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{
"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": {}
}
]
}
|
