{
"metadata": {
"name": "",
"signature": "sha256:efded2f677db2675356cffa3b1053d25367de2f521a0cbcad887abf7b22a8cb7"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter - 09 : Hydraulic Turbines"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ex9.1, page 305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#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)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 0.0\n",
"(b)The jet speed of the wheel is 0.98 m/s\n",
" Wheel speed is 0.5 m/s\n",
"(c)Dimensionless power specific speed is 0.084 rad\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.2, page 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import atan, degrees\n",
"#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=atan(degrees(Cr1/Cx1))#Guide vane angle in degree\n",
"C1=(Cr1**2+Cx1**2)**(1/2)#Inlet velocity in m/s\n",
"b1=atan(degrees(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 1.5 degree\n",
" (2)Inlet absolute velocity of water at entry to runner is 1.0 m/s\n",
"(b)Runner blade entry angle is 1.6 degree\n",
"(c)Total Loss of head in the runner is -44.51 m\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.3, page 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin, tan, pi, atan\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=atan(degrees(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=atan(degrees(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)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 %3.4f'''%(C1,Cx1,W1,b11,b22,b2,m,H,W,nH)"
],
"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 1.000 m/s\n",
"(d)Runner blade entry angle is 1.56 degree\n",
" Runner blade exit angle is 1.53 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 0.9834\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.4, page 312"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import atan\n",
"#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=atan(degrees(Cr1/Cx1))#Guide blade angle in degree\n",
"b11=atan(degrees(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=atan(degrees(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 0.15 m/s\n",
"(b)Discharge at outlet is 0.565 m**3/s\n",
"(c)Runner inlet diameter is 1.000 m\n",
"(d)Height of the runner vanes at inlet is 0.1000 m\n",
"(e)Guide blade angle is 0.48 degree\n",
"(f)Runner vane angle at inlet is -0.36 degree\n",
" Runner vane angle at outlet is 0.41 degree\n",
"(g)Runner outlet diameter is 0.5000 m\n",
"(h)Width at outlet is 0.2000 m\n",
"(i)Runner tip speed at inlet is 39.27 m/s\n",
"(j)Velocity of whirl at inlet is 16 m/s\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.5, page 316"
]
},
{
"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=atan(degrees(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 59.40 rpm\n",
"(b)Vane angle at exit is 1.54 degree\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.6, page 321"
]
},
{
"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=atan(degrees(Cr1/Wx1))#Vane angle at entrance in degree\n",
"b22=atan(degrees(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)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 %3.4f'''%(b11,b22,Wm,nH)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Inlet vane angle is 1.53 degree\n",
" Outlet vane angle is 1.52 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 0.9561\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9.7, page 326"
]
},
{
"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-(atan(degrees(Ca/(Um-Cx1))))#Inlet blade angle in degree\n",
"Wx2=Um#Outlet whirl velocity component in m/s\n",
"b22=atan(degrees(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 178.5 degree\n",
"(b)The outlet blade angle at mean radius is 1.5 degree\n"
]
}
],
"prompt_number": 24
}
],
"metadata": {}
}
]
}