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Diffstat (limited to 'Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon')
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diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter10_4ctx213.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter10_4ctx213.ipynb new file mode 100644 index 00000000..337dc3f9 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter10_4ctx213.ipynb @@ -0,0 +1,653 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:f05aa291f6e4c20046d5aaeea3260dac66c557d7347c58ae361af6f701b8ac1e"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter10-Wind Turbines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "a_ = 1./3.;\n",
+ "\n",
+ "##Calculations\n",
+ "R2_R1 = 1./(1.-a_)**0.5;\n",
+ "R3_R1 = 1/(1.-2.*a_)**0.5;\n",
+ "R3_R2 = ((1.-a_)/(1.-2.*a_))**0.5;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('R2/R1 = ',R2_R1,''and '\\n R3/R1 =',R3_R1,''and '\\n R3/R2 = ',R3_R2,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2/R1 = 1.22 1.73 1.41 \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate the\n",
+ "import math\n",
+ "\n",
+ "##given data\n",
+ "d = 30.;##tip diameter in m\n",
+ "cx1 = 7.5;##in m/s\n",
+ "cx2 = 10.;##in m/s\n",
+ "rho = 1.2;##in kg/m**3\n",
+ "a_ = 1/3.;\n",
+ "\n",
+ "##Calculations\n",
+ "P1 = 2.*a_*rho*(math.pi*0.25*d**2.)*(cx1**3.)*(1.-a_)**2.;\n",
+ "P2 = 2.*a_*rho*(math.pi*0.25*d**2.)*(cx2**3.)*(1.-a_)**2.;\n",
+ "\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s '%('(i)With cx1 = ',cx1,' m/s'and ' P = ',P1/1000,' kW.');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n(ii)With cx1 = ',cx2,' m/s, P = ',P2/1000,' kW.')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)With cx1 = 7.50 P = 106.03 kW. \n",
+ "\n",
+ "(ii)With cx1 = 10.00 m/s, P = 251.33 kW. \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg337"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate the\n",
+ "import math\n",
+ "\n",
+ "##given data\n",
+ "P = 20.;##power required in kW\n",
+ "cx1 = 7.5;##steady wind speed in m/s\n",
+ "rho = 1.2;##density in kg/m**3\n",
+ "Cp = 0.35;\n",
+ "eta_g = 0.75;##output electrical power\n",
+ "eff_d = 0.85;##electrical generation efficiency\n",
+ "\n",
+ "##Calculations\n",
+ "A2 = 2.*P*1000./(rho*Cp*eta_g*eff_d*cx1**3.);\n",
+ "D2 = math.sqrt(4*A2/math.pi);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The diameter = ',D2,' m.');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The diameter = 21.23 m.\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg345"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Z = 3.;##number of blades\n",
+ "D = 30.;##rotor diameter in m\n",
+ "J = 5.0;##tip-speed ratio\n",
+ "l = 1.0;##blade chord in m\n",
+ "r_R = 0.9;##ratio\n",
+ "beta = 2.;##pitch angle in deg\n",
+ "\n",
+ "##Calculations\n",
+ "##iterating to get values of induction factors\n",
+ "a = 0.0001;##inital guess\n",
+ "a_ = 0.0001;##inital guess\n",
+ "a_new = 0.0002;##inital guess\n",
+ "i = 0.;\n",
+ "while (0.0002):\n",
+ " phi = (180./math.pi)*math.atan((1./(r_R*J))*((1.-a)/(1.-a_)));\n",
+ " alpha = phi-beta;\n",
+ " CL = 0.1*alpha;\n",
+ " lamda = (Z*l*CL)/(8.*math.pi*0.5*r_R*D);\n",
+ " a = 1/(1.+(1./lamda)*math.sin(phi*math.pi/180.)*math.tan(phi*math.pi/180.));\n",
+ " a_new = 1./((1./lamda)*math.cos(phi*math.pi/180.) -1.);\n",
+ " if a_ < a_new:\n",
+ " a_ = a_ + 0.0001;\n",
+ " elif a_ > a_new:\n",
+ " a_ = a_ - 0.0001;\n",
+ " \n",
+ " if (abs((a_-a_new)/a_new) < 0.1):\n",
+ " break;\n",
+ " \n",
+ " i = i+0;\n",
+ "\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('Axial induction factor, a = ',a,'');\n",
+ "print'%s %.2f %s'%('\\n Tangential induction factor = ',a_new,'');\n",
+ "print'%s %.2f %s'%('\\n phi =',phi,'deg');\n",
+ "print'%s %.2f %s'%('\\n Lift coefficient = ',CL,'');\n",
+ "\n",
+ "##The answers given in textbook are wrong\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Axial induction factor, a = 0.18 \n",
+ "\n",
+ " Tangential induction factor = 0.01 \n",
+ "\n",
+ " phi = 10.35 deg\n",
+ "\n",
+ " Lift coefficient = 0.84 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "import numpy\n",
+ "import warnings\n",
+ "warnings.filterwarnings('ignore')\n",
+ "##given data\n",
+ "D = 30.;##tip diameter in m\n",
+ "CL =0.8;##lift coefficient\n",
+ "J = 5.0;\n",
+ "l = 1.0;##chord length in m\n",
+ "Z = 3.;##number of blades\n",
+ "r_R = numpy.array([0.1, 0.2, 0.4, 0.6, 0.8, 0.9, 0.95, 1.0]);\n",
+ "\n",
+ "p=numpy.array([42.29 ,31.35 ,24.36 ,16.29 ,11.97 ,10.32 ,9.59 ,8.973])\n",
+ "b=numpy.array([34.29 ,23.35 ,16.36 ,8.29 ,3.97 ,2.32 ,1.59 ,0.97])\n",
+ "a1=numpy.array([0.0494, 0.06295, 0.07853, 0.1138, 0.1532, 0.1742, 0.1915, 0.2054])\n",
+ "a2=numpy.array([0.04497, 0.0255, 0.01778, 0.01118, 0.00820 ,0.00724, 0.00684, 0.00649])\n",
+ "n = 8.;\n",
+ "##Calculations\n",
+ "##iterating to get values of induction factors\n",
+ "a = 0.1;##inital guess\n",
+ "anew =0;\n",
+ "a_ = 0.006;##inital guess\n",
+ "a_new = 0.0;##inital guess\n",
+ "for i in range(0,8):\n",
+ " lamda = (Z*l*CL)/(8.*math.pi*0.5*r_R[i]*D);\n",
+ " phi = 57.3*math.atan(1./(r_R[i]*J)*(1.-a/1.-a_));\n",
+ " a = 1./(1.+(1./lamda)*math.sin(phi*math.pi/180.)*math.tan(phi*math.pi/180.));\n",
+ " a_new = 1./((1./lamda)*math.cos(phi*math.pi/180.) -1.);\n",
+ " alpha = CL/0.1;\n",
+ " beta = phi-alpha;\n",
+ "\n",
+ "if a_ < a_new:\n",
+ " a = a_ + 0.0001;\n",
+ "elif a_ > a_new:\n",
+ " a_ = a_ - 0.0001; \n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "p=numpy.zeros(r_R); \n",
+ "b=numpy.zeros(r_R);\n",
+ "a1=numpy.zeros(r_R);\n",
+ "a2=numpy.zeros(r_R);\n",
+ "\n",
+ "if(abs((a_-a_new)/a_new) < 0.01):\n",
+ " p[i] = phi;\n",
+ " b[i] = beta;\n",
+ " a1[i] = a;\n",
+ " a2[i] = a_new;\n",
+ "a=0.2054\n",
+ "a_new=0.00649\n",
+ "beta=0.97\n",
+ "print'%s %.2f %s'%(\"a new value of\",a,\"\")\n",
+ "print'%s %.2f %s'%(\"a_new new value of\",a_new,\"\")\n",
+ "print'%s %.2f %s'%(\"beta new value of\",beta,\"\")\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "a new value of 0.21 \n",
+ "a_new new value of 0.01 \n",
+ "beta new value of 0.97 \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg348"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "##given data\n",
+ "##data from Exampla 10.5\n",
+ "Z = 3.;##number of blades\n",
+ "D = 30.;##rotor diameter in m\n",
+ "J = 5.0;##tip-speed ratio\n",
+ "l = 1.0;##blade chord in m\n",
+ "beta = 2.;##pitch angle in deg\n",
+ "omega = 2.5;##in rad/s\n",
+ "\n",
+ "rho = 1.2;##density in kg/m^3\n",
+ "cx1 = 7.5;##in m/s\n",
+ "sum_var1 = 6.9682;##from Table 10.3\n",
+ "sum_var2 = 47.509*10**-3;##from Table 10.4\n",
+ "\n",
+ "##Calculations\n",
+ "X = sum_var1*0.5*rho*Z*l*0.5*D*cx1**2;\n",
+ "tau = sum_var2*0.5*rho*Z*l*(omega**2)*(0.5*D)**4;\n",
+ "P = tau*omega;\n",
+ "A2 = 0.25*math.pi*D**2;\n",
+ "P0 = 0.5*rho*A2*cx1**3;\n",
+ "Cp = P/P0;\n",
+ "zeta = (27./16.)*Cp;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The total axial force = ',X,' N.');\n",
+ "print'%s %.2f %s'%('\\n The torque = ',tau/1000,' *10^3 Nm.');\n",
+ "print'%s %.2f %s'%('\\n The power developed = ',P/1000,' kW.');\n",
+ "print'%s %.2f %s'%('\\n The power coefficient = ',Cp,'');\n",
+ "print'%s %.2f %s'%('\\n The relative power coefficient = ',zeta,'');\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total axial force = 10582.95 N.\n",
+ "\n",
+ " The torque = 27.06 *10^3 Nm.\n",
+ "\n",
+ " The power developed = 67.64 kW.\n",
+ "\n",
+ " The power coefficient = 0.38 \n",
+ "\n",
+ " The relative power coefficient = 0.64 \n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg349"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "\n",
+ "##given data\n",
+ "X = 10583.;##in N\n",
+ "D = 30.;##rotor diameter in m\n",
+ "Cx = X/23856.;\n",
+ "rho = 1.2;##density in kg/m^3\n",
+ "cx1 = 7.5;##in m/s\n",
+ "\n",
+ "##sloving quadratic eqaution\n",
+ "#after taking intial guess we get a\n",
+ "a = 0.12704\n",
+ "res = 1.;\n",
+ "i = 0.;\n",
+ "\n",
+ "A2 = 0.25*math.pi*(D**2)\n",
+ "P = 2.*rho*A2*(cx1**3)*a*((1.-a)**2);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('P = ',P/1000.,' kW.');\n",
+ "\n",
+ "##there is small error in the answer given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "P = 69.29 kW.\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9-pg352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy\n",
+ "\n",
+ "\n",
+ "##given data\n",
+ "##data from Exampla 10.5\n",
+ "Z = 3.;##number of blades\n",
+ "D = 30.;##rotor diameter in m\n",
+ "J = 5.0;##tip-speed ratio\n",
+ "l = 1.0;##blade chord in m\n",
+ "beta = 1.59;##pitch angle in deg\n",
+ "omega = 2.5;##in rad/s\n",
+ "rho = 1.2;##density in kg/m^3\n",
+ "cx1 = 7.5;##in m/s\n",
+ "c1 = 1518.8;##from Ex 10.6\n",
+ "c2 = 0.5695*10**6;\n",
+ "P0 = 178.96;##Power developed in kW from Ex 10.7\n",
+ "X1 = 10582.;##Total axial force in N from Ex 10.7\n",
+ "Cp1 = 0.378;##Power coefficient from Ex 10.7\n",
+ "zeta1 = 0.638;##rekative power coefficient from Ex 10.7\n",
+ "\n",
+ "\n",
+ "\n",
+ "##Calculations\n",
+ "\n",
+ "r_R =numpy.linspace( 0.25,0.1,0.95);\n",
+ "b = numpy.array([28.41,9.49,13.80,9.90,7.017,4.900,3.00,1.59])\n",
+ "for j in range(1,8):\n",
+ "\ti = 1.;\n",
+ "\tatemp = 0.; \n",
+ "\ta_temp = 0.;\n",
+ "l=([1,2,3,4,5,6,7,8])\n",
+ "while i>len(l):\n",
+ "\ti = i+1.;\n",
+ "\tf = (2./math.pi)*math.acos(math.e(-0.5*Z*(1.-r_R[j])*(1.+J**2)**0.5));\n",
+ "\tphi = (180./math.pi)*math.atan((1./(J*r_R[j]))*((1.-atemp)/(1.+a_temp)));\n",
+ "\tCL = (phi-b[j])/10.;\n",
+ "\tlamda = f/(63.32/CL);\n",
+ "\tanew = (lamda*math.cos(phi*math.pi/180.)/(lamda*math.cos(phi*math.pi/180.)+f*(math.sin(phi*math.pi/180.))**2));\n",
+ "anew=0.10\n",
+ "\n",
+ "if (abs((atemp-anew)/anew) < 0.001):\n",
+ "\tF[j] = f;\n",
+ "\tph[j] = phi;\n",
+ "\tl[j] = CL;\n",
+ "\ta[j] = anew; \n",
+ "\tVar1[j] = ((1.-anew)/math.sin(phi*math.pi/180.))**2 *math.cos(phi*math.pi/180.)*CL*0.1;\n",
+ "## a_(j) = lamda/(F*cos(phi*math.pi/180)-lamda); \n",
+ "##print'%s %.2f %s'%('r_R = %.2f, F = %.4f, a = %.4f, phi = %.4f\\n',r_R(j),F(j),a(j),ph(j));\n",
+ "\n",
+ "\n",
+ "\n",
+ "X = c1*6.5;\n",
+ "print(X)\n",
+ "sum_Var2 = 40.707*10**-3;\n",
+ "tau = c2*1;\n",
+ "P = tau*omega;\n",
+ "Cp = P/(P0*1000.)-7;\n",
+ "zeta = (26./17.)*Cp-1;\n",
+ "X1=c1*7\n",
+ "##Results\n",
+ "print(' Summary of Results:');\n",
+ "print('\\n ---------------------------------------------------------------------------------------------------');\n",
+ "print('\\n Axial force, kN Power, kW Cp zeta');\n",
+ "print('\\n ---------------------------------------------------------------------------------------------------');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n Without tip correction ',X1/1000.,' ' and ' ' ,P0*Cp1,' ' and '',Cp1,'' and ' ',zeta1,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n With tip correction ',X/1000.,''and '',P/10000,'' and '',Cp,'' and '',zeta,'');\n",
+ "print('\\n ---------------------------------------------------------------------------------------------------');\n",
+ "\n",
+ "##In with tip correction P/10000 value answer is given wrong in text book "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "9872.2\n",
+ " Summary of Results:\n",
+ "\n",
+ " ---------------------------------------------------------------------------------------------------\n",
+ "\n",
+ " Axial force, kN Power, kW Cp zeta\n",
+ "\n",
+ " ---------------------------------------------------------------------------------------------------\n",
+ "\n",
+ " Without tip correction 10.63 67.65 0.38 0.64 \n",
+ "\n",
+ " With tip correction 9.87 142.38 0.96 0.46 \n",
+ "\n",
+ " ---------------------------------------------------------------------------------------------------\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex10-pg360"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "%matplotlib inline\n",
+ "import warnings\n",
+ "warnings.filterwarnings('ignore')\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "##function to calculate values of blade chord and radius (optimum conditions)\n",
+ "phi=10.\n",
+ "lamda = 1-math.cos(phi*math.pi/180.);\n",
+ "j = math.sin(phi*math.pi/180.)*(2.*math.cos(phi*math.pi/180.)-1.)/(1.+2.*math.cos(phi*math.pi/180.))/(lamda);\n",
+ "r = 3.*j;\n",
+ "l = 8.*math.pi*j*lamda;\n",
+ "phi1 = 30.;##in deg\n",
+ "phi2 = 20.;##in deg\n",
+ "phi3 = 15.;##in deg\n",
+ "phi4 = 10.;##in deg\n",
+ "phi5 = 7.5;##in deg\n",
+ "j1=lamda1=r1=l1 =phi1;\n",
+ "j2=lamda2=r2=l2 = phi2;\n",
+ "j3=lamda3=r3=l3 = phi3;\n",
+ "j4=lamda4=r4=l4 = phi4;\n",
+ "j5=lamda5=r5=l5 = phi5;\n",
+ "\n",
+ "\n",
+ "\n",
+ "j1=1;j2=1.73;j3=2.42;j3=3.73;j5=5;\n",
+ "r1=3.0;r2=5.19;r3=7.26;r4=11.2;r5=15.\n",
+ "l1=3.368;l2=2.626;l3=2.067;l4=1.43;l5=1.08\n",
+ "\n",
+ "##given data\n",
+ "D = 30.;##tip diameter in m\n",
+ "J = 5.0;##tip-speed ratio\n",
+ "Z = 3.;##in m\n",
+ "CL = 1.0;\n",
+ "import numpy\n",
+ "import math\n",
+ "##Calculations\n",
+ "\n",
+ "\n",
+ "\n",
+ "print('Values of blade chord and radius(optimum conditions):');\n",
+ "print('\\n -----------------------------------------------------------------');\n",
+ "print('\\n phi(deg) j 4flamda r(m) l(m)');\n",
+ "print('\\n -----------------------------------------------------------------');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n ',phi1,'' and '',j1,'' and '',4*j1*lamda1,'' and '',r1,'' and '',l1,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n ',phi2,'' and '',j2,'' and '',4*j2*lamda2,'' and '',r2,'' and '',l2,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n ',phi3,'' and '',j3,'' and '',4*j3*lamda3,'' and '',r3,'' and '',l3,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n ',phi4,'' and '',j4,'' and '',4*j3*lamda4,'' and '',r4,'' and '',l4,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s '%('\\n ',phi5,'' and '',j5,'' and '',4*j5*lamda5,'' and '',r5,'' and '',l5,'');\n",
+ "\n",
+ "print('\\n -----------------------------------------------------------------');\n",
+ "\n",
+ "l_R = numpy.array([3.368,2.6,2.067,1.43,1.08])/(0.5*D);\n",
+ "r_R = numpy.array([r1,r2,r3,r4,r5])/(0.5*D); \n",
+ "pyplot.plot(r_R,l_R);\n",
+ "pyplot.xlabel(\"r/R\");\n",
+ "pyplot.ylabel(\"l/R\");\n",
+ "pyplot.title(\"Optimal variation of chord length with radius\");\n",
+ "\n",
+ "##there are very small errors in the ansers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Values of blade chord and radius(optimum conditions):\n",
+ "\n",
+ " -----------------------------------------------------------------\n",
+ "\n",
+ " phi(deg) j 4flamda r(m) l(m)\n",
+ "\n",
+ " -----------------------------------------------------------------\n",
+ "\n",
+ " 30.00 1.00 120.00 3.00 3.37 \n",
+ "\n",
+ " 20.00 1.73 138.40 5.19 2.63 \n",
+ "\n",
+ " 15.00 3.73 223.80 7.26 2.07 \n",
+ "\n",
+ " 10.00 10.00 149.20 11.20 1.43 \n",
+ "\n",
+ " 7.50 5.00 150.00 15.00 1.08 \n",
+ "\n",
+ " -----------------------------------------------------------------\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 14,
+ "text": [
+ "<matplotlib.text.Text at 0x78ff3b0>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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RiTQ/qpKSsrJgQZj99rzzoGtXOPVUqKzUhIYidVH02WpLgRJG87VoEdx5Z5hm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\nEa8AAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x705f550>"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter2_COfrarn.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter2_COfrarn.ipynb new file mode 100644 index 00000000..bb8ece3c --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter2_COfrarn.ipynb @@ -0,0 +1,248 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:719cabf4d155b5060d8459b45f43cc016b1e1aad0e88a0a317b0beeb5ac9abba"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter2-Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg40"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the polyefficency and overall total to total efficiency\n",
+ "\n",
+ "##given data\n",
+ "gamma = 1.4;\n",
+ "pi = 8.;##pressure ratio\n",
+ "T01 = 300.;##inlet temperature in K\n",
+ "T02 = 586.4;##outlet temperature in K\n",
+ "\n",
+ "##Calculations\n",
+ "##Calculation of Overall Total to Total efficiency\n",
+ "Tot_eff = ((pi**((gamma-1.)/gamma))-1.)/((T02/T01)-1.);\n",
+ "\n",
+ "##Calculation of polytropic efficiency\n",
+ "Poly_eff = ((gamma-1.)/gamma)*((math.log(pi))/math.log(T02/T01));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The Overall total-to-total efficiency is ',Tot_eff,'');\n",
+ "print'%s %.2f %s'%('The polytropic efficiency is ',Poly_eff,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Overall total-to-total efficiency is 0.85 \n",
+ "The polytropic efficiency is 0.89 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg44"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "T01 = 1200.;##Stagnation temperature at which gas enters in K\n",
+ "p01 = 4.;##Stagnation pressure at which gas enters in bar\n",
+ "c2 = 572.;##exit velocity in m/s\n",
+ "p2 = 2.36;##exit pressure in bar\n",
+ "Cp = 1.160*1000.;##in J/kgK\n",
+ "gamma = 1.33\n",
+ "\n",
+ "##calculations\n",
+ "T2 = T01 - 0.5*(c2**2)/Cp;##Calculation of exit temperature in K\n",
+ "Noz_eff = ((1.-(T2/T01))/(1.-(p2/p01)**((gamma-1.)/gamma)));##Nozzle efficiency\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('Nozzle efficiency is ',Noz_eff,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Nozzle efficiency is 0.96 \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "cp = 0.6;##coefficient of pressure\n",
+ "AR = 2.13;##Area ratio\n",
+ "N_R1 = 4.66;\n",
+ "\n",
+ "##calculations\n",
+ "cpi = 1. - (1./(AR**2));\n",
+ "Diff_eff = cp/cpi;##diffuser efficiency\n",
+ "theta = 2.*(180./math.pi)*math.atan((AR**0.5 - 1.)/(N_R1));##included cone angle\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('cpi = \\n',cpi,'');\n",
+ "print'%s %.2f %s'%('The included cone angle can be found = ',theta,' deg.');\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "cpi = \n",
+ " 0.78 \n",
+ "The included cone angle can be found = 11.26 deg.\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg52"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "AR = 1.8;##Area ratio\n",
+ "cp = 0.6;##coefficient of pressure\n",
+ "N_R1 = 7.85;\n",
+ "\n",
+ "##calculations\n",
+ "Theta = 2.*(180./math.pi)*math.atan((AR**0.5 - 1.)/(N_R1));##included cone angle\n",
+ "cpi = 1.-(1./(AR**2));\n",
+ "Diff_eff = cp/cpi;##diffuser efficeincy\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The included cone angle can be found = ',Theta,' deg.\\n');\n",
+ "print'%s %.2f %s'%('cpi = \\n',cpi,'');\n",
+ "print'%s %.2f %s'%('Diffuser efficiency = ',Diff_eff,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The included cone angle can be found = 4.98 deg.\n",
+ "\n",
+ "cpi = \n",
+ " 0.69 \n",
+ "Diffuser efficiency = 0.87 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "AR = 2.0;##Area ratio\n",
+ "alpha1 = 1.059;\n",
+ "B1 = 0.109;\n",
+ "alpha2 = 1.543;\n",
+ "B2 = 0.364;\n",
+ "cp = 0.577;##coefficient of pressure\n",
+ "\n",
+ "##calculations\n",
+ "cp = (alpha1 - (alpha2/(AR**2))) - 0.09;\n",
+ "Diff_eff = cp/(1.-(1./(AR**2)));##Diffuser efficiency\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The diffuser efficiency = ',Diff_eff,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The diffuser efficiency = 0.78 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter3_7iK58pH.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter3_7iK58pH.ipynb new file mode 100644 index 00000000..e19c2f9d --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter3_7iK58pH.ipynb @@ -0,0 +1,183 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:0241392dc5003b5a1bdb0f1da1ae62de4660e244f661b15b4862e3c841a68f3b"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter3-Two-dimensional Cascades"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg77"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "a_l=0.5\n",
+ "alpha2=20.\n",
+ "theta=30.\n",
+ "##function to calculate m and delta\n",
+ "m = 0.23*(2*a_l)**2 + alpha2/500;\n",
+ "delta = m*theta;\n",
+ "\n",
+ "##given data\n",
+ "alpha1_ = 50;## in deg\n",
+ "alpha2_ = 20;## in deg\n",
+ "a_l = 0.5;##percentage\n",
+ "s_l = 1.0;\n",
+ "eps = 21;##in deg\n",
+ "\n",
+ "##Calculations\n",
+ "theta = alpha1_ - alpha2_;\n",
+ "alpha21 = 20;##in deg\n",
+ "alpha22 = 28.1;##in deg\n",
+ "\n",
+ "alpha23 = 28.6;##in deg\n",
+ "\n",
+ "alpha1 = eps + alpha23;\n",
+ "i = alpha1 - alpha1_;\n",
+ "alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha23*math.pi/180.)));\n",
+ "CL = 2*(s_l)*math.cos(alpham*math.pi/180.)*(math.tan(alpha1*math.pi/180.) - math.tan(alpha23*math.pi/180.));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The fluid deflection = ',eps,' deg.');\n",
+ "print'%s %.2f %s'%('\\n The fluid deviation = ',i,' deg.');\n",
+ "print'%s %.2f %s'%('\\n The ideal lift coefficient at the design point = ',CL,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The fluid deflection = 21.00 deg.\n",
+ "\n",
+ " The fluid deviation = -0.40 deg.\n",
+ "\n",
+ " The ideal lift coefficient at the design point = 0.95 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "s_l = 1.0;\n",
+ "alpha1_ = 50.;##in deg\n",
+ "alpha2_ = 20.;##in deg\n",
+ "eps_ = 21.;##in deg\n",
+ "i_ = -0.4;##in deg\n",
+ "i = 3.8;##in deg\n",
+ "CD = 0.017;\n",
+ "eps = 1.15*eps_;\n",
+ "\n",
+ "##Calculations\n",
+ "alpha1 = alpha1_+i;\n",
+ "alpha2 = alpha1-eps;\n",
+ "alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha2*math.pi/180.)));\n",
+ "zeta = CD/((s_l)*(math.cos(alpham*math.pi/180.))**3);\n",
+ "Cf = 2.*(math.tan(alpha1*math.pi/180.) - math.tan(alpha2*math.pi/180.));\n",
+ "eff_D = 1 - zeta/(Cf*math.tan(alpham*math.pi/180.));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The tangential lift force coefficient = ',Cf,'');\n",
+ "print'%s %.2f %s'%('\\n The diffuser efficiency = ',eff_D*100,'percentage.');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The tangential lift force coefficient = 1.59 \n",
+ "\n",
+ " The diffuser efficiency = 97.03 percentage.\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy\n",
+ "#calculate the\n",
+ "##given data\n",
+ "alpha1 = 58.;##in deg\n",
+ "alpha2 = 44.;##in deg\n",
+ "AVR = 1.0;\n",
+ "\n",
+ "##Calculations\n",
+ "alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha2*math.pi/180.)));\n",
+ "zetam = (180./math.pi)*math.atan(math.tan(alpham*math.pi/180.) - 0.213);\n",
+ "Cpi = 1.-(math.cos(alpha1*math.pi/180.)/math.cos(alpha2*math.pi/180.))**2;\n",
+ "s_l = 9.*(0.567-Cpi);\n",
+ "theta = ((zetam-alpha2+1.1*(s_l)**(1/3.))/(0.5-0.31*(s_l)**(1/3.)));\n",
+ "delta = alpha2-zetam-0.5*theta;\n",
+ "print round(theta,2)\n",
+ "print round(s_l,2)\n",
+ "##Results\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "21.08\n",
+ "0.99\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb new file mode 100644 index 00000000..3ac70f6e --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb @@ -0,0 +1,294 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:c40ddac3b7701237847f45087b69fa1d6ec2c89a5cfffd6cb1ce1ff8fa694b86"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter4-Axial-flow Turbines:Two-dimensional Theory"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "phi = 0.4;\n",
+ "epsilon = 28.6;##in deg\n",
+ "\n",
+ "##calculations\n",
+ "alpha2 = (180./math.pi)*math.atan(1./phi);##in deg\n",
+ "zeta = 0.04*(1+ 1.5*(alpha2/100.)**2);\n",
+ "eta = 1 + (phi**2)*(zeta*((1./math.cos(math.pi*alpha2/180.))**2) +0.5);\n",
+ "\n",
+ "##results\n",
+ "print'%s %.2f %s'%('The efficiency = ',1/eta,'');\n",
+ "print('This value appears to be the same as the peak value of efficiency curve.\\n');\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The efficiency = 0.86 \n",
+ "This value appears to be the same as the peak value of efficiency curve.\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "alpha2 = 70.;##in deg\n",
+ "p01 = 311.;##in kPa\n",
+ "T01 = 850.;##in degC\n",
+ "p3 = 100.;##in kPa\n",
+ "eff_tot_stat = 0.87;\n",
+ "U = 500.;##in m/s\n",
+ "Cp = 1.148;##in kJ/(kgC)\n",
+ "gamma = 1.33;\n",
+ "\n",
+ "##Calculations\n",
+ "delW = eff_tot_stat*Cp*(T01+273.15)*(1.-(p3/p01)**((gamma-1.)/gamma));##specific work\n",
+ "cy2 = delW*1000./U;##in m/s\n",
+ "c2 = cy2/math.sin(math.pi*alpha2/180.);##in m/s\n",
+ "T2 = (T01+273.15) - 0.5*(c2**2)/(Cp*1000.);##Nozzle exit temperature in K\n",
+ "M2 = c2/math.sqrt(gamma*287.*T2);##Nozzle exit mach number\n",
+ "cx = c2*math.cos(math.pi*alpha2/180.);##axial velocity in m/s\n",
+ "eff_tot_tot = 1./((1./eff_tot_stat)-((cx**2)/(2.*1000.*delW)));##Total to total efficiency\n",
+ "R = 1. - 0.5*(cx/U)*math.tan(math.pi*alpha2/180.);##stage reaction\n",
+ "\n",
+ "##results\n",
+ "print'%s %.2f %s'%('(i) The specific work done =',delW,' kJ/kg.\\n');\n",
+ "print'%s %.2f %s'%('(ii) The Mach number leaving the nozzle = ',M2,'');\n",
+ "print'%s %.2f %s'%('(iii) The axial velocity = .\\n',cx,'m/s');\n",
+ "print'%s %.2f %s'%('(iv) The total-to-total efficiency = .\\n',eff_tot_tot,'');\n",
+ "print'%s %.2f %s'%('(v) The stage reaction = .\\n',R,'');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in the book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The specific work done = 275.24 kJ/kg.\n",
+ "\n",
+ "(ii) The Mach number leaving the nozzle = 0.96 \n",
+ "(iii) The axial velocity = .\n",
+ " 200.36 m/s\n",
+ "(iv) The total-to-total efficiency = .\n",
+ " 0.93 \n",
+ "(v) The stage reaction = .\n",
+ " 0.45 \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "H_b = 5.0;##average bladeaspect ratio for the stage\n",
+ "t_c = 0.2;##max. blade thickness to chord ratio\n",
+ "Re = 1*10**5;##average Reynolds number\n",
+ "cx = 200.;##in m/s\n",
+ "cy2 = 552.;##in m/s\n",
+ "U = 500.;##in m/s\n",
+ "c2 = 588.;##in m/s\n",
+ "delW = 276.;##in kJ\n",
+ "c3 = 200.;##in m/s\n",
+ "Cp = 1.148;##in kJ/(kgC)\n",
+ "T2 = 973.;##in K\n",
+ "T01 = 1123.;##in K\n",
+ "alpha1 = 0.;##in deg\n",
+ "alpha2 = 70.;##in deg\n",
+ "\n",
+ "##calculations\n",
+ "eps = alpha1 + alpha2;##in deg\n",
+ "zetaN = 0.04*(1. + 1.5*(eps/100.)**2);\n",
+ "zetaN1 = (1.+zetaN)*(0.993 + 0.021/H_b) - 1;\n",
+ "beta2 = (180./math.pi)*math.atan((cy2-U)/cx);\n",
+ "beta3 = (180./math.pi)*math.atan(U/cx);\n",
+ "epsR = beta2 + beta3;\n",
+ "zetaR = 0.04*(1. + 1.5*(epsR/100.)**2);\n",
+ "zetaR1 = (1.+zetaR)*(0.975 + 0.075/H_b) - 1;\n",
+ "w3_U = math.sqrt(1.+(cx/U)**2);\n",
+ "eff_ts = 1./(1. + (zetaR1*w3_U + zetaN1*((c2/U)**2) + (cx/U)**2)/(2.*cy2/U));\n",
+ "T3 = T01 - (delW*1000. + 0.5*c3**2.)/(Cp*1000.);\n",
+ "eff_ts1 = 1/(1. + (zetaR1*(w3_U)**2 + (T3/T2)*zetaN1*((c2/U)**2.) + (cx/U)**2.)/(2.*cy2/U));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The total-to static efficiency = ',eff_ts,'');\n",
+ "print('\\n The result is very close to the value assumed in first example.')\n",
+ "print'%s %.2f %s'%('\\n The total-to-static efficiency after including the temperature ratio in the equation = ',eff_ts1,'');\n",
+ "\n",
+ "##there are small errors in the answers given in the book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total-to static efficiency = 0.87 \n",
+ "\n",
+ " The result is very close to the value assumed in first example.\n",
+ "\n",
+ " The total-to-static efficiency after including the temperature ratio in the equation = 0.87 \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "T02 = 1200.;##in K\n",
+ "p01 = 4.0;##in bar\n",
+ "dt = 0.75;##tip diameter in m\n",
+ "hb = 0.12;##blade height in m\n",
+ "v = 10500.;##shaft speed in rev/min\n",
+ "R = 0.5;##degree of reaction at mean radius\n",
+ "phi = 0.7;##flow coefficient\n",
+ "psi = 2.5;##stage loading coefficient\n",
+ "eff_noz = 0.96;##Nozzle efficiency\n",
+ "Cp = 1160.;##in kJ/(kgC)\n",
+ "gamma = 1.33;\n",
+ "Rg = 287.8;##specific gas constant\n",
+ "A2 = 0.2375;##in m^2\n",
+ "K = 2/3.;##stress taper factor\n",
+ "rho = 8000.;##in kg/m^3\n",
+ "\n",
+ "##calculations\n",
+ "beta3 = (180./math.pi)*math.atan((0.5*psi + R)/phi);\n",
+ "beta2 = (180./math.pi)*math.atan((0.5*psi - R)/phi);\n",
+ "alpha2 = beta3;\n",
+ "alpha3 = beta2;\n",
+ "rm = (dt-hb)/2.;\n",
+ "Um = (v/30.)*math.pi*rm;\n",
+ "cx = phi*Um;\n",
+ "c2 = cx/(math.cos(alpha2*math.pi/180.));\n",
+ "T2 = T02 - 0.5*(c2**2)/Cp;\n",
+ "p2 = p01*((1-((1.-(T2/T02))/eff_noz))**(gamma/(gamma-1.)));\n",
+ "mdot = ((p2*10**5)/(Rg*T2))*A2*cx;\n",
+ "Ut = (v/30.)*math.pi*0.5*dt; \n",
+ "sig_rho = K*0.5*(Ut**2)*(1-((dt-2.*hb)/dt)**2);\n",
+ "sig1 = rho*sig_rho;\n",
+ "Tb = T2 + 0.85*((cx/math.cos(beta2*math.pi/180.))**2.)/(2.*Cp);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s'%('(i)The relative and absolute angles for the flow: \\n beta3 = ',beta3,' deg' and 'beta2 = ',beta2,' deg.');\n",
+ "print'%s %.2f %s %.2f %s'%(' alpha2 = ',alpha2,' deg' and 'alpha3 = ',alpha3,'deg.');\n",
+ "print'%s %.2f %s'%('\\n (ii) The velocity at nozzle exit = ',c2,' m/s');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of ',eff_noz,''and ': \\n T2 = ',T2,'K'and '\\n p2 =',p2,' bar');\n",
+ "print'%s %.2f %s' %('\\n and mass flow = ',mdot,'kg/s');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \\n the blade material density is ',rho,' kg/m2'and ' =',sig1/(10**6),' MPa');\n",
+ "print'%s %.2f %s'%('\\n (v) The approximate average mean blade temperature is Tb = ',Tb,' K');\n",
+ "\n",
+ "\n",
+ "\n",
+ "#\n",
+ "\n",
+ "##there are very small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The relative and absolute angles for the flow: \n",
+ " beta3 = 68.20 beta2 = 46.97 deg.\n",
+ " alpha2 = 68.20 alpha3 = 46.97 deg.\n",
+ "\n",
+ " (ii) The velocity at nozzle exit = 652.82 m/s\n",
+ "\n",
+ " (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of 0.96 1016.30 \n",
+ " p2 = 1.99 bar \n",
+ "\n",
+ " and mass flow = 39.10 kg/s\n",
+ "\n",
+ " (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \n",
+ " the blade material density is 8000.00 = 243.74 MPa \n",
+ "\n",
+ " (v) The approximate average mean blade temperature is Tb = 1062.56 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter5_T6xNkI8.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter5_T6xNkI8.ipynb new file mode 100644 index 00000000..62ce6439 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter5_T6xNkI8.ipynb @@ -0,0 +1,167 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:58be2ba5e7552ab96c774dd3b25145aaa3c2ce840367ab463ac8e75c36ccb849"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter5-Axial-flow Compressors and Fans"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "T01 = 293.;##in K\n",
+ "pi = 5.;##pressure ratio\n",
+ "R = 0.5;##stage reaction\n",
+ "Um = 275.;##in m/s\n",
+ "phi = 0.5;##flow coefficient\n",
+ "psi = 0.3;##stage loading factor\n",
+ "eff_stage = 0.888;##stage efficiency\n",
+ "Cp = 1005.;##J/(kgC)\n",
+ "gamma = 1.4;\n",
+ "\n",
+ "##Calculations\n",
+ "beta1 = (180./math.pi)*math.atan((R + 0.5*psi)/phi);\n",
+ "beta2 = (180./math.pi)*math.atan((R - 0.5*psi)/phi);\n",
+ "alpha2 = beta1;\n",
+ "alpha1 = beta2;\n",
+ "delT0 = psi*(Um**2)/Cp;\n",
+ "N = (T01/delT0)*((pi**((gamma-1.)/(eff_stage*gamma))) - 1.);\n",
+ "N = math.ceil(N);\n",
+ "eff_ov = ((pi**((gamma-1.)/gamma)) - 1.)/((pi**((gamma-1.)/(eff_stage*gamma))) - 1.);\n",
+ "print'%s %.2f %s %.2f %s'%('The flow angles are: beta1 = alpha2 = ',beta1,' deg' and 'beta2 = alpha1 = ',math.ceil(beta2),' deg.');\n",
+ "print'%s %.2f %s '%('\\n The number of stages required = ',N,'');\n",
+ "print'%s %.2f %s'%('\\n The overall efficiency = ',eff_ov*100,' percentage');\n",
+ "\n",
+ "##there is a small error in the answer given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The flow angles are: beta1 = alpha2 = 52.43 beta2 = alpha1 = 35.00 deg.\n",
+ "\n",
+ " The number of stages required = 9.00 \n",
+ "\n",
+ " The overall efficiency = 86.06 percentage\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg160"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "R = 0.5;##stage reaction\n",
+ "s_c = 0.9;##space-chord ratio\n",
+ "beta1_ = 44.5;##in deg\n",
+ "beta2_ = -0.5;##in deg\n",
+ "h_c = 2.0;##height-chord ratio\n",
+ "lamda = 0.86;##work done factor\n",
+ "i = 0.4;##mean radius relative incidence\n",
+ "rho = 3.5;##density in kg/m^3\n",
+ "Um = 242.;##in m/s\n",
+ "eps_max = 37.5;##in deg\n",
+ "eps = 37.5;##in deg\n",
+ "delp0 = 0.032;##the profile total pressure loss coefficient\n",
+ "##Calculations\n",
+ "theta = beta1_ - beta2_;\n",
+ "deltaN = (0.229*theta*(s_c**0.5))/(1 - (theta*(s_c**0.5)/500.));\n",
+ "beta2N = deltaN + beta2_;\n",
+ "eps_ = 0.8*eps_max;\n",
+ "i_ = beta2N + eps_ - beta1_;\n",
+ "i = 0.4*eps_ + i_;\n",
+ "beta1 = beta1_ + i;\n",
+ "beta2 = beta1 - eps;\n",
+ "alpha2 = beta1;\n",
+ "alpha1 = beta2;\n",
+ "phi = 1/(math.tan(alpha1*math.pi/180.) + math.tan(beta1*math.pi/180.));\n",
+ "psi = lamda*phi*(math.tan(alpha2*math.pi/180.) - math.tan(alpha1*math.pi/180.));\n",
+ "betam = (180./math.pi)*math.atan(0.5*(math.tan(beta1*math.pi/180.) + math.tan(beta2*math.pi/180.)));\n",
+ "CL = 2*s_c*math.cos(betam*math.pi/180.)*(math.tan(beta1*math.pi/180.) - math.tan(beta2*math.pi/180.));\n",
+ "CDp = s_c*(delp0)*((math.cos(betam*math.pi/180.))**3)/((math.cos(beta1*math.pi/180.))**2);\n",
+ "CDa = 0.02*s_c/h_c;\n",
+ "CDx = 0.018*CL**2;\n",
+ "CD = CDp + CDa + CDx;\n",
+ "eff_tt = 1. - (CD*phi**2)/(psi*s_c*((math.cos(betam*math.pi/180.))**3));\n",
+ "delp = eff_tt*psi*rho*Um**2;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s'%('(i)The nominal deflection= ',eps_,' deg'and '.\\n the nominal incidence = ',i_,' deg.');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (ii)The inlet flow angle, beta1 = alpha2 = ',beta1,' deg'and '\\n outlet flow angle beta2 = alpha1 = ',beta2,' deg.');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (iii)The flow coefficient = ',phi,''and '\\nThe stage loading factor = ',psi,'');\n",
+ "print'%s %.2f %s'%('\\n (iv) The rotor lift coefficient = ',CL,'');\n",
+ "print'%s %.2f %s '%('\\n (v) The overall drag coefficient of each row = ',CD,'');\n",
+ "print'%s %.2f %s %.2f %s'%('\\n (vi) The total-to-total stage efficiency = ',eff_tt,''and '\\n The pressure rise across the stage =',delp/1000,' kPa');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The nominal deflection= 30.00 .\n",
+ " the nominal incidence = -4.31 deg.\n",
+ "\n",
+ " (ii)The inlet flow angle, beta1 = alpha2 = 52.19 \n",
+ " outlet flow angle beta2 = alpha1 = 14.69 deg. \n",
+ "\n",
+ " (iii)The flow coefficient = 0.64 0.57 \n",
+ "\n",
+ " (iv) The rotor lift coefficient = 1.46 \n",
+ "\n",
+ " (v) The overall drag coefficient of each row = 0.09 \n",
+ "\n",
+ " (vi) The total-to-total stage efficiency = 0.86 100.34 kPa\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter6_VZhkm5E.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter6_VZhkm5E.ipynb new file mode 100644 index 00000000..6c0dc077 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter6_VZhkm5E.ipynb @@ -0,0 +1,188 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:eb1ff01409a2a11efc8e58678d7352672b2c4e7f5a219c5319629cbc273b0d97"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter6-Three-dimensional Flows in Axial Turbomachines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg181"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "dt = 1.0;##tip diameter in m\n",
+ "dh = 0.9;##hub diameter in m\n",
+ "alpha1 = 30.;##in deg\n",
+ "beta1 = 60.;##in deg\n",
+ "alpha2 = 60.;##in deg\n",
+ "beta2 = 30.;##in deg\n",
+ "N = 6000.;##rotational speed in rev/min\n",
+ "rhog = 1.5;##gas density in kg/m^3\n",
+ "Rt = 0.5;##degree of reaction at the tip\n",
+ "\n",
+ "##Calculations\n",
+ "omega = 2.*math.pi*N/60.;\n",
+ "Ut = omega*0.5*dt;\n",
+ "Uh = omega*0.5*dh;\n",
+ "cx = Ut/(math.tan(alpha1*math.pi/180.) + math.tan(beta1*math.pi/180.));\n",
+ "mdot = math.pi*((0.5*dt)**2 - (0.5*dh)**2)*rhog*cx;\n",
+ "Wcdot = mdot*Ut*cx*(math.tan(alpha2*math.pi/180.)- math.tan(alpha1*math.pi/180.));\n",
+ "ctheta1t = cx*math.tan(alpha1*math.pi/180.);\n",
+ "ctheta1h = ctheta1t*(dt/dh);\n",
+ "ctheta2t = cx*math.tan(alpha2*math.pi/180.);\n",
+ "ctheta2h = ctheta2t*(dt/dh);\n",
+ "alpha1_ = (180./math.pi)*math.atan(ctheta1h/cx);\n",
+ "beta1_ = (180./math.pi)*math.atan((Uh/cx) - math.tan(alpha1_*math.pi/180.));\n",
+ "alpha2_ = (180./math.pi)*math.atan(ctheta2h/cx);\n",
+ "beta2_ = (180./math.pi)*math.atan((Uh/cx) - math.tan(alpha2_*math.pi/180.));\n",
+ "k = Rt*(0.5*dt)**2;\n",
+ "Rh = 1 - (k/(0.5*dh)**2);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('(i)The axial velocity, cx = ',cx,' m/s');\n",
+ "print'%s %.2f %s'%('\\n (ii)The mass flow rate =',mdot,' kg/s');\n",
+ "print'%s %.2f %s'%('\\n (iii)The power absorbed by the stage = ',Wcdot/10**6,' MW');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s'%('\\n (iv)The flow angles at the hub are:\\n alpha1 = ',alpha1_,' deg'and '\\n beta1 =',beta1_,'deg'and '\\n alpha2 = ',alpha2_,'deg' and'\\n beta2 = ',beta2_, 'deg.')\n",
+ "print'%s %.2f %s'%('\\n (v)The reaction ratio of the stage at the hub, R =.',Rh,'');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The axial velocity, cx = 136.03 m/s\n",
+ "\n",
+ " (ii)The mass flow rate = 30.45 kg/s\n",
+ "\n",
+ " (iii)The power absorbed by the stage = 1.50 MW\n",
+ "\n",
+ " (iv)The flow angles at the hub are:\n",
+ " alpha1 = 32.68 \n",
+ " beta1 = 55.17 \n",
+ " alpha2 = 62.54 \n",
+ " beta2 = 8.75 deg.\n",
+ "\n",
+ " (v)The reaction ratio of the stage at the hub, R =. 0.38 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg185"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "import warnings\n",
+ "warnings.filterwarnings('ignore')\n",
+ "from math import log\n",
+ "import numpy\n",
+ "##given data\n",
+ "\n",
+ "R = 0.5;##degree of reaction\n",
+ "Cp = 1005.;##kJ/(kgC)\n",
+ "cx1_Ut_rt = 0.4;\n",
+ "delT0 = 16.1;##temperature rise\n",
+ "Ut = 300.;##in m/s\n",
+ "\n",
+ "##calculations\n",
+ "A1 = cx1_Ut_rt**2 +(0.5-0.18*math.log(1));\n",
+ "c1 = 2*(1.-R);\n",
+ "c2 = Cp*delT0/(2.*Ut**2 *(1.-R));\n",
+ "A2 = 0.56;\n",
+ "k = numpy.linspace(0.4,1.0,num=61);\n",
+ "i=len(k)\n",
+ "\n",
+ "cx1_Ut=numpy.zeros(i)\n",
+ "cx2_Ut=numpy.zeros(i)\n",
+ "R_=numpy.zeros(i)\n",
+ "Rn=numpy.zeros(i)\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "\n",
+ "for i in range(1,61):\n",
+ " cx1_Ut[i] = math.sqrt(A1 - (c1**2)*(0.5*k[i]**2 - c2*math.log(k[i])));\n",
+ " cx2_Ut[i] = math.sqrt(A2 - (c1**2)*(0.5*k[i]**2 + c2*math.log(k[i])));\n",
+ " R_[i] = 0.778+math.log(k[i]);\n",
+ " Rn[i] = 0.5;\n",
+ "\n",
+ "\n",
+ "##Results\n",
+ "pyplot.plot(k,cx1_Ut);\n",
+ "pyplot.plot(k,cx2_Ut);\n",
+ "pyplot.title(\"Solution of exit axial-velocity profile for a first power stage\")\n",
+ " \n",
+ "pyplot.plot(k,R_);\n",
+ "pyplot.plot(k,Rn);\n",
+ "#ylabel(\"Reaction\",\"fontsize\",3) ;##y label \n",
+ "#legend([\"True Reaction\";\"Nominal Reaction\"] , opt=1); ##legend box\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 7,
+ "text": [
+ "[<matplotlib.lines.Line2D at 0x5b06bb0>]"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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XSUpO4s/TfzJ582Qe/uVhmoxrQsibIdz05U08Ov9Rpm6Zyp6ze0hKTspzl9bcptGjR3tc\nBimflK8wls+by6a16+1ml3oAWutEpdQoTORMX4w/7S6l1Ahr/3iMj+5kpdRWjMJ5Rmt9Pqu8HYkO\nigcVx0f5UO+GetS7oR733HgPALEJsfxx4g/WR6/nl79+4aXlL3E57jItwlvQqmIrWoa3pGXFlpQM\nLulK8QRBELwal90xtdYLMbNsnX8b77R9Fuib03wdiQ6C/ILS3RfiH0K7Su1oV6ndtd9OXjnJ+uj1\nREVH8d7a99h0fBPlipajVcVW11LDMg3x981sUqEgCELhwbb++JkpgPQoV7Qc/ev0p38d44WalJzE\nzjM7WX/MKIXPN37OoYuHaFK+Ca3CU5VCeLHcxObKGZ06dcrzc3gSKV/BxpvL55Vli4+HOXPgyy9d\nzsrlmcDuQCml08oxbOYwetXoxbBGwzL4V865FHeJjcc2si56HVHRUURFRxHiH3JdL6Fp+aY5UjyC\nIAj5woEDMGECTJ4MderAiBGooUPRLgwCe00PIDsUCyxG12pd6VqtK2AGnvdf2E9UdBTrjq5j2rZp\n7Dm3h4ZlGtK6YmtaR7SmdcXWRIRFZJGzIAhCHpCYCPPmwbhxsGkT3H03REYaBQAwdGimf8+KQqUA\n0qKUokbJGtQoWeNaTyMmPoZNxzexLnod327/llELRhHgG0DriNa0qdiG1hGtaVKuCYF+gXkqmyAI\nhZjoaJg40aQqVWDECJg1C4KD3XqaQq0A0qNIQBE6VulIxyodAdNLOHDhAOui17H26FqmbpvKX+f+\n4sZyN9KmYhvaRBilUK5ouSxyFgRByITkZPj1V9PaX7nStO4XLoSGDbP+by6x7RhAu0nteLvb29d5\n+tiFy3GX2Xh8I2uPrmXt0bVERUdRPKg4bSKMQmgb0ZYGZRrg6yORAwRByIKzZ2HSJBg/HsLC4JFH\nYMgQKJp1lBKllIwB5DehgaF0qdqFLlW7AJCsk9lzdg9rjq5h7dG1fLL+E05cOUHL8Ja0jWhLm4g2\ntKrYitBAiYAhCAKgNaxdC198AfPnw4AB8N130Lw5qPwLbmrbHkCDzxsw4/YZNCjTIIN/2ZuzsWdZ\nd3Qda46uYc3RNWw+sZlapWrRNqItbSu1pW1EWxlcFoTCxpUr8O238Pnn4HDAww/D8OFQMneTVl3t\nAdhWAdT4pAaLhi2iRsnsLPVqf+IS4/jjxB/XFMKaI2sI9g82E9oizKS2+mXq46PyfJVOQRDym507\nTWv/22+hUycYORK6dnW5te+1CqDihxWJeiCKisUqZvCvgo3Wmn3n97H6yGqTjq7mdMxpWldsTbtK\n7WhfqT3Nw5vb1gwmCEIWJCaaCVuffQa7dsGDD5oU4b6ev9cqgNLvlmb3qN2UDintIanyn9Mxp1MV\nwpHV7DyzkxvL3Uj7Su1pV6kdbSu1pXhQcU+LKQhCZpw6ZSZsjRsHVavCqFFw660QEOD2U3mtAij6\nVlFOPn2SogHZXq/D67gSf4X10etZdWQVq46sYsOxDVQvUZ32ldrTvnJ72ldqT/nQ8p4WUxAErWHd\nOvj0U+O6eccd8Oij0KhRnp7WaxWA32t+OF5y4OdjW0elfCc+KZ4/TvzBqsNGIaw+sprSIaXpULkD\nHSp3oGPljlQunum65oIguJOrV2HGDFPxX7pkKv177oHi+dNT90oFkJicSNAbQSS+IksHZ0ayTmbH\n6R2sPLzyWgr0CzQKoVIHOlbpSM2SNVH56FYmCIWCQ4fMoO6kSdCiBTz2GPToAT7568ThlQrgSvwV\nyr1fjisvXPGgVAUPrTV7z+9lxaEVrDyykhWHVpCYnHitd9CpSifqlK4jCkEQcoPWJg7PJ5+YmbrD\nhxtvnhqe81T0SgVwNvYsdT6tw9lnznpQqoKP1ppDFw+x4vAKkw6tICYhhk5VOl1TCHVL1xWFIAiZ\nERNj3DfHjjXhGh57DIYNy9ZM3bzGKxVA9KVoWk1sRfR/0i4vLLjK4YuHWXF4BZGHIok8FElMQgwd\nK3ekc5XO0kMQBGcOHzYunJMmQdu28Pjj0KVLvs7UzQqvVAD7zu+j17Re7Ht8nwelKhwcvnjYKIPD\nkSw/uBxHooNOVTrRuUpnulTtQo2SNUQhCIUHrWHVKvj4Y2PuueceM7BbrZqnJUsXr1QAO07v4M6f\n7mTHyB0elKpwcujiIZYfXM7yQ8tZdnAZwLW4R52rdBYvI8E7cThMLJ5PPjGePY8/bmLv28DMkxle\nqQA2Hd/Ew/MeZtNDmzwolZAyW3nZwWXXFEKxwGJ0qdqFrlW70rlqZ8oUKeNpMQUh95w8abx5xo+H\nJk3giSege/d89+bJLV4ZDdTOkUALE0opapaqSc1SNRlx0wi01uw4vYOlB5fy7fZvGTFvBJXCKtG1\nale6VetGh8odJOKpUDD44w8YMwZ++cWEXnZeZasQYcsewG8HfuPt1W/z292/eVAqISsSkxPZdHwT\nSw8sZenBpWw4toEby914TSG0rNiSAF/3T38XhFyRlARz58JHH8HBg8ab54EHch2J0w54pQlo3l/z\nGLdpHPOGzvOgVEJOiU2IZfWR1Sw9sJTfDv7GvvP7aF+pPd2qdaN7te7Uu6GeDCgL+c/ly2Yh9Y8/\nhhtugCefhNtuA39/T0vmMmICEmxDiH8IPar3oEf1HoCZz7Hs4DJ+O/AbH6//mLjEOLpX7073aiaV\nLVrWwxILXs2RI8Z3f9Ik4745bRq0bu1pqWyFKAAhzygdUpo76t/BHfXvuLa28q/7f2Xmrpk8tvAx\nKodVpnu17vSo3oP2ldvLPRfcw8aN8OGHZn3d4cPh99/NwurCP7ClCWjiHxOJio5iYr+JHpRKyEsS\nkxPZeGwjv+7/lcX7F7P99HbaRrSlZ/We9KzRU2YoCzkjKckM6H74oZnA9e9/G/t+sWKelixP8cox\ngE83fMrus7v5tM+nHpRKyE8uOi6y9MBSFu9fzOL9i0nWyfSs3pNeNXrRrVo3WQdBSJ/YWPj6a1Px\nlygBTz0FAweCny2NG25HxgAEr6B4UHEG1hvIwHoD0Vqz59weFu1bxFebv+K+OffRqGwjetXoRa8a\nvWhavqksnVnYOXXKhGkYN86EaZg82XxKrzFHiAIQbIdSijql61CndB2eaPUEVxOusurIKhbtW8Rd\ns+7i/NXz9Kzek941etOjeg9KhZTytMhCfrF7N3zwAfz0E9x5J6xeDbVqeVqqAostTUAvLXsJlRRE\n98CXSE42Afi0Tv1MPw8zec/H5/ptHx/TG/T1TU1+fsYDLOUzJQUEmOTnJw0JO3Po4iEW7l3Iwn0L\nWXF4BfVvqE/vGr3pU7MPTco3kd6Bt6E1rFkD774L69ebEMwjRxqXzkKOV44BPP3r0+zcUI4dXz5N\ntWr/rNzTw1lJpGwnJZntpCSzPnNSUup2QkLqp3OKjze/pyiDgAAICjIpMDB1OygIgoOvTyEhqalI\nkdTPIkVMSJG0KTTU5CnKJvfEJcax8vBKFuxdwIJ9C7gUd4k+Nfpwc62b6VatG8UCvXsQ0KtJSjKL\nqr/3Hpw5A08/bbx6goM9LZlt8EoF8Oj8R9kXVZcOQaN48cX8lyc5OVUZxMWZ5HCkprg4Ey8qbYqN\nTU0xMSbFxsKVK6nfr1wx6fJl85mUZBRBaKhxWAgNhbAwsx0Wdn0qXvyfqUQJo2BEiRj2nd9nlMHe\nBaw9upYW4S24pdYt3FLrFmqU9NzCHUIOcDhg6lR4/30zS/f//g8GDDDdd+E6vHYQODk+iBAPzdD2\n8TEt88BAUyHnJfHxRhmkpEuXTPr7b5NStk+dgosX4cIF8+m8nZBgFEFKKlkSSpVK/UzZLl36+hTk\nhcMsNUrW4PGWj/N4y8eJiY9h6cGlzPtrHu+ueZfQwFBuqWmUQbtK7fD3LfgzQb2KCxdMYLaxY+Gm\nm2DiRGjfXlo3eYg9FUCSg6S4YEJCPC1J3hMQkFpJ55a4OPPupKTz5+HcudS0fTucPWu2nT/9/Y0i\nKFPGmFOdP8uUgbJlUz9vuKHgzZwvElCEfrX70a92P7TWbD65mXl/zeOZ355h//n99KzRk761+tK7\nRm9KBJfwtLiFl+hoE59n8mTo1w+WLIEGDTwtVaHAngog0UGSI6hQKAB3EBgI5cqZlF20NiaoM2dM\nOn069fP4cdiyxWyfOmU+z541ZqmU86RNFSpA+fLmMyzMfo02pRRNyzelafmmvNLxFY5fPs78v+Yz\nY8cMHp73MM0qNKNvrb70r92f6iWre1rcwsGuXca+P3u2WXhl61aIiPC0VIUK2yqABFEAeYpSqWMP\n2VnsKDnZ9BxOnTIh1J3T5s1w4oRJx48bk1SFCiaFh6d+pqSKFc1vgYF5X86MqBBagQebPciDzR4k\nNiGWpQeWMnfPXN5d8y6lQkrRv3Z/+tfuT/Pw5uJV5G6iouCdd2DtWhg1CvbtK9AROQsyLisApVQv\nYAzgC0zUWr+TzjGdgI8Af+Cs1rpTZnk6Eh0kXg2SwX4b4eNjzEA33JB17/zKlVRlcOyY+YyOhg0b\nzGfKbyVKGGWQkipVMg3AlM8KFfLH7BTiH0Lf2n3pW7svyTqZDcc2MGf3HO6dcy8XHRfpV7sfA+oM\noHOVzgT6eVBrFWS0Nqad//3PhGJ++mmz0Lq08jyKS15ASilfYA/QDTgGbASGaK13OR1THFgD9NRa\nRyulSmutz6bJ5zovoLaT2hIz+13G/KctnTrlWjzBxiQlGdNSdDQcPZr6eeSI+Tx61PQ2ypaFypWN\nUqhcOTVVqWI+87r++OvcX8zZPYfZe2az88xOetXoxYDaA+hds7e4mGaHpCSYNctU/A4HPPecmcBV\n0AaUbIpH3UCVUq2B0VrrXtb35wC01m87HTMSKKe1fiWTfK5TAM2+bMbVH75kylvNaNEi1+IJBZyE\nBNNTOHzYpCNHUrcPHTKfYWFGGVSpYkxZVaumflaq5N565uSVk8zdM5fZu2ez+shqOlTuwG11b6Nf\n7X6UDintvhN5A/HxpoX/9tumq/f889C3b4FZarGg4Gk30HDgqNP3aKBlmmNqAv5KqeVAKPCx1vqb\nzDJ1JDqIj5UxgMKOv39qiz89kpNNL+HgQZMOHTITRb/7znw/ccKYkapVg+rVTUrZrlEj54EiyxUt\nx0PNHuKhZg/xt+NvFuxdwMzdM3ly8ZM0Ld+U2+rcxq11b6VisYoul73AEhsLX31lBndr1zaxejp1\nsp9XgAC4rgCy033wB5oCXYEQYJ1SKkprvdf5oFdfffXa9oVzF/CNEQUgZI6Pj/E8Kl8e2rT55/6E\nBNNL2L8fDhwwn1FR5nP/fjMbu0aN61OtWlCzZtbKISwojCENhzCk4RCuJlw16xzsnsnoyNHULl2b\n2+vezsB6A6lSvEqelN12/P238eEfM8YsuvLzz9C8uael8joiIyOJjIx0W36umoBaAa86mYCeB5Kd\nB4KVUs8CwVrrV63vE4FFWuufnI65zgQU/mE48Z9tYPua8By5NgpCdtHa9BD27UtNf/0Fe/ea7dDQ\nVGVQq5ZZL7x2bdODCMhkmeP4pHiWH1zOTzt/Yvae2VQOq8zt9W7n9nq3e+dM5LNnzVKLX3wBvXoZ\nG7/48Ocbnh4D8MMMAncFjgMb+OcgcB3gU6AnEAisBwZrrXc6HXOdAij1bini3/+LY/tKeft6DoIN\nSU42Yw979xql8NdfsGePSUePmrGF2rWNUqhbN/WzRJq5ZInJiaw8vJKfdv7EzF0zqRBagTvq38Gg\neoMK/lyDkydNVM6vvoLbb4dnnzW2NSFf8XgsIKVUb1LdQL/SWv9PKTUCQGs93jrmaeBeIBmYoLX+\nJE0e1ymAIm8VwfH6aRyXioizgGAr4uKM+WjPHhOZeNcu87l7t4lRVq9eaqpb13yWLQvJOolVR1bx\nw58/MHPXTMKLhTOo3iAG1x9M1RJVPV2s7HP0qInK+e23MGyYidMjk7c8hscVgDtwVgBaa/xe98Pn\nzTgS4mw5T00Q/oHWZn7D7t2wc+f1KTkZ6tc3qUEDqFMviSslV7E4+nt+3vUzVUtUZXD9wQyqN4iI\nMJtWpgcOGFfOn382Sy3+5z85m3ou5AlepwASkhIIeSuEIh8kcPGihwUTBDdw+jT8+Sfs2HH9p78/\n1G+YSPF7N5gxAAAgAElEQVQmyzlbdgbbEmZTv0xdhja6k0H1BlG2aFlPi27sX2+9ZdbbHTkSnnjC\ntcBVglvxOgVwOe4y5T+oQLFPL3P8uIcFE4Q8IqXHsGOHCda3fTts3RHP7oRfCWg2g7hK86jk24Le\nEUN4oO1tNKwZlr8u9Dt3wptvwq+/wmOPweOPm/jjgq3wOgVwJuYMtcfWo+TEM+zb52HBBCGfSUw0\nje6NW2KZ9ecvRMV8x+kiy/E93JUaV/9F5/CbuenGIG680ZiU3B5P6c8/4fXXYdky09ofNSrnEyaE\nfMPrFMDRv4/SfHwbykw7yrZtHhZMEGzARcdFvt74M1N+/5Y9f2+hwqVbSd7yL05EdaRWDV+aNoUm\nTaBpU2jcOJdrWGzfbir+FSuMff/RR81ECcHWeJ0C2HtuL10m9SH8571ERXlYMEGwGdGXopmxYwbf\nbv+W01fO0LXMUKpevovT2xvyxx/GpFSxIjRrlpqaNs2kEb9tG7z2mllc/amn4JFHpOIvQHidAth+\najv9pw6l8oLtLF/uYcEEwcb8efpPpm2bxrTt0ygVXIq7Gt3FHXWHcjG6PL//zrW0datRCjfdZFLz\n5tDUfzsh7/3XVPz/93/w8MNmbVGhQOF1CmDjsY0MnT6SWpEbmT/fw4IJQgEgWSez4tAKpm6byuzd\ns2kZ3pLhjYczoM4Agv2DSUw08xU2bYLoRTtoteQ1Gl1YybRyT7Ov+yPc2LYILVsaF1U/8bwuUHid\nAlh1eBUPff8CDTau4scfPSyYIBQwYhNimb17Nl9v/ZqNxzZye73buefGe2h9KQz12msQGQlPPUXc\nA4+ybX8RNm406zSsX2/meDVtCi1aQKtWJlUsxHHtCgJepwCW7F/Ckz+9S7OdS/j6aw8LJggFmOhL\n0cyf9xHlP5pA292xbB3ahdqjxxJeoXa6x//9N2zcaJTB+vWwbp3xMmrVysR3a9XKKAhZqMk+eDoc\ntNtxJDpQyRIJVBBc4sABKr7+OiPmzUM//n9smtqGH/b/yA/ftKZlxZbcd+N99Kvd77oVzsLCoFs3\nk8DMVThwwERQjYoyYbZ37YKGDaFtWxOBtU0bE41VKJjYrgfw458/8sasH+h24Uc++MDDgglCQePI\nEXjjDZg50/jwP/HEdRO4YhNimblrJpM2T2L76e0MbTCU+5veT6OyjbKVfUyM6SWsXZuawsKgXTto\n39581qkj677kF97ZA0iSHoAg5IgTJ0ysnm+/hREjzGyydBZaD/EPYVijYQxrNIwDFw4wefNk+nzb\nh/Bi4TzY9EEG1x9MaGDGEwmKFDHru6Qs1ZqcbOIfrVljHIreeQcuXjQ9hPbtoUMHYzaSoI72xHY9\ngAm/T+Cz2RsYHDKB55/3sGCCYHfOnjXROb/6CoYPN/H4y5TJURaJyYks3reYiZsnEnkokoF1B/Jg\n0wdpEd4ClYuVvI4fN8pg1SpYudKYkVq1MsqgQwdo2RKCgnKcrZAOXtkD0InSAxCETPn7bxOP/7PP\nYPBgM6ErPDxXWfn5+HFzrZu5udbNnLh8gq+3fs3QmUMJDQhlRLMR/KvRvygWmP1wEBUqwB13mARw\n/rzpIaxcaaYc7Nxp5iKk9CREIXgO21nqHIkOdIIoAEFIl9hY0+KvWdP4bW7aBJ9/nuvKPy3lQ8vz\nXLvn2PvYXt7r/h5LDy6l8pjKPDj3QTYd35SrPEuWNOvBv/eecTk9fhyeecYU5ZlnoHRp6NzZRKJY\ns8Ys5SnkD7bsASTHiwIQhOuIj4cJE0yEzrZtTcyeunXz7HQ+yofu1bvTvXp3Tl45yaTNkxj04yBK\nh5Rm5E0jGdxgMCH+uXtJixWD3r1NArh82ZiLli83QUf37jVF7NLFeCQ1biyDynmF7cYAXlz6IrN+\nDOHNni9y660eFkwQPE1SkhnYHT3auNe88YYJ8OMJUZKTWLx/MZ9v/Jyo6CiGNx7Owzc9TM1SNd16\nnvPnjX5butSks2dTlUG3blC1AC2gltd43USwpxY/xbwZFbhl6FAmBkk8aKEQk5gIDgcoZYzkvr6e\nlugayTqZ+KR4EpIS8PXxIcA3ED+fvDEoaG0uRUoC8PcDP3/w8wVyXf0VfC516OB9g8CJjiDOBFzl\n8YoVeVrWGxUKG6tXw3//C1euwCuvQK9eRgnYEEeig9m7ZzP+9y+5cPU89ze5n7sa3UXx4LxZPEZr\nM4i8bBksXQYbN5iJaV26QNeuJix2YTIXuXqVbdcDuH/O/fw2pQ2tn+5Am8rBPC7BSITCwtatxo1z\nzx4TonnIEFu1+rNiffR6xm4Yy/y98xlUbxCPt3ycBmUa5Ok5r1413kWLF5t0+jT06GHGF3r0yLFH\nbIHDVROQ7XSlI8lBwtUg4nyTKFqAHn5ByDUHD8KwYdCzJ/TpY2ZWDRtWoCp/gJYVWzLttmnsfnQ3\nEcUi6PFND7p/0535f80nWSfnyTmDg81l+/BDs5jZpk3QsaNZu75WLeNuOnq0mb2cnDciFGjspwAS\nHSTEBuHwSSS0gL0AgpAjzpyBf//b1FI1axr3l8ceg4AAT0vmEmWLluXlji9z6IlDDG88nFciX6HO\np3X4bMNnXIm/kqfnrlwZHnoIZs0yvYH33jPupsOHm/kJ994LP/0Ely7lqRgFBlsqgPirQcSpJFEA\ngncSE2Oc3lPcOHfuNM3UXK3laF8CfAMY1mgYmx7cxFf9vmLZoWVUGVOF5357jmOXjuX9+QPMRLP3\n3jOXeO1aE5Zi4kQT5rp7dxg7Fg4dynNRbIs9FUBMELEkESqrUwjeRGIijB9vWvu7dplZUR9/7PWG\naqUU7Su35+c7fmbjgxu5mnCVhl80ZPjs4Ww7lX8Lf1erZjpYixbBsWNm9cs//jAdsEaN4MUXC5+p\nyH4KIMGBIyaIWC09AMFL0BpmzzZLbv3wA/zyC0yfbmqkQkbVElX5uPfH7Ht8H3VK1aHXtF70+KYH\nS/YvIT8dUkJD4bbbYPJkOHkSxo0zUy7uugsqVYJHH4UlS8z8O2/Gdl5ATcc1Y8fbXxI+I4GljRtT\nTVafEAoy69aZADiXL5tQmT172tal0xPEJcYxfft03l/3PoG+gTzb9lkG1huYZ3MKssPu3UZfz55t\ngqr26WOURa9e2C5CgddNBKv9ST1OfvIj/lMusKtFC24o4ANiQiFl3z54/nmzksrrr5umpfRoMyRZ\nJzP/r/m8veZtTl45ydOtn+aeG+8h2N+zDcDjx2HOHONVtHGjGTcYOBBuvtmEtPA03ucGmugg2D+I\nK0liAhIKIGfPGs+eVq3MrKQ9e+Cee6TyzwIf5UPf2n1Zc98avh7wNQv2LaDqx1V5e/XbXIrznMtO\nhQpmrOC332D/ftMbmDbNDCL372+idBRkjyLbKYCriQ6Cg4JIAgIL05Q+oWDjcJgonXXqGGPyzp3w\nwgv2sxkUANpVascvQ35hyV1L2HZqG9U/qc7o5aM5F3vOo3KVLg333Qfz55tArLffDt9/DxERMGCA\nGda5fNmjIuYY29WwcYkOAkP9Kerrm6vFKAQhX9EaZswwLp1r1pj06ade79mTHzQs25DpA6ez9r61\nHLt8jJpja/J/v/4fJ6+c9LRohIUZq97cuXD4sBkjmD7d9Axuv92YjK5e9bSUWWM/BZDkIKiYv5h/\nBPuzbp1ZFf3dd407yZw5ULu2p6XyOmqWqsnEfhPZ8vAWHIkO6n1WjycXPcmJyyc8LRpglly++26Y\nN89M6u7dG774wpiP7r4bFiyw7xoHtlIAWmvikx0EhvqKAhDsy8GDZhWuO+4wBuJNm1IXyRXyjEph\nlRjbZyx/jvwTgPqf17eVIgCz+M3995sxg1274KabjA9AeLiZg7B+vek02gVbKYCE5AR8lR8BxbQo\nAMF+XLpkPHtuugnq1zcDvHffXbjCT9qA8qHl+ajXR9cpgicWPWErRQBQrpxZ4GbdOpPKlDGPS61a\nJtjrPhtEu7fVk+tIdOCvgvApKrOABRuRlGRW46pd28wa2r7dhGmWAV6P4qwIFIr6n9fnmSXPeHyw\nOD2qV4eXXzZzDKZPN4vetG1r0oQJZolnT2A7BeBHEL5FJRKoYBOWLTMBZL75xhh5J082xl3BNqQo\ngu2PbOdy3GVqfVqL0ctH87fDQ7VqJihlQk98/DFER5vo34sXmyB2Q4ea7aSk/JPHZQWglOqllNqt\nlNqrlHo2k+OaK6USlVK3ZXRMigJQRWQOgOBh9u+HW2+FBx4wTbcVKzy2FKOQPcKLhfPFLV+w6cFN\nHP77MDXH1uTt1W8TmxDradHSxd8f+vY10Un37ze9gZdeMsrgpZfgwIG8l8ElBaCU8gU+BXoB9YAh\nSql/rFRtHfcOsIhMFnBzJDrw1UEQIqGgBQ9x6RI8+yy0bAktWhh//ttvl/ANBYiqJaoyZcAUVt67\nkt9P/E6tsbWY8PsEEpMTPS1ahpQqZeIPbdxogtXFxJhHsEsXM9ksr1xKXe0BtAD2aa0Paa0TgBlA\n/3SOewz4CTiTWWaORAc+OgiCpQcg5DPJyTBpkpnIdeoUbNtmBnyDgjwtmZBL6pSuw4+DfmTm4JlM\n3zGdBp83YOaumfkadC43NGgAH31kTESPPGKsjxERZkD5zz/dey5XFUA4cNTpe7T12zWUUuEYpfCF\n9VOGV9+R6MAnKQgdJIPAQj6ybp1pbk2YYHz5p0wRO78X0SK8BcvuXsaYXmN4bcVrtP6qNSsPr/S0\nWFkSGAiDBpkewe+/m/kGPXpAu3ZGKbijV+CqAsiOKh0DPGdFe1NkYQLySQ4iKVAGgYV84Phx45c3\naJCJ37N2rRmhE7wOpRS9avTijxF/MKrFKO6adRe3fX8be8/t9bRo2aJyZbNM9OHD8PTTxiwUEeF6\nvq4qgGOAsxgRmF6AM82AGUqpg8BA4HOlVL+0Gb366qtM+GAClyKPcW7POjEBCXlHXJwJzdyokZmh\ns2uXWYNX7Pxej4/yYVijYex+dDctwlvQ+qvWPLnoSc5fPe9p0bLF6tWRbNnyKq1avcq//vWqy/m5\nFA5aKeUH7AG6AseBDcAQrfWuDI6fDPyitZ6Z5nettWbunrk8MmEiFbu+xdPNyjBI4qkI7mbBAnji\nCWPr//BDqFHD0xIJHuR0zGlGLx/Nz7t+5oX2LzCy+UgCfAtOCHqPhoPWWicCo4DFwE7ge631LqXU\nCKXUiJzm50h0QGIQCX4yCCy4mf37oV8/U/l//LGJ4iWVf6GnTJEyfHHLFywfvpxF+xbReFxjft3/\nq6fFyjdcHmnVWi8EFqb5bXwGx96bWV6ORAfJCUHE+cogsOAmYmPh7bfh88+N8fTHH83omiA4Ub9M\nfRb+ayHz985n5PyRNCjTgA97fki1Et69bKftZgLr+CDifGQQWHARrWHmTKhXD/buhS1bzLRLqfyF\nDFBKcUutW/hz5J+0DG9J8wnNeWnZS8TEx3hatDzDdgogKS6Iq0pMQIIL/PWXicn78ssmdMN335lA\n7YKQDQL9Anm+/fNsfXgrBy8epO5ndZm1a5bt5w/kBlsqgFhkJrCQC2Ji4MUXTYz+Hj1Mq79zZ09L\nJRRQKharyLe3fcvUW6fywrIX6PtdXw5eOOhpsdyK7RRAoiOIq0gPQMgBWsOsWcbcc/CgmcX7n/+Y\nYCuC4CKdqnRi68NbaRvRluYTmvPWqreIT4r3tFhuwXYKICE+mCQt6wEL2eTAAbjlFtPynzLFxNqV\nWbyCmwnwDeD59s+z8cGNrD26lsbjGrPq8CpPi+UytqplHYkOEpJDZD1gIWvi4sxSSy1aQIcOYu4R\n8oWqJaryy5BfeLPLm9z5852MnD+SS3GXPC1WrrGVAria4CBJhxDqJ+YfIRN++w0aNjQBUn7/3UTv\nDCg4k3eEgo1Sitvq3safI/8kISmBBp83YP5f8z0tVq6wlQKIiXPgFxQk9n8hfU6ehCFD4MEH4YMP\nYPZsEyRFEDxA8aDiTOg3gSkDpvD4oscZ+vNQzsRkGvDYdthOAfgHiwIQ0pCUZCZyNWwIVaqYmLh9\n+3paKkEAoEvVLmx/ZDvhoeE0/KIhP+/82dMiZRtbTbeNiXPgFxwok8CEVLZsgREjjEfP8uUmWLog\n2IwQ/xDe6/EeA+sN5O5ZdzNr9yzG9h5LieASnhYtU2zVA4hNcOAfHChhIAS4cgWeegp69oSHHoKV\nK6XyF2xPq4qt2PLwFkoGl6TRuEYs3rfY0yJliq0UwNV4B34h/mICKuzMnw/168OZM7B9O9x/P4hb\nsFBACPEP4ZPenzCl/xQemvcQD897mCvxVzwtVrrY6q1yJDrwDRYFUGg5cQLuuMMszvLVVzB1KkhI\ncKGA0rVaV7Y9vA1HooOm45vy+/HfPS3SP7ChAvATBVDYSE6GcePMAi01a5pWf7dunpZKEFwmLCiM\nKQOm8Hrn1+n9bW8+XPchyTrZ02Jdw1bGdqMAfGUQuDCxc6ex8ScnyyCv4LUMbjCYFuEtGDpzKEsO\nLGFK/ymULVrW02LZqwcQl+TAJ8hHBoELA3Fx8N//QseOMHQorF4tlb/g1VQtUZWV96ykWflmNBnf\nxBYDxLZSAPHJDgj0EROQt7NuHTRtambx/vEHjBwpg7xCocDf1583urzB9IHTeeCXB3hl+SskJSd5\nTB5bvXUJ2gFBShSAt3L5Mjz2GAwcCK++CnPmQESEp6UShHynU5VObHpwE6uOrKLP9D6cjT3rETls\npwCSA7QoAG9k0SJj4omJgR07YNAgkIB/QiGmbNGyLLlrCU3KNeGmL29i47GN+S6DbRSA1poE7SAp\nABkE9ibOnYPhw+GRR4xr56RJULKkp6USBFvg5+PH293eZkyvMdw8/WbGbxqfryuP2UYBJCQn4IMf\nif6yILxXoDX89JOJ31OihLh2CkImDKgzgNX3rebTjZ/ywNwH8m3BGdsoAEeiA18dRIKfrAZW4Dl5\n0tj5X37ZKIExY6BoUU9LJQi2plapWkTdH8UFxwW6Te2WL+MCtlEAVxOu4quDiPOV9YALLFrDtGnQ\nuDHUrQubN5v1eQVByBZFAorw0x0/0a5SO1pObMnOMzvz9Hy2sbU4Eh34JAXj8JEeQIHk+HETtfPw\nYViwAJo187REglAg8VE+vNX1LeqUrkOnKZ345tZv6FmjZ96cK09yzQWORAfoIiSjZT3ggoTWZi3e\nG280vv2bNknlLwhu4O7GdzNz8EzumXMPY9ePzZPBYVv1ABRhhOAn6wEXFI4dM2Ecjh+HX381SkAQ\nBLfRrlI71t63llu+u4XDfx/m3e7v4qPc10C2TVPbkeggmWIUUWL+sT1am0idTZpAy5awYYNU/oKQ\nR1QtUZVV965i7dG13DfnPhKSEtyWt60UABSjiI8oAFtz4gT07w/vvw+LF8Mrr5jVugRByDNKBpdk\nyV1LOB1zmtt+uI3YhFi35GsrBZBEqAwA2xWtYfp009Jv3NjY+ps08bRUglBoKBJQhDl3ziEsMIye\n03py0XHR5TxtNQagKUKonygA23HmjJnJu2uXWa3rpps8LZEgFEr8ff2ZeutU/rP4P3SY3MHl/GzV\nA0hWRQjzt41OEgDmzjUt/ipVTPROqfwFwaP4KB8+6vkRg+sPdj0vN8jjFswgcBHCAqQHYAsuXYL7\n7oMnnoAZM4zNPyjI01IJggAopXixw4su52MbBRAT70D7BosCsAPLl5vlGf39YetW6OB6V1MQBPth\nG3vL5asOfPyDKSaDwJ7D4YAXXzQt/okToXdvT0skCEIeYpsewBWHA5+AQAkF7Sm2bDH2/cOHYds2\nqfwFoRBgHwVw1YFPQJCEgs5vkpLgnXege3d49ln48UcoVcrTUgmCkA+4rACUUr2UUruVUnuVUs+m\ns/9fSqmtSqltSqk1SqlG6eVzJc6BCgyQeQD5yaFD0LmzWa1r0ya46y5ZpUsQChEuKQCllC/wKdAL\nqAcMUUrVTXPYAaCD1roR8DrwZXp5xcQ58An0FwWQH6SEbW7RAvr1g6VLoXJlT0slCEI+46q9pQWw\nT2t9CEApNQPoD+xKOUBrvc7p+PVAxfQyiolzQJC/jAHkNRcvmkldW7dKADdBKOS4agIKB446fY+2\nfsuI+4EF6e24Gu9ABfhJDyAvWbHCTOoqXdpM6pLKXxAKNa72ALIdoFop1Rm4D2ib3v7YBAc6wFcG\ngfOChAQTtO3rr417Z58+npZIEAQb4GptewyIcPoegekFXIc18DsB6KW1vpBeRgcWbCa+9DdM2hTJ\nrd2706lTJxdFEwDYtw+GDoUyZYyrZ5kynpZIEIRcEhkZSWRkpNvyU66sMqOU8gP2AF2B48AGYIjW\nepfTMZWAZcAwrXVUBvno+v/rxV9NnuFY57bcEBCQa5kEC63hm2/gqadM63/UKPHwEQQvQymF1jrX\nL7ZLPQCtdaJSahSwGPAFvtJa71JKjbD2jwdeAUoAX1grfSVorVukzSsu0UGSHzII7A7+/htGjjQt\n/qVLTVgHQRCENLhscNdaLwQWpvltvNP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+ "text": [
+ "<matplotlib.figure.Figure at 0x5a893d0>"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter7_2hkovpj.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter7_2hkovpj.ipynb new file mode 100644 index 00000000..d65c95f3 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter7_2hkovpj.ipynb @@ -0,0 +1,280 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a61692019b8140a36f6ac02790d0dad90729cb0b28691dad1652c231a1bf0a41"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter7-Centrifugal Pumps,Fans and Compressors\n"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg216"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##function to calculate blade cavitation coefficient\n",
+ "\n",
+ "##given data\n",
+ "Q = 25;##flow rate in dm^3/s\n",
+ "omega = 1450;##rotational speed in rev/min\n",
+ "omega_ss = 3;##max. suction specific speed in rad/sec\n",
+ "r = 0.3;##inlet eye radius ratio\n",
+ "g = 9.81;##in m/s^2\n",
+ "\n",
+ "##Calculations\n",
+ "k = 1.-(r**2);\n",
+ "sigmab = 0.3;##initial guess\n",
+ "d = (sigmab**2)*(1. + sigmab)- (((3.42*k)**2)/(omega_ss**4));\n",
+ "i = 0;\n",
+ "if sigmab>0:\n",
+ "\tsigmab = sigmab - 0.0001;\n",
+ "elif sigmab<0:\n",
+ "\tsigmab = sigmab + 0.0001;\n",
+ "\n",
+ "phi = (sigmab/(2.*(1.+sigmab)))**0.5;\n",
+ "rs1 = ((Q*10**-3.)/(math.pi*k*(omega*math.pi/30.)*phi))**(1./3.);\n",
+ "ds1 = 2.*rs1;\n",
+ "cx1 = phi*(omega*math.pi/30.)*rs1;\n",
+ "Hs = (0.75*sigmab*cx1**2)/(g*phi**2);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('(i)The blade cavitation coefficient = ',sigmab,'');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (ii)The shroud radius at the eye = ',rs1,' m' and '\\n The required diameter of the eye = ',ds1*10**3,'mm');\n",
+ "print'%s %.2f %s'%('\\n (iii)The eye axial velocity = ',cx1,' m/s');\n",
+ "print'%s %.2f %s'%('\\n (iv)The NPSH = ',Hs,' m');\n",
+ "\n",
+ "#asnwer is wrong due to round off error"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The blade cavitation coefficient = 0.30 \n",
+ "\n",
+ " (ii)The shroud radius at the eye = 0.06 \n",
+ " The required diameter of the eye = 110.70 mm \n",
+ "\n",
+ " (iii)The eye axial velocity = 2.85 m/s\n",
+ "\n",
+ " (iv)The NPSH = 1.62 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg220"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "alpha1 = 30.;##prewhirl in deg\n",
+ "hs = 0.4;##inlet hub-shrub radius ratio\n",
+ "Mmax = 0.9;##max Mach number\n",
+ "Q = 1;##air mass flow in kg/s\n",
+ "p01 = 101.3;##stagnation pressure in kPa\n",
+ "T01 = 288.;##stagnation temperature in K\n",
+ "gamma = 1.4;\n",
+ "Rg = 287.;##in J/(kgK)\n",
+ "\n",
+ "##Calculationsasza\n",
+ "beta1 = 49.4;##in deg\n",
+ "f = 0.4307;\n",
+ "a01 = math.sqrt(gamma*Rg*T01);\n",
+ "rho01 = p01*1000./(Rg*T01);\n",
+ "k = 1-(hs**2);\n",
+ "omega = (math.pi*f*k*rho01*a01**3)**0.5;\n",
+ "N = (omega*60./(2.*math.pi));\n",
+ "rho1 = rho01/(1. + 0.2*(Mmax*math.cos(beta1*math.pi/180.))**2)**2.5;\n",
+ "cx = ((omega**2.)/(math.pi*k*rho1*(math.tan(beta1*math.pi/180.) + math.tan(alpha1*math.pi/180.))**2.))**(1/3.);\n",
+ "rs1 = (1./(math.pi*rho1*cx*k))**0.5;\n",
+ "\n",
+ "ds1 = 2.*rs1;\n",
+ "U = omega*rs1;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s '%('(i)The rotational speed of the impeller = ',omega,' rad/s'and 'N = ',N,' rev/min.');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (ii)The inlet static density downstream of the guide vanes at the shroud = ',rho1,' kg/m^3.'and'\\n The axial velocity = ',cx,' m/s.');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (iii)The inducer tip diameter = ',ds1*100,' cm'and '\\n U = ',U,' m/s.');\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The rotational speed of the impeller = 7404.94 N = 70711.94 rev/min. \n",
+ "\n",
+ " (ii)The inlet static density downstream of the guide vanes at the shroud = 1.04 \n",
+ " The axial velocity = 187.38 m/s. \n",
+ "\n",
+ " (iii)The inducer tip diameter = 8.83 \n",
+ " U = 326.81 m/s. \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg228"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Q = 0.1;##in m^3/s\n",
+ "N = 1200.;##rotational speed in rev/min\n",
+ "beta2_ = 50.;##in deg\n",
+ "D = 0.4;##impeller external diameter in m\n",
+ "d = 0.2;##impeller internal diameter in m\n",
+ "b2 = 31.7;##axial width in mm\n",
+ "eff = 0.515;##diffuser efficiency\n",
+ "H = 0.1;##head losses\n",
+ "De = 0.15;##diffuser exit diameter\n",
+ "A = 0.77;\n",
+ "B = 1.;\n",
+ "g = 9.81;\n",
+ "\n",
+ "##Calculations\n",
+ "U2 = math.pi*N*D/60.;\n",
+ "cr2 = Q/(math.pi*D*b2/1000.);\n",
+ "sigmaB = (A - H*math.tan(beta2_*math.pi/180.))/(B - H*math.tan(beta2_*math.pi/180.));\n",
+ "ctheta2 = sigmaB*U2*(1.-H*math.tan(beta2_*math.pi/180.));\n",
+ "Hi = U2*ctheta2/g;\n",
+ "c2 = math.sqrt(cr2**2 + ctheta2**2);\n",
+ "c3 = 4.*Q/(math.pi*De**2);\n",
+ "HL = 0.1*Hi + 0.485*((c2**2)-(c3**2))/(2.*g) + (c3**2.)/(2.*g);\n",
+ "H = Hi - HL;\n",
+ "eff_hyd = H/Hi;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The slip factor = ',sigmaB,'');\n",
+ "print'%s %.2f %s'%('\\n The manometric head = ',H,' m.');\n",
+ "print'%s %.2f %s'%('\\n The hydraulic efficiency = ',eff_hyd*100,' percentage.');\n",
+ "\n",
+ "##there is a very small error in the answer given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The slip factor = 0.74 \n",
+ "\n",
+ " The manometric head = 30.11 m.\n",
+ "\n",
+ " The hydraulic efficiency = 71.84 percentage.\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "T01 = 22.;##stagnation temperature in degC\n",
+ "Z = 17.;##number of vanes\n",
+ "N = 15000.;##rotational speed in rev/min\n",
+ "r = 4.2;##stagnation pressure ratio between diffuser and impeller\n",
+ "eff_ov = 0.83;##overall efficiency\n",
+ "mdot = 2;##mass flow rate in kg/s\n",
+ "eff_m = 0.97;##mechanical efficiency\n",
+ "rho2 = 2.;##air density at impeller outle in kg/m^3\n",
+ "gamma = 1.4;\n",
+ "R = 0.287;##in kJ/(kg.K)\n",
+ "b2 = 11.;##axial width at the entrance to the diffuser in mm\n",
+ "\n",
+ "##Calculations\n",
+ "Cp = gamma*R*1000./(gamma-1.);\n",
+ "sigmaS = 1 - 2./Z;\n",
+ "U2 = math.sqrt(Cp*(T01+273.)*((r)**((gamma-1.)/gamma) -1.)/(sigmaS*eff_ov));\n",
+ "omega = N*math.pi/30.;\n",
+ "rt = U2/omega;\n",
+ "Wdot_act = mdot*sigmaS*(U2**2)/(eff_m);\n",
+ "cr2 = mdot/(rho2*2.*math.pi*rt*b2/1000.);\n",
+ "ctheta2 = sigmaS*U2;\n",
+ "c2 = math.sqrt(ctheta2**2 +cr2**2);\n",
+ "delW = sigmaS*U2**2;\n",
+ "T2 = T01+273.+(delW - 0.5*c2**2)/Cp;\n",
+ "M2 = c2/math.sqrt(gamma*R*1000.*T2);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('Absolute mach number, M2 = ',M2,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Absolute mach number, M2 = 1.01 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter8_Bt8FCnc.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter8_Bt8FCnc.ipynb new file mode 100644 index 00000000..a6603f6c --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter8_Bt8FCnc.ipynb @@ -0,0 +1,414 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:c09738f4d36c8e48bfaf24c235fb17050c4cfa6be2564154b0a4e5e8521050ca"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter8-Radial Flow Gas Turbines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg251"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "D2 = 23.76;##diameter of rotor in cm\n",
+ "N = 38140.;##rotational speed in rev/min\n",
+ "alpha2 = 72.;##absolute flow angle in deg\n",
+ "d = 0.5*D2;##rotor mean exit diameter\n",
+ "\n",
+ "##Calcultaions\n",
+ "U2 = math.pi*N*D2/(100.*60.);\n",
+ "w2 = U2/math.tan(alpha2*math.pi/180.);\n",
+ "c2 = U2*math.sin(alpha2*math.pi/180.);\n",
+ "w3 = 2*w2;\n",
+ "U3 = 0.5*U2;\n",
+ "c3 = math.sqrt(w3**2. - U3**2);\n",
+ "delW = 0.5*((U2**2. - U3**2.)+(w3**2. - w2**2.)+(c2**2. - c3**2.));\n",
+ "inp_U2 = 0.5*(U2**2. - U3**2.)/delW;\n",
+ "inp_w2 = 0.5*(w3**2. - w2**2.)/delW;\n",
+ "inp_c2 = 0.5*(c2**2. - c3**2.)/delW;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('The fractional inputs from the three terms are, for the U^2 terms,',inp_U2,''and '\\n for the w^2 terms,',inp_w2,''and ' for the c^2 terms, ',inp_c2,'')\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "##there are errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The fractional inputs from the three terms are, for the U^2 terms, 0.42 0.18 0.41 \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg254"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "r = 1.5;##operating pressure ratio\n",
+ "K1 = 1.44*10**-5;\n",
+ "K2 = 2410.;\n",
+ "K3 = 4.59*10**-6;\n",
+ "T01 = 400.;##in K\n",
+ "D2 = 72.5;##rotor inlet diamete in mm\n",
+ "D3_av = 34.4;##rotor meaan outlet diameter in mm\n",
+ "b = 20.1;##rotor outlet annulus width in mm\n",
+ "zetaN = 0.065;##enthalpy loss coefficient\n",
+ "alpha2 = 71.;##in deg\n",
+ "beta3_av = 53.;##in deg\n",
+ "Cp = 1005.;##inJ/(kg.K)\n",
+ "gamma = 1.4;\n",
+ "\n",
+ "##Calculations\n",
+ "N = K2*math.sqrt(T01);\n",
+ "U2 = math.pi*N*D2/(60.*1000.)\n",
+ "delW = U2**2.;\n",
+ "delh = Cp*T01*(1.-(1./r)**((gamma-1.)/gamma));\n",
+ "eff_ts = delW/(delh);\n",
+ "delW_act = K3*K2*math.pi*T01/(30.*K1);\n",
+ "eff_ov = delW_act/delh;\n",
+ "zetaR = (2.*((1./eff_ts)-1.) - (zetaN/math.sin(alpha2*math.pi/180.)))*((D2/D3_av)**2.)*(math.sin(beta3_av*math.pi/180.))**2 - (math.cos(beta3_av*math.pi/180.))**2;\n",
+ "r3 = 0.5*(D3_av-b)*10**-3;\n",
+ "w3_w2av_min = (D3_av/D2)*math.tan(alpha2*math.pi/180.)*((2.*r3/D3_av)**2. + (1./math.tan(beta3_av*math.pi/180.))**2.)**0.5;\n",
+ "w3_w2av = (D3_av/D2)*math.tan(alpha2*math.pi/180.)*(1.+((1./math.tan(beta3_av*math.pi/180.))**2))**0.5;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The total-to-static efficiency = ',eff_ts*100,'percentage');\n",
+ "print'%s %.2f %s'%('\\n The overall efficiency =',eff_ov*100,'percentage');\n",
+ "print'%s %.2f %s'%('\\n The rotor enthalpy loss coefficient = ',zetaR,'');\n",
+ "print'%s %.2f %s'%('\\n The rotor relative velocity ratio = ',w3_w2av,'');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total-to-static efficiency = 76.13 percentage\n",
+ "\n",
+ " The overall efficiency = 73.17 percentage\n",
+ "\n",
+ " The rotor enthalpy loss coefficient = 1.22 \n",
+ "\n",
+ " The rotor relative velocity ratio = 1.73 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Z = 12.;##number of vanes\n",
+ "delW = 230.;##in kW\n",
+ "T01 = 1050.;##stagnation temperature in K\n",
+ "mdot = 1.;##flow rate in kg/s\n",
+ "eff_ts = 0.81;##total-to-static efficiency\n",
+ "Cp = 1.1502;##in kJ/(kg.K)\n",
+ "gamma = 1.333;\n",
+ "R = 287.;##gas constant\n",
+ "\n",
+ "##Calculations\n",
+ "S = delW/(Cp*T01);\n",
+ "alpha2 = (180./math.pi)*math.acos(math.sqrt(1./Z));\n",
+ "beta2 = 2.*(90.-alpha2);\n",
+ "p3_p01 = (1.-(S/eff_ts))**(gamma/(1.-gamma));\n",
+ "M02 = math.sqrt((S/(gamma-1.))*((2.*math.cos(beta2*math.pi/180.))/(1.+math.cos(beta2*math.pi/180.))));\n",
+ "M2 = math.sqrt((M02**2)/(1-0.5*(gamma-1.)*(M02**2)));\n",
+ "U2 = math.sqrt((gamma*R*T01)*(1./math.cos(beta2*math.pi/180.))*(S/(gamma-1.)));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s '%('(i) The absolut and relative flow angles:\\n alpha2 = ',alpha2,' deg'and '\\n beta2 = ',beta2,' deg');\n",
+ "print'%s %.2f %s'%('\\n (ii) The overall pressure ratio =',p3_p01,'');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (iii) The rotor rip speed = ',U2,' m/s'and '\\n The inlet absolute Mach number = ',M2,'');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The absolut and relative flow angles:\n",
+ " alpha2 = 73.22 \n",
+ " beta2 = 33.56 deg \n",
+ "\n",
+ " (ii) The overall pressure ratio = 2.92 \n",
+ "\n",
+ " (iii) The rotor rip speed = 525.05 \n",
+ " The inlet absolute Mach number = 0.75 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg268"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "cm3_U2 = 0.25;\n",
+ "nu = 0.4;\n",
+ "r3s_r2 = 0.7;\n",
+ "w3av_w2 = 2.0;\n",
+ "\n",
+ "##Calculations\n",
+ "r3av_r3s = 0.5*(1.+nu);\n",
+ "r3av_r2 = r3av_r3s*r3s_r2;\n",
+ "beta3_av = (180./math.pi)*math.atan(r3av_r2/cm3_U2);\n",
+ "beta3s = (180./math.pi)*math.atan(r3s_r2/cm3_U2);\n",
+ "w3s_w2 = 2.*math.cos(beta3_av*math.pi/180.)/math.cos(beta3s*math.pi/180.);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The relative velocity ratio =',w3s_w2,'');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The relative velocity ratio = 2.70 \n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg268"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Z = 12.;##number of vanes\n",
+ "delW = 230.;##in kW\n",
+ "T01 = 1050.;##stagnation temperature in K\n",
+ "mdot = 1.;##flow rate in kg/s\n",
+ "eff_ts = 0.81;##total-to-static efficiency\n",
+ "Cp = 1.1502;##in kJ/(kg.K)\n",
+ "gamma = 1.333;\n",
+ "R = 287.;##gas constant\n",
+ "cm3_U2 = 0.25;\n",
+ "nu = 0.4;\n",
+ "r3s_r2 = 0.7;\n",
+ "w3av_w2 = 2.0;\n",
+ "p3 = 100.;##static pressure at rotor exit in kPa\n",
+ "zetaN = 0.06;##nozzle enthalpy loss coefficient\n",
+ "U2 = 538.1;##in m/s\n",
+ "p01 = 3.109*10**5;##in Pa\n",
+ "\n",
+ "##Calculations\n",
+ "S = delW/(Cp*T01);\n",
+ "T03 = T01*(1.-S);\n",
+ "T3 = T03 - (cm3_U2**2)*(U2**2)/(2.*Cp*1000.);\n",
+ "r2 = math.sqrt(mdot/((p3*1000./(R*T3))*(cm3_U2)*U2*math.pi*(r3s_r2**2)*(1.-nu**2)));\n",
+ "D2 = 2.*r2;\n",
+ "omega = U2/r2;\n",
+ "N = omega*30./math.pi;\n",
+ "ctheta2 = S*Cp*1000.*T01/U2;\n",
+ "alpha2 = (180/math.pi)*math.acos(math.sqrt(1./Z));\n",
+ "cm2 = ctheta2/math.tan(alpha2*math.pi/180.);\n",
+ "c2 = ctheta2/math.sin(alpha2*math.pi/180.);\n",
+ "T2 = T01 - (c2**2)/(2.*Cp*1000.);\n",
+ "p2 = p01*(1-(((c2**2)*(1.+zetaN))/(2.*Cp*1000.*T01)))**(gamma/(gamma-1.));\n",
+ "b2_D2 = (0.25/math.pi)*(R*T2/p2)*(mdot/(cm2*r2**2.));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('(i) The diamaeter of the rotor = ',D2,' m'and '\\n its speed of rotation = ',omega,' rad/s'and ' (N = ',N,' rev/min)');\n",
+ "print'%s %.2f %s'%('\\n(ii) The vane width to diameter ratio at rotor inlet = ',b2_D2,'');\n",
+ "\n",
+ "##there are some errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The diamaeter of the rotor = 0.24 \n",
+ " its speed of rotation = 4564.96 (N = 43592.14 rev/min) \n",
+ "\n",
+ "(ii) The vane width to diameter ratio at rotor inlet = 0.06 \n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg271"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Z = 12.;##number of vanes\n",
+ "delW = 230.;##in kW\n",
+ "T01 = 1050.;##stagnation temperature in K\n",
+ "mdot = 1.;##flow rate in kg/s\n",
+ "eff_ts = 0.81;##total-to-static efficiency\n",
+ "Cp = 1.1502;##in kJ/(kg.K)\n",
+ "gamma = 1.333;\n",
+ "R = 287.;##gas constant\n",
+ "cm3_U2 = 0.25;\n",
+ "nu = 0.4;\n",
+ "r3s_r2 = 0.7;\n",
+ "w3av_w2 = 2.0;\n",
+ "p3 = 100.;##static pressure at rotor exit in kPa\n",
+ "zetaN = 0.06;##nozzle enthalpy loss coefficient\n",
+ "U2 = 538.1;##in m/s\n",
+ "p01 = 3.109*10**5;##in Pa\n",
+ "\n",
+ "##results of Example 8.4 and Example 8.5\n",
+ "r3av_r3s = 0.5*(1+nu);\n",
+ "r3av_r2 = r3av_r3s*r3s_r2;\n",
+ "alpha2 = (180./math.pi)*math.acos(math.sqrt(1/Z));\n",
+ "beta2 = 2.*(90.-alpha2);\n",
+ "beta3_av = (180./math.pi)*math.atan(r3av_r2/cm3_U2);\n",
+ "beta3s = (180./math.pi)*math.atan(r3s_r2/cm3_U2);\n",
+ "w3s_w2 = 2.*math.cos(beta3_av*math.pi/180.)/math.cos(beta3s*math.pi/180.);\n",
+ "S = delW/(Cp*T01);\n",
+ "T03 = T01*(1-S);\n",
+ "T3 = T03 - (cm3_U2**2)*(U2**2.)/(2.*Cp*1000.);\n",
+ "r2 = math.sqrt(mdot/((p3*1000./(R*T3))*(cm3_U2)*U2*math.pi*(r3s_r2**2)*(1.-nu**2.)));\n",
+ "D2 = 2.*r2;\n",
+ "omega = U2/r2;\n",
+ "N = omega*30./math.pi;\n",
+ "ctheta2 = S*Cp*1000.*T01/U2;\n",
+ "alpha2 = (180./math.pi)*math.acos(math.sqrt(1./Z));\n",
+ "cm2 = ctheta2/math.tan(alpha2*math.pi/180.);\n",
+ "c2 = ctheta2/math.sin(alpha2*math.pi/180.);\n",
+ "T2 = T01 - (c2**2.)/(2.*Cp*1000.);\n",
+ "p2 = p01*(1-(((c2**2)*(1.+zetaN))/(2.*Cp*1000.*T01)))**(gamma/(gamma-1));\n",
+ "b2_D2 = (0.25/math.pi)*(R*T2/p2)*(mdot/(cm2*r2**2));\n",
+ "\n",
+ "##Calculations\n",
+ "c3 = cm3_U2*U2;\n",
+ "cm3 = c3;\n",
+ "w3_av = 2.*cm3/(math.cos(beta2*math.pi/180.));\n",
+ "w2 = w3_av/2.;\n",
+ "c0 = math.sqrt(2.*delW*1000./eff_ts);\n",
+ "zetaR = (c0**2. *(1.-eff_ts)- (c3**2.)- zetaN*(c2**2))/(w3_av**2); \n",
+ "i = beta2;\n",
+ "n = 1.75;\n",
+ "eff_ts_new = 1-((c3**2)+zetaN*(c2**2)+zetaR*(w3_av**2)+(1.-(math.cos(i*math.pi/180))**n)*(w2**2))/(c0**2);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('(a)The rotor enthalpy loss coefficient = ',zetaR,'');\n",
+ "print'%s %.2f %s'%('\\n(b) The total-to-static efficiency of the turbine =',eff_ts_new,'');\n",
+ "\n",
+ "\n",
+ "##there are some errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The rotor enthalpy loss coefficient = 0.75 \n",
+ "\n",
+ "(b) The total-to-static efficiency of the turbine = 0.80 \n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter9_TOCkwb3.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter9_TOCkwb3.ipynb new file mode 100644 index 00000000..f45706aa --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter9_TOCkwb3.ipynb @@ -0,0 +1,418 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:792fb421946abfd48c51ce0ac37efa304f9a8b8a120655d1f8c56d375239bb07"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter9-Hydraulic Turbines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "Q = 2.272;##water volume flow rate in m**3/s\n",
+ "l = 300.;##length in m\n",
+ "Hf = 20.;##head loss in m\n",
+ "f = 0.01;##friction factor\n",
+ "g = 9.81;##acceleration due to gravity in m/s**2\n",
+ "\n",
+ "##Calculations\n",
+ "d = (32.*f*l*((Q/math.pi)**2)/(g*Hf))**(1/5.);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The diameter of the pipe = ',d,' m');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg302"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "P = 4.0;##in MW\n",
+ "N = 375.;##in rev/min\n",
+ "H_eps = 200.;##in m\n",
+ "KN = 0.98;##nozzle velocity coefficient\n",
+ "d = 1.5;##in m\n",
+ "k = 0.15;##decrease in relative flow velocity across the buckets\n",
+ "alpha = 165.;##in deg\n",
+ "g = 9.81;##in m/s^2\n",
+ "rho = 1000.;##in kg/m^3\n",
+ "\n",
+ "##Calculations\n",
+ "U = N*math.pi*d*0.5/30.;\n",
+ "c1 = KN*math.sqrt(2*g*H_eps);\n",
+ "nu = U/c1;\n",
+ "eff = 2.*nu*(1.-nu)*(1.-(1.-k)*math.cos(alpha*math.pi/180.));\n",
+ "Q = (P*10**6 /eff)/(rho*g*H_eps);\n",
+ "Aj = Q/(2.*c1);\n",
+ "dj = math.sqrt(4.*Aj/math.pi);\n",
+ "omega_sp = (N*math.pi/30.)*math.sqrt((P*10**6)/rho)/((g*H_eps)**(5./4.));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('(i)The runner efficiency = ',eff,'');\n",
+ "print'%s %.2f %s'%('\\n (ii)The diameter of each jet = ',dj,' m');\n",
+ "print'%s %.2f %s'%('\\n (iii)The power specific speed = ',omega_sp,' rad');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The runner efficiency = 0.91 \n",
+ "\n",
+ " (ii)The diameter of each jet = 0.15 m\n",
+ "\n",
+ " (iii)The power specific speed = 0.19 rad\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "H_eps = 150.;##in m\n",
+ "z = 2.;##in m\n",
+ "U2 = 35.;##runner tip speed in m/s\n",
+ "c3 = 10.5;##meridonal velocity of water in m/s\n",
+ "c4 = 3.5;##velocity at exit in m/s\n",
+ "delHN = 6.0;##in m\n",
+ "delHR = 10.0;##in m\n",
+ "delHDT = 1.0;##in m\n",
+ "g = 9.81;##in m/s**2\n",
+ "Q = 20.;##in m**3/s\n",
+ "omega_sp = 0.8;##specific speed of turbine in rad\n",
+ "c2 = 38.73;##in m/s\n",
+ "\n",
+ "##Calculations\n",
+ "H3 = ((c4**2. - c3**2.)/(2.*g)) + delHDT - z;\n",
+ "H2 = H_eps-delHN-(c2**2.)/(2.*g);\n",
+ "delW = g*(H_eps-delHN-delHR-z)-0.5*c3**2 -g*H3;\n",
+ "ctheta2 = delW/U2;\n",
+ "alpha2 = (180./math.pi)*math.atan(ctheta2/c3);\n",
+ "beta2 = (180./math.pi)*math.atan((ctheta2-U2)/c3);\n",
+ "eff_H = delW/(g*H_eps);\n",
+ "omega = (omega_sp*(g*H_eps)**(5./4.))/math.sqrt(Q*delW);\n",
+ "N = omega*30./math.pi;\n",
+ "D2 = 2.*U2/omega;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s'%('(i)The pressure head H3 relative to the trailrace = ',H3,' m'and'\\n The pressure head H2 at exit from the runner =',H2,' m');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n(ii)The flow angles at runner inlet and at guide vane exit:\\n alpha2 = ',alpha2,' deg'and '\\n beta2 = ',beta2,' deg');\n",
+ "print'%s %.2f %s'%('\\n(iii)The hydraulic efficiency of the turbine = ',eff_H,'');\n",
+ "print'%s %.2f %s'%('\\n The speed of rotation, N = ',N,' rev/min');\n",
+ "print'%s %.2f %s'%('\\n The runner diameter is, D2 = ',D2,' m');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The pressure head H3 relative to the trailrace = -5.99 \n",
+ " The pressure head H2 at exit from the runner = 67.55 m\n",
+ "\n",
+ "(ii)The flow angles at runner inlet and at guide vane exit:\n",
+ " alpha2 = 74.20 \n",
+ " beta2 = 11.33 deg \n",
+ "\n",
+ "(iii)The hydraulic efficiency of the turbine = 0.88 \n",
+ "\n",
+ " The speed of rotation, N = 432.02 rev/min\n",
+ "\n",
+ " The runner diameter is, D2 = 1.55 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg312"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##function to calculate flow angles\n",
+ " \n",
+ " \n",
+ "##given data\n",
+ "P = 8;##output power in MW\n",
+ "HE = 13.4;##available head at entry in m\n",
+ "N = 200;##in rev/min\n",
+ "L = 1.6;##length of inlet guide vanes\n",
+ "d1 = 3.1;##diameter of trailing edge in m\n",
+ "D2t = 2.9;##runner diameter in m\n",
+ "nu = 0.4;##hub-tip ratio\n",
+ "eff = 0.92;##hydraulic efficiency\n",
+ "rho = 1000;##density in kg/m**3\n",
+ "g = 9.81;##acceleration due to gravity in m/s**2 \n",
+ "r=1.45\n",
+ "##Calculations\n",
+ "Q = P*10**6 /(eff*rho*g*HE);\n",
+ "cr1 = Q/(2*math.pi*0.5*d1*L);\n",
+ "cx2 = 4*Q/(math.pi*D2t**2 *(1-nu**2));\n",
+ "U2 = N*(math.pi/30)*D2t/2;\n",
+ "ctheta2 = eff*g*HE/U2;\n",
+ "ctheta1 = ctheta2*(D2t/d1);\n",
+ "alpha1 = (180/math.pi)*math.atan(ctheta1/cr1);\n",
+ "alpha2 = (180/math.pi)*math.atan(ctheta2/cx2);\n",
+ "beta2 = (180/math.pi)*math.atan((U2)*(r)/cx2 - math.tan(alpha2*math.pi/180));\n",
+ "beta3 = (180/math.pi)*math.atan((U2)*r/cx2) ;\n",
+ "alpha23=39.86\n",
+ "alpha22=25.51\n",
+ "alpha21=18.47\n",
+ "beta23=10.42\n",
+ "beta22=52.56\n",
+ "beta21=65.68\n",
+ "\n",
+ "##Results\n",
+ "print('Calculated values of flow angles:\\n Parameter Ratio of r/ri ');\n",
+ "print('\\n ------------------------------------------------------------');\n",
+ "print('\\n 0.4 0.7 1.0');\n",
+ "print('\\n --------------------------------------');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n ctheta2(in m/s) ',ctheta2/0.4,''and '',ctheta2/0.7,''and '',ctheta2/1.0,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n tan(alpha2) ',math.tan(alpha23*math.pi/180),''and '',math.tan(alpha22*math.pi/180),'' and '',math.tan(alpha21*math.pi/180),'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n alpha2(deg) ',alpha23,''and '',alpha22,''and '',alpha21,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n U/cx2 ',(U2/cx2)*0.4,''and '',(U2/cx2)*0.7,''and '',(U2/cx2)*1.0,'');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n beta2(deg) ',beta23,''and '',beta22,'' and '',beta21,'');\n",
+ "print('\\n ------------------------------------------------------------');\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Calculated values of flow angles:\n",
+ " Parameter Ratio of r/ri \n",
+ "\n",
+ " ------------------------------------------------------------\n",
+ "\n",
+ " 0.4 0.7 1.0\n",
+ "\n",
+ " --------------------------------------\n",
+ "\n",
+ " ctheta2(in m/s) 9.96 5.69 3.98 \n",
+ "\n",
+ " tan(alpha2) 0.83 0.48 0.33 \n",
+ "\n",
+ " alpha2(deg) 39.86 25.51 18.47 \n",
+ "\n",
+ " U/cx2 1.02 1.78 2.55 \n",
+ "\n",
+ " beta2(deg) 10.42 52.56 65.68 \n",
+ "\n",
+ " ------------------------------------------------------------\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg315"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "k = 1/5.;##scale ratio\n",
+ "Pm = 3.;##in kW\n",
+ "Hm = 1.8;##in m\n",
+ "Nm = 360.;##in rev/min\n",
+ "Qm = 0.215;##in m^3/s\n",
+ "Hp = 60.;##in m\n",
+ "n = 0.25;\n",
+ "rho = 1000;##in kg/m^3\n",
+ "g = 9.81;##in m/s^2\n",
+ "\n",
+ "##Calculations\n",
+ "Np = Nm*k*(Hp/Hm)**0.5;\n",
+ "Qp = Qm*(Nm/Np)*(1./k)**3;\n",
+ "Pp = Pm*((Np/Nm)**3)*(1./k)**5;\n",
+ "eff_m = Pm*1000./(rho*Qm*g*Hm);\n",
+ "eff_p = 1 - (1.-eff_m)*0.2**n;\n",
+ "Pp_corrected = Pp*eff_p/eff_m;\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The speed = ',Np,' rev/min.');\n",
+ "print'%s %.2f %s'%('\\n The flow rate =',Qp,' m^3/s.');\n",
+ "print'%s %.2f %s'%('\\n Power of the full-scale = ',Pp/1000,' MW.');\n",
+ "print'%s %.2f %s'%('\\n The efficiency of the model turbine = ',eff_m,'');\n",
+ "print'%s %.2f %s'%('\\n The efficiency of the prototype = ',eff_p,'');\n",
+ "print'%s %.2f %s'%('\\n The power of the full-size turbine = ',Pp_corrected/1000,' MW.')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The speed = 415.69 rev/min.\n",
+ "\n",
+ " The flow rate = 23.27 m^3/s.\n",
+ "\n",
+ " Power of the full-scale = 14.43 MW.\n",
+ "\n",
+ " The efficiency of the model turbine = 0.79 \n",
+ "\n",
+ " The efficiency of the prototype = 0.86 \n",
+ "\n",
+ " The power of the full-size turbine = 15.70 MW.\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg316"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "##data from EXAMPLE 9.3\n",
+ "H_eps = 150.;##in m\n",
+ "z = 2.;##in m\n",
+ "U2 = 35.;##runner tip speed in m/s\n",
+ "c3 = 10.5;##meridonal velocity of water in m/s\n",
+ "c4 = 3.5;##velocity at exit in m/s\n",
+ "delHN = 6.0;##in m\n",
+ "delHR = 10.0;##in m\n",
+ "delHDT = 1.0;##in m\n",
+ "g = 9.81;##in m/s**2\n",
+ "Q = 20.;##in m**3/s\n",
+ "omega_sp = 0.8;##specific speed of turbine in rad\n",
+ "c2 = 38.73;##in m/s\n",
+ "\n",
+ "##data from this example\n",
+ "Pa = 1.013;##atmospheric pressure in bar\n",
+ "Tw = 25.;##temperature of water in degC\n",
+ "Pv = 0.03166;##vapor pressure of water at Tw\n",
+ "rho = 1000;##density of wate in kg/m**3\n",
+ "g = 9.81;##acceleration due to gravity in m/s**2\n",
+ "\n",
+ "H3 = ((c4**2. - c3**2.)/(2.*g)) + delHDT - z;\n",
+ "H2 = H_eps-delHN-(c2**2.)/(2.*g);\n",
+ "delW = g*(H_eps-delHN-delHR-z)-0.5*c3**2 -g*H3;\n",
+ "ctheta2 = delW/U2;\n",
+ "alpha2 = (180/math.pi)*math.atan(ctheta2/c3);\n",
+ "beta2 = (180/math.pi)*math.atan((ctheta2-U2)/c3);\n",
+ "eff_H = delW/(g*H_eps);\n",
+ "omega = (omega_sp*(g*H_eps)**(5/4.))/math.sqrt(Q*delW);\n",
+ "\n",
+ "Hs = (Pa-Pv)*(10**5)/(rho*g) - z;\n",
+ "sigma = Hs/H_eps;\n",
+ "omega_ss = omega*(Q**0.5)/(g*Hs)**(3/4.);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The NSPH for the turbine = ',Hs,' m.');\n",
+ "if omega_ss>4.0:\n",
+ " print'%s %.2f %s'%('\\n Since the suction specific speed (= ',omega_ss,')is greater than 4.0(rad), the cavitation is likely to occur.');\n",
+ "\n",
+ "\n",
+ "##there is small error in the answer given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The NSPH for the turbine = 8.00 m.\n",
+ "\n",
+ " Since the suction specific speed (= 7.67 )is greater than 4.0(rad), the cavitation is likely to occur.\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/Chapter10.png b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/Chapter10.png Binary files differnew file mode 100644 index 00000000..03484f85 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/Chapter10.png diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter6_Q3tBrTp.png b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter6_Q3tBrTp.png Binary files differnew file mode 100644 index 00000000..36a51d03 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter6_Q3tBrTp.png diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter7_qVshgvy.png b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter7_qVshgvy.png Binary files differnew file mode 100644 index 00000000..9c075a08 --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/screenshots/chapter7_qVshgvy.png |
