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author | tslee | 2014-11-27 17:17:59 +0530 |
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committer | tslee | 2014-11-27 17:17:59 +0530 |
commit | 6e3407ba85ae84e1cee1ae0c972fd32c5504d827 (patch) | |
tree | b89808101c39b1db1e3793eada2c8b702f856606 /Fluid_Mechanics_With_Engineering_Applications/ch9.ipynb | |
parent | 36a03d6d76bac315dba73b2ba9555c7e3fe0234f (diff) | |
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diff --git a/Fluid_Mechanics_With_Engineering_Applications/ch9.ipynb b/Fluid_Mechanics_With_Engineering_Applications/ch9.ipynb new file mode 100644 index 00000000..569ffde1 --- /dev/null +++ b/Fluid_Mechanics_With_Engineering_Applications/ch9.ipynb @@ -0,0 +1,494 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e6f28e03dfd837b5aed00ee85654c1040a3b0c8129a67f41e8f2e4ba487b8f35" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9 : Steady Flow of Compressible Fluids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1 Page No : 268" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\n", + "#Initialization of variables\n", + "T2 = 30. \t#C\n", + "T1 = 20. \t#C\n", + "cv = 716.\n", + "m = 15. \t#kg\n", + "cp = 1003.\n", + "\t\n", + "#calculations\n", + "di = cv*(T2-T1)\n", + "dU = di*m\n", + "dh = cp*(T2-T1)\n", + "dH = dh*m\n", + "\t\n", + "#Results\n", + "print \"Change in Internal energy = %d N m\"%(dU)\n", + "print \" Change in Enthalpy = %d Nm\"%(round(dH,-3))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Change in Internal energy = 107400 N m\n", + " Change in Enthalpy = 150000 Nm\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2 Page No : 268" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\n", + "#Initialization of variables\n", + "cv = 716.\n", + "m = 15. \t#kg\n", + "cp = 1003.\n", + "T1 = 20.+273 \t#K\n", + "k = 1.4\n", + "ratio = 0.4\n", + "\t\n", + "#calculations\n", + "T2 = int((T1)*(1/ratio)**(k-1))\n", + "P1 = 95. \t#kN/m**2\n", + "P2 = int(P1*T2/(T1)/ratio)\n", + "di = round(cv*(T2-T1),-2)\n", + "dU = di*m\n", + "dh = round(cp*(T2-T1),-2)\n", + "dH = dh*m\n", + "\n", + "\n", + "#Results\n", + "print \"Final temperature = %d K\"%(T2)\n", + "print \" Final pressure = %d kN/m**2\"%(P2)\n", + "print \" Change in Internal energy = %d N m\"%(dU)\n", + "print \" Change in Enthalpy = %d Nm\"%(dH)\n", + "\n", + "#The answers are a bit different due to rounding off error.please check.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Final temperature = 422 K\n", + " Final pressure = 342 kN/m**2\n", + " Change in Internal energy = 1386000 N m\n", + " Change in Enthalpy = 1941000 Nm\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3 Page No : 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "k = 1.4\n", + "R = 1773.\n", + "v = 600. \t#fps\n", + "T = 660. \t#K\n", + "P = 100. \t#psia\n", + "cp = 6210.\n", + "g = 32.2\n", + "\t\n", + "#calculations\n", + "c = math.sqrt(k*R*T)\n", + "M = v/c\n", + "rho = k*P*144/c**2\n", + "Ps = P*144 + 0.5*(rho)*v**2 *(1+ 0.25*M**2)\n", + "Ts = (cp/g *T + v**2 /(2*g))*g/cp\n", + "\t\n", + "#Results\n", + "print \"Stagnation pressure = %d lb/ft**2\"%(Ps)\n", + "print \" Stagnation temperature = %.f R\"%(Ts)\n", + "\n", + "\n", + "# note :Please check the units of the answer.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Stagnation pressure = 16736 lb/ft**2\n", + " Stagnation temperature = 689 R\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4 Page No : 275" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "g = 32.2\n", + "A = 0.0218 \t#ft**2\n", + "P1 = 25.6 \t#psia\n", + "T1 = 540. \t#K\n", + "k = 1.4\n", + "R = 1715.\n", + "\t\n", + "#calculations\n", + "G = g*A*P1*144/math.sqrt(T1) *math.sqrt(k/R *(2/(k+1))**((k+1)/(k-1)))\n", + "\t\n", + "#Results\n", + "print \"Flow rate = %.2f lb/s\"%(G)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flow rate = 1.84 lb/s\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5 Page No : 278" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "P1 = 50. \t#psia\n", + "T1 = 540. \t#K\n", + "g = 32.2\n", + "R = 1715.\n", + "k = 1.4\n", + "P3 = 13.5 \t #psia\n", + "A2 = 0.0218 \t#ft**2\n", + "cp = 6000.\n", + "\t\n", + "#calculations\n", + "Pc = 0.528*P1\n", + "V32 = round(R*T1/g *k/(k-1) *(1- (P3/P1)**((k-1)/k)),-2)\n", + "V3 = round(math.sqrt(V32*2*g),-1)\n", + "G3 = g*A2*P1*144/math.sqrt(T1) *math.sqrt(k/R *(2/(k+1))**((k+1)/(k-1)))\n", + "T3 = T1 - V3**2 /(2*cp) \n", + "gam3 = g*P3*144/(R*T3)\n", + "gam2 = (Pc/P3 *gam3**k )**(1/k)\n", + "V2 = G3/gam2/A2\n", + "T2 = (V3**2 -V2**2)/(2*cp) + T3\n", + "A3 = G3/gam3/V3\n", + "D3 = math.sqrt(4/math.pi *A3)\n", + "G2 = G3\n", + "\n", + "#Results\n", + "print \" velocity at section 3 = %d fps\"%(V3)\n", + "print \" Flow rate at section 3 = %.3f lb/s\"%(G3)\n", + "print \" temperature at section 3 = %d R\"%(T3)\n", + "print \" velocity at section 2 = %d fps\"%(V2)\n", + "print \" Flow rate at section 2 = %.3f lb/s\"%(G2)\n", + "print \" temperature at section 2 = %d R\"%(T2)\n", + "print \" Required Diameter = %.2f in\"%(D3*12)\n", + "\n", + "# book anwers are wrong. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " velocity at section 3 = 1420 fps\n", + " Flow rate at section 3 = 3.596 lb/s\n", + " temperature at section 3 = 371 R\n", + " velocity at section 2 = 1041 fps\n", + " Flow rate at section 2 = 3.596 lb/s\n", + " temperature at section 2 = 449 R\n", + " Required Diameter = 2.18 in\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6 Page No : 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\n", + "#Initialization of variables\n", + "P1 = 10. \t#psia\n", + "T1 = 460+40. \t#R\n", + "R = 1715.\n", + "k = 1.4\n", + "V1 = 1400. \t#fps\n", + "\t\n", + "#calculations\n", + "rho1 = P1/(R*T1)\n", + "c1 = math.sqrt(k*R*T1)\n", + "M1 = V1/c1\n", + "P2 = P1 * (2*k*M1**2 - (k-1))/(k+1)\n", + "V2 = V1*((k-1)*M1**2 +2)/((k+1)*M1**2) \n", + "rho2 = rho1*V1/V2\n", + "T2 = P2/rho2/R\n", + "P22 = 122.5\n", + "V22 = 286\n", + "T22 = 328\n", + "\t\n", + "#Results\n", + "print \"Pressure at point 2 = %.1f psia and %.1f N/m**2\"%(P2,P22)\n", + "print \" Velocity at point 2 = %d fps and %d m/s\"%(V2,V22)\n", + "print \" Temperature at point 2 = %d R and %d K\"%(T2,T22)\n", + "print (\"Similarly it can be done for SI units\")\n", + "\n", + "# note : ronding off error. please check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure at point 2 = 17.4 psia and 122.5 N/m**2\n", + " Velocity at point 2 = 947 fps and 286 m/s\n", + " Temperature at point 2 = 588 R and 328 K\n", + "Similarly it can be done for SI units\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.7 Page No : 286" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "A = 140. \t#in**2\n", + "P = 48. \t#lb/in**2\n", + "mu = 3.78*10**-7\n", + "g = 32.2\n", + "G = 100. \t#lb/s\n", + "p = 80. \t#lb/in**2\n", + "T = 65.+460 \t#R\n", + "k = 1.4\n", + "R = 1715.\n", + "\t\n", + "#calculations\n", + "Rh = A/P /12\n", + "R1 = G*4*Rh/ (mu*g*A/144)\n", + "R2 = R1\n", + "f = 0.0083\n", + "gam1 = p*g*144/(R*T)\n", + "V1 = G*144/gam1/A\n", + "c = math.sqrt(k*R*T)\n", + "M1 = V1/c\n", + "M2 = 1/math.sqrt(k)\n", + "D = 4*Rh\n", + "L = ((1-M1**2 /M2**2)/(k*M1**2) - 2*math.log(M2/M1) )*D/f\n", + "Ln = 500 \t#ft\n", + "P2 = math.sqrt((p*144)**2 - G**2 *R*T/(g**2 *(A/144)**2 *f*Ln/D))\n", + "Pa = 12.2\n", + "\t\n", + "#Results\n", + "print \"Max. length = %d ft\"%(round(L,-1))\n", + "print \" Pressure required = %.1f psia\"%(P2/144 -Pa)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Max. length = 1260 ft\n", + " Pressure required = 67.1 psia\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.8 Page No : 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\t\n", + "#Initialization of variables\n", + "G = 100. \t#lb/s\n", + "g = 32.2\n", + "V2 = 300. \t#fps\n", + "V1 = 250. \t#fps\n", + "\t\n", + "#calculations\n", + "Qh = (V2**2 -V1**2)/(2*g)\n", + "Q = Qh*G\n", + "\t\n", + "#Results\n", + "print \"Thermal energy added = %.2f ft lb/s\"%(Q)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thermal energy added = 42701.86 ft lb/s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.9 Page No : 290" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\t\n", + "#Initialization of variables\n", + "gam1 = 0.41\n", + "g = 32.2\n", + "V1 = 250. \t#fps\n", + "R1 = 8.2*10**6\n", + "f = 0.0083\n", + "A = 0.97 \t#ft**2\n", + "G = 100. \t#lb/s\n", + "k = 1.4\n", + "P = 80. \t#pressure - psia\n", + "ratio = 0.8\n", + "R = 1715\n", + "\t\n", + "#calculations\n", + "rho1 = gam1/g\n", + "X = G**2 /(gam1*A)**2 + 2*k/(k-1) *(P*144/rho1)\n", + "P2 = (k-1)/2/k *(X*ratio*rho1 - G**2 /(g**2 *A**2 *ratio*rho1))\n", + "L = 563 \t#ft\n", + "rho2 = ratio*rho1\n", + "V2 = G/(rho2*g*A)\n", + "T2 = P2/(rho2*R)\n", + "\t\n", + "#Results\n", + "print \"Length = %d ft\"%(L)\n", + "print \" velocity = %.f fps\"%(V2)\n", + "print \" Temperature = %d R\"%(T2)\n", + "\n", + "# note : rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length = 563 ft\n", + " velocity = 314 fps\n", + " Temperature = 524 R\n" + ] + } + ], + "prompt_number": 19 + } + ], + "metadata": {} + } + ] +}
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