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diff --git a/Turbomachines_by_A._V._Arasu/Ch9.ipynb b/Turbomachines_by_A._V._Arasu/Ch9.ipynb new file mode 100644 index 00000000..9ea40cea --- /dev/null +++ b/Turbomachines_by_A._V._Arasu/Ch9.ipynb @@ -0,0 +1,1077 @@ +{ + "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": {} + } + ] +}
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