{ "metadata": { "name": "", "signature": "sha256:7a16c4d96ee700a37dba4a242e55bbbe161eeaa4c40448cf9c981c1c38399b2e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 6 : Momentum and Forces in Fluid Flow" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.1 Page No : 153" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "g = 9.81 \t#kN/m**3\n", "V2 = 12. \t#velocity - m/s\n", "V3 = 12. \t#m/s\n", "A2 = 10.**2\n", "A1 = 15.**2\n", "A3 = 7.5**2\n", "t1 = 15. \n", "t2 = 30.\n", "\t\n", "#calculations\n", "V1 = (A2*V2 + A3*V3)/A1\n", "Q1 = round(math.pi /4 *A1*10**-4 *V1,3)\n", "Q2 = round(math.pi /4 *A2*10**-4 *V2,3)\n", "Q3 = round(math.pi /4 *A3*10**-4 *V3,3)\n", "P1g = round(V3**2 /(2*g) - V1**2 /(2*g),2)\n", "P1 = round(P1g*g,1)\n", "rho = 10**3 \n", "V2x = V2*math.cos(math.radians(t1))\n", "V3x = V3*math.cos(math.radians(t2))\n", "V1x = V1\n", "Fx = -P1*A1*10**-4 + (rho*Q2*V2x + rho*Q3*V3x - rho*Q1*V1x)\n", "Fx = Fx*10**-3 \n", "V2y = V2*math.sin(math.radians(t1))\n", "V3y = -V3*math.sin(math.radians(t2))\n", "V1y = 0\n", "Fy = rho*Q2*V2y +rho*Q3*V3y -rho*Q1*V1y\n", "Fy = Fy*10**-3\n", "Fnlx = 0.659 - Fx\n", "\n", "#Results\n", "print \"Force in x directio = %.3f kN\"%(Fx)\n", "print \" Force in y direction = %.3f kN\"%(Fy)\n", "print \"(Fl/n)x = %.3f kN\"%Fnlx\n", "print \"(Fl/n)y = %.3f kN\"%-Fy\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Force in x directio = 0.415 kN\n", " Force in y direction = -0.026 kN\n", "(Fl/n)x = 0.244 kN\n", "(Fl/n)y = 0.026 kN\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.2 Page No : 155" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\t\n", "#Initialization of variables\n", "V1x = 100. \t#ft/sec\n", "V2x = 0.866*95\n", "V1y = 0.\n", "V2y = .5*95\n", "A1 = 0.0218 \t#ft**2\n", "\t\n", "#calculations\n", "Q = A1*V1x\n", "rho = 1.94\n", "Fx = rho*Q*(V2x-V1x)\n", "Fxr = -Fx\n", "Fy = rho*Q*(V2y-V1y)\n", "\t\n", "#Results\n", "print \"Horizontal force on the blade = %.1f lb\"%(Fxr)\n", "print \" Vertical force on the blade = %.f lb\"%(Fy)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Horizontal force on the blade = 75.0 lb\n", " Vertical force on the blade = 201 lb\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.3 Page No : 159" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "v2 = 36. \t#fps\n", "beta = 150. \t#degrees\n", "u = 60. \t#velocity - fps\n", "rho = 1.94\n", "Qd = 0.0218\n", "V1 = 100. \t#fps\n", "gam = 62.4\n", "g = 32.2\n", "\t\n", "#calculations\n", "v2s = v2*math.sin(math.radians(beta))\n", "v2c = u+v2*math.cos(math.radians(beta))\n", "V2 = 34. \t#fps\n", "alpha = 32 \t #degrees\n", "Fx = rho*Qd*(v2c-V1)*(V1-u)\n", "Fy = -rho*Qd*(V1-u)*v2s\n", "Fx2 = rho*Qd*V1*(v2c-V1)\n", "HPin = gam*Qd*V1*(V1**2 /(2*g))/550\n", "HPout = gam*Qd*V1*(V2**2 /(2*g))/550\n", "HPtransfer = -Fx2*u/550\n", "HPfl = HPin-HPout-HPtransfer\n", "\t\n", "#Results\n", "print \"Force exerted by water on the vane = %d lb\"%(Fx2)\n", "print \" Friction loss = %.1f hp \"%(HPfl)\n", "\n", "# rounding off error" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Force exerted by water on the vane = -301 lb\n", " Friction loss = 1.1 hp \n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.4 Page No : 162" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "z1 = 35. \t#ft\n", "z3 = 20. \t#ft\n", "P1 = 30. \t#psi\n", "g = 32.2\n", "z2 = 10. \t#ft\n", "d2 = 4. \t#in\n", "rho = 1.94\n", "be = 20. \t#degrees\n", "W = 150. \t#lb\n", "\t\n", "#calculations\n", "V3 = math.sqrt(2*g*(P1*144/55 + z1-z3))\n", "Q = 3.81 \t#cfs\n", "V2 = 43.6 \t#fps\n", "P2 = round(55*(z3+ V3**2/(2*g) - z2 - V2**2/(2*g))/144,1)\n", "Fx = round(P2*math.pi/4 *d2**2 - rho*55/62.4 *Q*(V3*math.cos(math.radians(be)) - V2) )\n", "Fy = rho*55/62.4 *Q*(V3*math.sin(math.radians(be)) ) + W\n", "Fres = math.sqrt(Fx**2 + Fy**2)\n", "Fsx = rho*Q*55/62.4*(V3*math.cos(math.radians(be)) )\n", "\n", "#calculations\n", "print \" resultant force = %.f lb\"%(Fy)\n", "print \" horizontal component of force = %d lb\"%(Fsx)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " resultant force = 323 lb\n", " horizontal component of force = 475 lb\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.5 Page No : 168" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "omega = 300. \t#rpm\n", "r1 = 1.6 \t #ft\n", "Q = 120. \t #cfs\n", "z = 0.8 \t#ft\n", "beta1 = 80. \t#degrees\n", "r2 = 1. \t#ft\n", "rho = 1.94\n", "g = 32.2\n", "gam = 62.4\n", "\t\n", "#calculations\n", "print (\"part a\")\n", "u1 = round((2*math.pi/60)*omega*r1,1)\n", "Vr1 = round(Q/(2*math.pi*r1*z),2)\n", "v1 = round(Vr1/math.sin(math.radians(beta1)),2)\n", "v2c = round(v1*math.cos(math.radians(beta1)),1)\n", "V1c = round(u1+v2c,1)\n", "u2 = round((2*math.pi/60)*omega*r2,1)\n", "Vr2 = round(Vr1*(r1/r2),1)\n", "beta2 = Vr2/u2 \n", "beta = 37.2\n", "print \"required Blade angle = %.1f degrees\"%(180-beta)\n", "print (\"part b\")\n", "T = round(rho*Q*(r1*V1c),-2)\n", "power = round(T*u2,-3)\n", "print \"Torque exerted = %d ft lb/s\"%(power)\n", "print (\"part c\")\n", "h2 = round(u1*V1c/g,1)\n", "Power = round(gam*Q*h2,-3)\n", "print \"Torque exerted = %d ft lb/s\"%(Power)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "part a\n", "required Blade angle = 142.8 degrees\n", "part b\n", "Torque exerted = 619000 ft lb/s\n", "part c\n", "Torque exerted = 619000 ft lb/s\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.6 Page No : 174" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\n", "#Initialization of variables\n", "V1 = 150.*44/30\n", "Q = 20000./2\n", "d = 6.5 \t #diameter - ft\n", "rho = 0.072\n", "\t\n", "#calculations\n", "A = math.pi/4 *(d)**2\n", "V = int(Q/A)\n", "dV = 2*(V-V1)\n", "Ft = round(rho/32.2 *Q*2*dV,-1)\n", "eta = round(1/(1+ dV/(2*V1)),2)\n", "dP = Ft/2 /(math.pi/4) /d**2\n", "hpp = Q*dP/550\n", "\n", "#Results\n", "print \"pressure rise = %d psf\"%(dP)\n", "print \" horsepower input = %d hp \"%(round(hpp,-1))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "pressure rise = 109 psf\n", " horsepower input = 1980 hp \n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.7 Page No : 175" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\t\n", "#Initialization of variables\n", "V1 = 8.02 \t#fps\n", "V2 = 16.04 \t#fps\n", "Q = 481. \t#cfs\n", "rho = 1.94\n", "A = 10*6\n", "d = 3.\n", "\t\n", "#calculations\n", "Fx = 62.4*d*A - 62.4*d/2 *A/2 - rho*Q*(V2-V1)\n", "V1m = 2.56 \t#m/s\n", "V2m = 5.12 \t#m/s\n", "Qm = 15.4 \t#m**2/s\n", "dm = 1\n", "Am = 2*3\n", "rhom = 1\n", "Fxm = 9.81*dm*Am - 9.81*dm/2 *Am/2 - rhom*Qm*(V2m-V1m)\n", "\t\n", "#Results\n", "print \"Force in x- direction = %d lb\"%(Fx)\n", "print \"Force in x- direction = %.1f kN\"%(Fxm)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Force in x- direction = 940 lb\n", "Force in x- direction = 4.7 kN\n" ] } ], "prompt_number": 9 } ], "metadata": {} } ] }