.pi)\n", "\t\n", "#Results\n", "print \" Jet diameter = %.3f ft\"%(Dj)\n", "print \" Specific speed = %.2f \"%(ns1)\n", "print \" Pitch Diameter = %.2f ft\"%(D)\n", "print \" Operating speed = %d rpm\"%(ne2)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Pitch diameter = 6.26 ft\n", " Jet diameter = 0.288 ft\n", " Specific speed = 3.68 \n", " Pitch Diameter = 4.17 ft\n", " Operating speed = 600 rpm\n" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }