{
"metadata": {
"name": "",
"signature": "sha256:52c2219fbd43444e9f10668aa35432419392cd1b075ad84ee07b92a8e31571e1"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 - Hydraulic Turbines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.1 Page 406"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"#input data\n",
"H=91.5#Head of the pelton wheel at inlet in m\n",
"Q=0.04#Discharge of the pelton wheel in m**3/s\n",
"N=720#Rotating speed of the wheel in rpm\n",
"Cv=0.98#Velocity coefficient of the nozzle \n",
"n0=0.8#Efficiency of the wheel\n",
"UC1=0.46#Ratio of bucket speed to jet speed\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"P=dw*g*H*Q*n0*10**-3#Power developed in kw\n",
"C1=Cv*(2*g*H)**(1/2)#Jet speed in m/s\n",
"U=UC1*C1#Wheel speed in m/s\n",
"w=(2*3.1415*N)/60#Angular velocity of the wheel in rad/s\n",
"D=(2*U)/w#Diameter of the wheel in m\n",
"A=Q/C1#Jet area in m**2\n",
"d=((4*A)/3.1415)**(1/2)#Jet diameter in m\n",
"Dd=D/d#Wheel to jet diameter ratio at centre line of the buckets\n",
"Nsp=((1/(g*H))**(5/4))*(((P*10**3)/dw)**(1/2))*(N/60)*2*3.1415#Dimensionless power specific speed in rad\n",
"\n",
"#output\n",
"print '(a)Wheel-to-jet diameter ratio at the centre line of the buckets is %3.1f \\n(b)\\n The jet speed of the wheel is %3.2f m/s\\n Wheel speed is %3.1f m/s\\n(c)Dimensionless power specific speed is %3.3f rad'%(Dd,C1,U,Nsp)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Wheel-to-jet diameter ratio at the centre line of the buckets is 14.5 \n",
"(b)\n",
" The jet speed of the wheel is 41.52 m/s\n",
" Wheel speed is 19.1 m/s\n",
"(c)Dimensionless power specific speed is 0.082 rad\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.2 Page 407"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=500#Head over which pelton wheel works in m\n",
"P=13000#Power which pelton wheel produces in kW\n",
"N=430#Speed of operation of pelton wheel in rpm\n",
"n0=0.85#Efficiency of the wheel \n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"Cv=0.98#Veloity coefficient\n",
"UC=0.46#Speed ratio\n",
"\n",
"#calculations\n",
"Q=(P*10**3)/(dw*g*H*n0)#Discharge of the turbine in m**3/s\n",
"C=Cv*(2*g*H)**(1/2)#Jet speed in m/s\n",
"U=UC*C#Wheel speed in m/s\n",
"D=(U*60)/(3.1415*N)#Wheel diameter in m\n",
"d=((Q/C)*(4/3.1415))**(1/2)#Diameter of the nozzle in m\n",
"\n",
"#output\n",
"print '(a)Discharge of the turbine is %3.2f m**3/s\\n(b)Diameter of the wheel is %3.2f m\\n(c)Diameter of the nozzle is %3.3f m'%(Q,D,d)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Discharge of the turbine is 3.12 m**3/s\n",
"(b)Diameter of the wheel is 1.98 m\n",
"(c)Diameter of the nozzle is 0.202 m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.3 Page 409"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi, cos\n",
"#input data\n",
"D=0.8#Mean diameter of the bucket in m\n",
"N=1000#Running speed of the wheel in rpm\n",
"H=400#Net head on the pelton wheel in m\n",
"Q=0.150#Discharge through the nozzle in m**3/s\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"UC1=0.46#Ratio of bucket speed to jet speed\n",
"dw=1000#Density of water in kg/m**3\n",
"a=15#Side clearance angle in degree\n",
"\n",
"#calculations\n",
"m=dw*Q#Mass flow rate through the nozzle in kg/s\n",
"U=(3.1415*D*N)/60#Wheel speed in m/s\n",
"C1=U/UC1#Jet speed in m/s\n",
"P=(1/2)*m*C1**2*(10**-3)#Power available at the nozzle in kW\n",
"W1=C1-U#Relative inlet fluid velocity in m/s\n",
"W2=W1#Relative exit fluid velocity in m/s assuming no loss of relative velocity\n",
"Wx2=W2*cos(a*pi/180)#Exit whirl velocity component in m/s\n",
"Cx2=Wx2-U#Absolute exit whirl velocity in m/s\n",
"Cx1=C1#Absolute inlet whirl velocity in m/s\n",
"Wm=U*(Cx1+Cx2)#Work done per unit mass flow rate in W/(kg/s)\n",
"nH=(Wm/g)/((C1**2/2)/g)#Hydrualic effciency \n",
"\n",
"#output\n",
"print '(a)Power available at the nozzle is %3.3f kW\\n(b)Hydraulic efficiency is %.1f %%'%(P,nH*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Power available at the nozzle is 621.867 kW\n",
"(b)Hydraulic efficiency is 97.7 %\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.4 Page 409"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"n=2#Number of jets \n",
"SP=20000*0.736#Shaft power of the wheel in kW\n",
"D=0.15#Diameter of each jet in m\n",
"H=500#Net head on the turbine in m\n",
"Cv=1.0#Velocity coefficient\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"d=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"C1=Cv*(2*g*H)**(1/2)#Velocity of each jet in m/s\n",
"A=(3.1415/4)*D**2#Area of each jet in m**2\n",
"Qj=A*C1#Discharge of each jet in m**3/s\n",
"Q=2*Qj#Total discharge in m**3/s\n",
"P=d*g*Q*H*10**-3#Power at turbine inlet in kW\n",
"no=SP/P#Overall efficiency\n",
"\n",
"#output\n",
"print 'The overall efficiency of the turbine is %0.1f %%'%(no*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The overall efficiency of the turbine is 85.7 %\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.5 Page 410"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"a=170#Jet deflection angle in degree\n",
"K=1-0.12#Percentage of effective relative velocity after considering friction\n",
"UC1=0.47#Ratio of bucket speed to jet speed\n",
"GH=600#Gross head on the wheel in m\n",
"P=1250#Actual power developed by the wheel in kW\n",
"Hl=48#Head loss in nozzle due to pipe friction in m\n",
"D=0.9#Bucket circle diameter of the wheel in m\n",
"ATnH=0.9#The ratio between actual and calculated hydraulic efficiency\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"Cv=0.98#Velocity coefficient\n",
"\n",
"#calculations\n",
"H=GH-Hl#Net head after loses at entry to nozzle in m\n",
"C1=Cv*(2*g*H)**(1/2)#Jet speed in m/s\n",
"U=UC1*C1#Wheel bucket speed in m/s\n",
"N=(U*60)/(3.1415*D)#Wheel rotational speed in rpm\n",
"Wm=U*((C1-U)*(1-(K*cos(a*pi/180))))#Work done per unit mass flow rate in W/(kg/s)\n",
"Tnh=Wm/(C1**2/2)#Theoretical hydraulic efficiency \n",
"Anh=ATnH*Tnh#Actual hydrualic effficiency\n",
"m2=(P*10**3)/(Anh*(1/2)*C1**2)#Mass flow rate for both the nozzles in kg/s\n",
"m=m2/2#Mass flow rate of each nozzle in kg/s\n",
"d=((4*m)/(dw*C1*3.1415))**(1/2)#Nozzle diameter in m\n",
"\n",
"#output\n",
"print '(a)theoretical hydraulic efficiency is %3.2f \\n(b)Wheel rotational speed is %3.f rpm\\n(c)diameter of the nozzle is %0.1f mm'%(Tnh,N,d*1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)theoretical hydraulic efficiency is 0.93 \n",
"(b)Wheel rotational speed is 1017 rpm\n",
"(c)diameter of the nozzle is 42.3 mm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.6 Page 413"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=60#Head on the pelton wheel in m\n",
"N=200#Speed of the pelton wheel in rpm\n",
"P=100#Power developed by the pelton wheel in kW\n",
"Cv=0.98#Velocity coefficient\n",
"UC1=0.45#Speed ratio \n",
"n0=0.85#Overall efficiency of the wheel\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"C1=Cv*(2*g*H)**(1/2)#Velocity of the jet in m/s\n",
"U=UC1*(2*g*H)**(1/2)#Velocity of the buckets in m/s\n",
"D=(60*U)/(3.1415*N)#Diameter of the wheel in m\n",
"Q=(P*10**3)/(dw*g*H*n0)#Discharge of the wheel in m**3/s\n",
"d=((4*Q)/(3.1415*C1))**(1/2)#Diameter of the jet in m\n",
"Z=15+(D/(2*d))+1#Number of buckets rounding off to nearest decimal as the final answer has a decimal value less than 0.5\n",
"w=5*d#Width of the buckets in m\n",
"de=1.2*d#Depth of the buckets in m\n",
"\n",
"#output\n",
"print '(a)Diameter of the wheel is %3.2f m\\n(b)Diameter of the jet is %3.3f m\\n(c)Number of buckets is %3.f\\n(d)Size of the buckets is \\n width of the bucket is %3.3f m\\n Depth of the bucket is %3.3f m'%(D,d,Z,w,de)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Diameter of the wheel is 1.47 m\n",
"(b)Diameter of the jet is 0.087 m\n",
"(c)Number of buckets is 24\n",
"(d)Size of the buckets is \n",
" width of the bucket is 0.435 m\n",
" Depth of the bucket is 0.104 m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.7 Page 414"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"N=300#Running speed of the wheel in rpm\n",
"H=150#OPerating head of the wheel in m\n",
"dD=1/12#Ratio of nozzle diameter to wheel diameter\n",
"Cv=0.98#Velocity coefficient\n",
"UC1=0.46#Speed ratio\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"n0=0.84#Overall efficiency\n",
"\n",
"#calculations\n",
"C1=Cv*(2*g*H)**(1/2)#Velocity of jet in m/s\n",
"U=UC1*(2*g*H)**(1/2)#Velocity of the wheel in m/s\n",
"D=(60*U)/(3.14*N)#Diameter of the wheel in m\n",
"d=D*dD#Diameter of the jet in m\n",
"Q=(3.1415/4)*(d**2)*C1#Quantity of water required in m**3/s\n",
"Pa=dw*g*Q*H#Power available at the nozzle in kW\n",
"P=n0*Pa*10**-3#Power developed in kW\n",
"#output\n",
"print '(a)Diameter of the wheel is %3.2f m\\n(b)Diameter of the jet is %3.3f m\\n(c)Quantity of water required is %3.3f m**3/s\\n(d)Power developed is %3.1f kW'%(D,d,Q,P)\n",
"# Answer in the textbook is wrong."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Diameter of the wheel is 1.59 m\n",
"(b)Diameter of the jet is 0.132 m\n",
"(c)Quantity of water required is 0.733 m**3/s\n",
"(d)Power developed is 905.5 kW\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.8 Page 415"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import tan, pi\n",
"#input data\n",
"N=1260#Rotational speed of the francis turbine in rpm\n",
"H=124#The net head in m\n",
"Q=0.5#Volume flow rate of the turbine in m**3/s\n",
"r1=0.6#Radius of the runner in m\n",
"b1=0.03#Height of the runner vanes at inlet in m\n",
"b11=72#Angle of inlet guide vanes in radial direction in degree\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"Cx2=0#Absolute exit whirl velocity in m/s as flow is radial at outlet\n",
"\n",
"#calculations\n",
"m=dw*Q#Mass flow rate in kg/s\n",
"T1=-m*r1#Torque by the turbine in Nm in terms of Cx1\n",
"A=2*3.1415*r1*b1#Area at inlet in m**2\n",
"Cr1=Q/A#Inlet flow velocity in m/s\n",
"Cx1=Cr1*tan(b11*pi/180)#Absolute inlet whirl velocity in m/s\n",
"T=-T1*Cx1#Torque by water on the runner in Nm\n",
"w=(2*3.1415*N)/60#Angular velocity of the turbine in rad/s\n",
"W=T*w*10**-3#Power exerted in kW\n",
"nH=W*10**3/(dw*g*Q*H)#Hydraulic efficiency \n",
"\n",
"#output\n",
"print '(a)Torque by water on the runner is -%3.f Nm\\n(b)Power exerted is %3i kW\\n(c)Hydraulic efficiency is %0.1f %%'%(T,W,nH*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Torque by water on the runner is -4082 Nm\n",
"(b)Power exerted is 538 kW\n",
"(c)Hydraulic efficiency is 88.6 %\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.9 Page 416"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import atan, degrees\n",
"#input data\n",
"n0=0.74#Overall efficiency\n",
"H=5.5#Net head across the turbine in m\n",
"P=125#Required Power output in kW\n",
"N=230#Speed of the runner in rpm\n",
"nH=(1-0.18)#Hydraulic efficiency\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"U1=0.97*(2*g*H)**(1/2)#Runner tangential velocity in m/s\n",
"Cr1=0.4*(2*g*H)**(1/2)#Flow velocity in m/s\n",
"\n",
"#calculations\n",
"Cx1=(nH*g*H)/U1#Absolute inlet whirl velocity in m/s as flow is radial at outlet Cx2=0 in m/s\n",
"a11=degrees(atan(Cr1/Cx1))#Inlet guide vane angle in degree\n",
"b11=180+degrees(atan(Cr1/(Cx1-U1)))#Angle of inlet guide vanes in radial direction in degree\n",
"D1=(U1*60)/(3.1415*N)#Runner inlet diameter in m\n",
"Q=(P*10**3)/(n0*dw*g*H)#Flow rate in m**3/s\n",
"b1=Q/(3.1415*D1*Cr1)#Height of runner in m\n",
"\n",
"#output\n",
"print '(a)Inlet guide vane angle is %3.1f degree\\n(b)Angle of inlet guide vanes in radial direction is %3.1f degree\\n(c)Runner inlet diameter is %3.3f m\\n(d)Height of runner is %3.3f m'%(a11,b11,D1,b1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Inlet guide vane angle is 43.4 degree\n",
"(b)Angle of inlet guide vanes in radial direction is 143.8 degree\n",
"(c)Runner inlet diameter is 0.837 m\n",
"(d)Height of runner is 0.287 m\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.10 Page 418"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D=1.4#Diameter of the turbine in m\n",
"N=430#Speed of the turbine in rpm\n",
"Cr1=9.5#Flow velocity without shock at runner in m/s\n",
"C2=7#Absolute velocity at the exit without whirl in /s\n",
"dSPH=62#Difference between the sum of static and potential heads at entrance to runner and at exit from runner in m\n",
"W=12250#Power given to runner in kW\n",
"Q=12#Flow rate of water from the turbine in m**3/s\n",
"H=115#Net head from the turbine in m\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U1=(3.1415*D*N)/60#Runner tip speed in m/s\n",
"Cx1=(W*10**3)/(dw*Q*U1)#Absolute inlet velocity in m/s as flow is radial at outlet Cx2=0 in m/s as Cx2=0 as zero whirl at outlet\n",
"a1=degrees(atan(Cr1/Cx1))#Guide vane angle in degree\n",
"C1=(Cr1**2+Cx1**2)**(1/2)#Inlet velocity in m/s\n",
"b1=degrees(atan(Cr1/(Cx1-U1)))#Runner blade entry angle in degree\n",
"dHr=dSPH+(((C1**2)-(C2**2))/(2*g))-(U1*Cx1/g)#Loss of head in the runner in m\n",
"\n",
"#output\n",
"print '(a)\\n (1)Guide vane angle at inlet is %3.1f degree\\n (2)Inlet absolute velocity of water at entry to runner is %3.1f m/s\\n(b)Runner blade entry angle is %3.1f degree\\n(c)Total Loss of head in the runner is %3.2f m'%(a1,C1,b1,dHr)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)\n",
" (1)Guide vane angle at inlet is 16.3 degree\n",
" (2)Inlet absolute velocity of water at entry to runner is 33.8 m/s\n",
"(b)Runner blade entry angle is 84.8 degree\n",
"(c)Total Loss of head in the runner is 13.50 m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.11 Page 420"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin, tan, degrees\n",
"#input data\n",
"D1=0.9#External diameter of the turbine in m\n",
"D2=0.45#Internal diameter of the turbine in m\n",
"N=200#Speed of turbine running in rpm\n",
"b1=0.2#Width of turbine at inlet in m\n",
"Cr1=1.8#Velocity of flow through runner at inlet in m/s\n",
"Cr2=Cr1#Velocity of flow through runner at outlet in m/s\n",
"a11=10#Guide blade angle to the tangent of the wheel in degree\n",
"a22=90#Discharge angle at outlet of turbine in degree\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"C1=Cr1/sin(a11*pi/180)#Absolute velocity of water at inlet of runner in m/s\n",
"Cx1=Cr1/tan(a11*pi/180)#Velocity of whirl at inlet in m/s\n",
"U1=(3.1415*D1*N)/60#Runner tip speed at inlet in m/s\n",
"Wx1=Cx1-U1#Inlet whirl velocity component in m/s\n",
"W1=(Wx1**2+Cr1**2)**(1/2)#Relative velocity at inlet in m/s\n",
"b11=degrees(atan(Cr1/Wx1))#Runner blade entry angle in degree\n",
"U2=(3.1415*D2*N)/60#Runner tip speed at exit in m/s\n",
"b22=degrees(atan(Cr2/U2))#Runner blade exit angle in degree\n",
"b2=D1*b1/D2#Width of runner at outlet in m\n",
"Q=3.1415*D1*b1*Cr1#Discharge of water in turbine in m**3/s\n",
"m=dw*Q#Mass of water flowing through runner per second in kg/s\n",
"V2=Cr2#Velocity of water at exit in m/s \n",
"H=(U1*Cx1/g)+(V2**2/(2*g))#Head at the turbine inlet in m\n",
"W=m*U1*Cx1*10**-3#Power developed in kW\n",
"nH=(U1*Cx1/(g*H))#Hydraulic efficiency\n",
"\n",
"#output\n",
"print '(a)Absolute velocity of water at inlet of runner is %3.3f m/s\\n(b)Velocity of whirl at inlet is %3.3f m/s\\n(c)Relative velocity at inlet is %3.3f m/s\\n(d)\\n Runner blade entry angle is %3.2f degree\\n Runner blade exit angle is %3.2f degree\\n(e)Width of runner at outlet is %3.1f m\\n(f)Mass of water flowing through runner per second is %3.f kg/s\\n(g)Head at the turbine inlet is %3.3f m\\n(h)Power developed is %3.3f kW\\n(i)Hydraulic efficiency is %0.2f %%'%(C1,Cx1,W1,b11,b22,b2,m,H,W,nH*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Absolute velocity of water at inlet of runner is 10.366 m/s\n",
"(b)Velocity of whirl at inlet is 10.208 m/s\n",
"(c)Relative velocity at inlet is 1.963 m/s\n",
"(d)\n",
" Runner blade entry angle is 66.47 degree\n",
" Runner blade exit angle is 20.91 degree\n",
"(e)Width of runner at outlet is 0.4 m\n",
"(f)Mass of water flowing through runner per second is 1018 kg/s\n",
"(g)Head at the turbine inlet is 9.972 m\n",
"(h)Power developed is 97.925 kW\n",
"(i)Hydraulic efficiency is 98.34 %\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.12 Page 423"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"P=330#Power output from the turbine is kW\n",
"H=70#Head of operating turbine in m\n",
"N=750#Speed of the turbine in rpm\n",
"nH=0.94#Hydraulic efficiency\n",
"n0=0.85#Overall efficiency\n",
"FR=0.15#Flow ratio \n",
"BR=0.1#Breadth ratio\n",
"D1D2=2#Ratio inner and outer diameter of runner\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"Cr1=FR*(2*g*H)**(1/2)#Flow velocity at inlet in m/s\n",
"Q=(P*10**3)/(dw*g*H*n0)#Discharge at outlet in m**3/s\n",
"D1=(Q/(nH*3.1415*BR*Cr1))**(1/2)#Runner inlet diameter in m\n",
"b1=BR*D1#Height of the runner vanes at inlet in m\n",
"U1=(3.1415*D1*N)/60#Runner tip speed at inlet in m/s\n",
"Cx1=(nH*g*H)/(U1)#Velocity of whirl at inlet in m/s\n",
"a11=degrees(atan(Cr1/Cx1))#Guide blade angle in degree\n",
"b11=degrees(atan(Cr1/(Cx1-U1)))#Runner vane angle at inlet in degree\n",
"D2=D1/D1D2#Runner outlet diameter in m\n",
"U2=(3.1415*D2*N)/60#Runner tip speed at outlet in m/s\n",
"Cr2=Cr1#Flow velocity at outlet in m/s\n",
"b22=degrees(atan(Cr2/U2))#Runner vane angle at outlet in degree\n",
"b2=D1*b1/D2#Width at outlet in m\n",
"\n",
"#output\n",
"print '(a)Flow velocity at inlet is %3.2f m/s\\n(b)Discharge at outlet is %3.3f m**3/s\\n(c)Runner inlet diameter is %3.3f m\\n(d)Height of the runner vanes at inlet is %3.4f m\\n(e)Guide blade angle is %3.2f degree\\n(f) Runner vane angle at inlet is %3.2f degree\\n Runner vane angle at outlet is %3.2f degree\\n(g)Runner outlet diameter is %3.4f m\\n(h)Width at outlet is %3.4f m\\n(i)Runner tip speed at inlet is %3.2f m/s\\n(j)Velocity of whirl at inlet is %3.f m/s'%(Cr1,Q,D1,b1,a11,b11,b22,D2,b2,U1,Cx1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Flow velocity at inlet is 5.56 m/s\n",
"(b)Discharge at outlet is 0.565 m**3/s\n",
"(c)Runner inlet diameter is 0.587 m\n",
"(d)Height of the runner vanes at inlet is 0.0587 m\n",
"(e)Guide blade angle is 11.23 degree\n",
"(f) Runner vane angle at inlet is 48.23 degree\n",
" Runner vane angle at outlet is 25.75 degree\n",
"(g)Runner outlet diameter is 0.2934 m\n",
"(h)Width at outlet is 0.1174 m\n",
"(i)Runner tip speed at inlet is 23.05 m/s\n",
"(j)Velocity of whirl at inlet is 28 m/s\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.13 Page 424"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=30#Working head of the turbine in m\n",
"D1=1.2#Inlet wheel diameter in m\n",
"D2=0.6#Outlet wheel diameter in m\n",
"b11=90#Vane angle at entrance in degree\n",
"a11=15#Guide blade angle in degree\n",
"Cx2=0#Velocity of whirl at inlet in m/s\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U11=1/tan(a11*pi/180)#Runner tip speed at inlet in m/s in terms of Cr1\n",
"Cr1=(H/((U11**2/g)+(1/(2*g))))**(1/2)#Flow velocity at inlet in m/s\n",
"Cr2=Cr1#Flow velocity at outlet in m/s\n",
"U1=Cr1*U11#Runner tip speed at inlet in m/s \n",
"N=(60*U1)/(3.1415*D1)#Speed of the wheel in rpm\n",
"U2=(3.1415*D2*N)/60#Runner tip speed at inlet in m/s \n",
"b22=degrees(atan(Cr2/U2))#Vane angle at exit in degree\n",
"\n",
"#output\n",
"print '(a)Speed of the wheel is %3.2f rpm\\n(b)Vane angle at exit is %3.2f degree'%(N,b22)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Speed of the wheel is 268.27 rpm\n",
"(b)Vane angle at exit is 28.19 degree\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.14 Page 425"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D1=0.6#Internal runner diameter in m\n",
"D2=1.2#External runner diameter in m\n",
"a11=15#Guide blade angle in degree\n",
"Cr1=4#Flow velocity at inlet in m/s\n",
"Cr2=Cr1#Flow velocity at outlet in m/s\n",
"N=200#Speed of the turbine in rpm\n",
"H=10#Head of the turbine in m\n",
"a22=90#Discharge angle at outlet in degree\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U1=(3.1415*D1*N)/60#Runner tip speed at inlet in m/s \n",
"U2=(3.1415*D2*N)/60#Runner tip speed at outlet in m/s \n",
"Cx1=Cr1/tan(a11*pi/180)#Velocity of whirl at inlet in m/s\n",
"Wx1=Cx1-U1#Inlet whirl velocity component in m/s\n",
"b11=degrees(atan(Cr1/Wx1))#Vane angle at entrance in degree\n",
"b22=degrees(atan(Cr2/U2))#Vane angle at exit in degree\n",
"Wm=U1*Cx1#Work one per unit mass flow rate in W/(kg/s) as Cx2=0 in m/s\n",
"nH=(U1*Cx1/(g*H))#Hydraulic efficiency \n",
"\n",
"#output\n",
"print '(a)\\n Inlet vane angle is %3.2f degree\\n Outlet vane angle is %3.2f degree\\n(b)Work done by the water on the runner per kg of water is %3.2f W/(kg/s)\\n(c)Hydraulic efficiency is %0.2f %%'%(b11,b22,Wm,nH*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)\n",
" Inlet vane angle is 24.83 degree\n",
" Outlet vane angle is 17.66 degree\n",
"(b)Work done by the water on the runner per kg of water is 93.79 W/(kg/s)\n",
"(c)Hydraulic efficiency is 95.61 %\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.15 Page 427"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=23#Net head across the turbine in m\n",
"N=150#Speed of the turbine in rpm\n",
"P=23#Power developed by the turbine in MW\n",
"D=4.75#Blade tip diameter in m\n",
"d=2#Blade hub diameter in m\n",
"nH=0.93#Hydraulic efficiency\n",
"n0=0.85#Overall efficiency\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"dm=(D+d)/2#Mean diameter of the turbine in m\n",
"Pa=(P*10**6)/n0#Power available in MW\n",
"Q=(Pa/(dw*g*H))#Flow rate in the turbine in m**3/s\n",
"Um=(3.1415*dm*N)/60#Rotor speed at mean diameter in m/s\n",
"Pr=Pa*nH*10**-6#Power given to runner in MW\n",
"Cx1=Pr*10**6/(dw*Q*Um)#Velocity of whirl at inlet in m/s as Cx2=0 in m/s\n",
"Ca=Q/((3.1415/4)*(D**2-d**2))#Axial velocity in m/s\n",
"b11=180-degrees(atan(Ca/(Um-Cx1)))#Inlet blade angle in degree\n",
"Wx2=Um#Outlet whirl velocity component in m/s\n",
"b22=degrees(atan(Ca/Wx2))#Outlet blade angle in degree\n",
"\n",
"#output\n",
"print '(a)The inlet blade angle at mean radius is %3.1f degree\\n(b)The outlet blade angle at mean radius is %3.1f degree'%(b11,b22)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The inlet blade angle at mean radius is 156.1 degree\n",
"(b)The outlet blade angle at mean radius is 17.2 degree\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.16 Page 429"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"P=9100#Power developed by the turbine in kW\n",
"H=5.6#Net head available at the turbine in m\n",
"SR=2.09#Speed ratio\n",
"FR=0.68#Flow ratio\n",
"n0=0.86#Overall effiiciency of the turbine\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"DbD=1/3#Ratio of diameter of the boss to diameter of the runner\n",
"\n",
"#calculations\n",
"U1=SR*(2*g*H)**(1/2)#Runner tip speed at inlet in m/s\n",
"Cr1=FR*(2*g*H)**(1/2)#Flow velocity at inlet in m/s\n",
"Q=(P*10**3)/(n0*dw*g*H)#Discharge through the turbine in m**3/s\n",
"D=(Q*4/(3.1415*Cr1*((1**2)-(DbD**2))))**(1/2)#Diameter of the runner in m\n",
"N=(U1*60)/(3.1415*D)#Speed of the the turbine in rpm\n",
"Ns=(N*(P)**(1/2))/(H)**(5/4)#Specific speed \n",
"#output\n",
"print '(a)Diameter of the runner of the turbine is %3.2f m\\n(b)Speed of the turbine is %3.1f rpm\\n(c)The specific speed is %3.2f'%(D,N,Ns)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Diameter of the runner of the turbine is 6.22 m\n",
"(b)Speed of the turbine is 67.3 rpm\n",
"(c)The specific speed is 744.71\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.17 Page 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"H=20#Head developed over the turbine in m\n",
"P=11800#Power developed by turbine in kW\n",
"D=3.5#Outer diameter of the runner in m\n",
"Db=1.75#Hub diameter in m\n",
"a11=35#Guide blade angle in degree \n",
"nH=0.88#Hydraulic efficiency \n",
"n0=0.84#Overall efficiency\n",
"Cx2=0#Velocity of whirl at outlet in m/s\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"Q=(P*10**3)/(n0*g*H*dw)#Discharge of turbine in m**3/s\n",
"Cr1=Q/((3.1415/4)*(D**2-Db**2))#Flow velocity at inlet in m/s\n",
"Cx1=Cr1/tan(a11*pi/180)#Velocity of whirl at inlet in m/s\n",
"U1=(nH*H*g)/(Cx1)#Runner tip speed at inlet in m/s\n",
"Wx1=U1-Cx1#Inlet whirl velocity component in m/s\n",
"b11=180-degrees(atan(Cr1/-Wx1))#Runner inlet angle in degree\n",
"Cr2=Cr1#Flow velocity at outlet in m/s for a kaplan turbine\n",
"U2=U1#Runner tip speed at outlet in m/s for a kaplan turbine\n",
"b22=degrees(atan(Cr2/U2))#Runner outlet angle in degree \n",
"N=(U1*60)/(3.1415*D)#The speed of the turbine in rpm\n",
"\n",
"#output\n",
"print '(1)\\n (a)The runner inlet angle is %3.2f degree\\n (b)The runner outlet angle is %3.1f degree\\n(2)The speed of the turbine is %3.2f rpm'%(b11,b22,N)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(1)\n",
" (a)The runner inlet angle is 101.33 degree\n",
" (b)The runner outlet angle is 39.2 degree\n",
"(2)The speed of the turbine is 66.49 rpm\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.18 Page 432"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"N=50#Speed of the turbine in rpm\n",
"d=6#Runner diameter of the turbine in m\n",
"Ae=20#Effective area of flow in m**2\n",
"b11=150#The angle of the runner blades at inlet in degree\n",
"b22=20#The angle of the runner blade at outlet in degree\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U1=(3.141*d*N)/60#Runner tip speed at inlet in m/s\n",
"U2=U1#Runner tip speed at outlet in m/s\n",
"Cr2=U2*tan(b22*pi/180)#Flow velocity at outlet in m/s\n",
"Cr1=Cr2#Flow velocity at inlet in m/s\n",
"Q=Ae*Cr1#Discharge by the turbine in m**3/s\n",
"Cx1=U1-(Cr1/(tan((180-b11)*pi/180)))#Velocity of whirl at inlet in m/s\n",
"P=dw*g*Q*(U1*Cx1/g)*10**-3#Theoretical Power developed in kW\n",
"C2=Cr2#Absolute outlet velocity in m/s\n",
"H=(U1*Cx1/g)+(C2**2/(2*g))#Net head across the turbine in m\n",
"nH=(U1*Cx1/g)/(H)#Hydraulic efficiency\n",
"\n",
"#output\n",
"print '(a)Discharge of the turbine is %3.1f m**3/s\\n(b)Theoretical Power developed is %3.2f kW\\n(c)Hydraulic efficiency is %0.2f %%'%(Q,P,nH*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Discharge of the turbine is 114.3 m**3/s\n",
"(b)Theoretical Power developed is 10421.35 kW\n",
"(c)Hydraulic efficiency is 84.80 %\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.19 Page 433"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"D=8#Outer diameter of the turbine in m\n",
"Db=3#Inner diameter of the turbine in m\n",
"P=30000#Power developed by the turbine in kW\n",
"nH=0.95#Hydraulic efficiency\n",
"N=80#Speed of the turbine in rpm\n",
"H=12#Head operated by the turbine in m\n",
"Q=300#Discharge through the runner in m**3/s\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U1=(3.1415*D*N)/60#Runner tip speed at inlet in m/s\n",
"U2=U1#Runner tip speed at outlet in m/s as flow is axial\n",
"Cr1=Q/((3.1415/4)*(D**2-Db**2))#Flow velocity at inlet in m/s\n",
"Cr2=Cr1#Flow velocity at outlet in m/s as flow is axial\n",
"b22=degrees(atan(Cr2/U2))#The angle of the runner blade at outlet in degree\n",
"Cx1=(nH*g*H)/U1#Velocity of whirl at inlet in m/s\n",
"b11=180-degrees(atan(Cr1/(U1-Cx1)))#The angle of the runner blade at inlet in degree\n",
"nM=(P*10**3)/(dw*g*Q*(Cx1*U1/g))#Mechanical efficiency\n",
"n0=nM*nH#Overall efficiency\n",
"\n",
"#output\n",
"print '(a)Blade angle at\\n inlet is %3.2f degree\\n outlet is %3.2f degree\\n(b)Mechanical efficiency is %0.1f %%\\n(c)Overall efficiency is %0.1f %%'%(b11,b22,nM*100,n0*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Blade angle at\n",
" inlet is 167.04 degree\n",
" outlet is 11.71 degree\n",
"(b)Mechanical efficiency is 89.4 %\n",
"(c)Overall efficiency is 84.9 %\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.20 Page 434"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#input data\n",
"P=11500#Rated power of the turbine in kW\n",
"H=4.3#Average head of the turbine in m\n",
"n0=0.91#Overall efficiency of the turbine \n",
"DbD=0.3#Ratio of Diameters of runner boss and runner\n",
"SR=2#Speed ratio\n",
"FR=0.65#Flow ratio\n",
"g=9.81#Acceleration due to gravity in m/s**2\n",
"dw=1000#Density of water in kg/m**3\n",
"\n",
"#calculations\n",
"U=SR*(2*g*H)**(1/2)#Runner tip speed in m/s\n",
"Cr=FR*(2*g*H)**(1/2)#Flow velocity in m/s\n",
"Q=(P*10**3)/(n0*dw*g*H)#Discharge of the turbine in m**3/s\n",
"D=((4*Q)/(Cr*3.1415*(1**2-DbD**2)))**(1/2)#Runner diameter in \n",
"N=(60*U)/(3.1415*D)#Speed of the turbine in rpm \n",
"\n",
"#output\n",
"print '(a)Runner diameter of the turbine is %3.2f m\\n(b)Operating speed of the turbine is %3.1f rpm'%(D,N)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Runner diameter of the turbine is 8.38 m\n",
"(b)Operating speed of the turbine is 41.9 rpm\n"
]
}
],
"prompt_number": 20
}
],
"metadata": {}
}
]
}