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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:f90ad248f5346a845ec01efdf3c2941322625ecb2d8d238ed549e14c9d9de3bb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2 - Blade Theory"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.1 page 53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "c =2.25#Chord length of an aerofoil in m\n",
+ "l=13.5#Span of the aerofoil in m\n",
+ "C=125#Velocity of the aerofoil in m/s\n",
+ "Cl=0.465#Lift coefficient\n",
+ "Cd=0.022#Drag coefficient\n",
+ "d=1.25#Density of the air in kg/m**3\n",
+ "\n",
+ "#calculations\n",
+ "A=c*l#Area of cross section of the aerofoil in m**2\n",
+ "W=Cl*d*((C**2)/2)*A*10**-3#Weight carried by the wings of aerofoil in kN\n",
+ "D=Cd*d*((C**2)/2)*A#Drag force on the wings of aerofoil in N\n",
+ "P=D*C*10**-3#Power required to the drive the aerofoil in kW\n",
+ "\n",
+ "#output\n",
+ "print '''(a)Weight carrried by the wings is %3.2f kN\n",
+ "(b)Drag force on the wings of aerofoil is %3.2f N\n",
+ "(c)Power required to drive the aerofoil is %3.3f kW'''%(W,D,P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)Weight carrried by the wings is 137.92 kN\n",
+ "(b)Drag force on the wings of aerofoil is 6525.46 N\n",
+ "(c)Power required to drive the aerofoil is 815.683 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.2 page 53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "#input data\n",
+ "W=980#The weight of the object being dropped by parachute in N\n",
+ "C=5#The maximum terminal velocity of dropping in m/s\n",
+ "d=1.22#The density of the air in kg/m**3\n",
+ "Cd=1.3#The drag coefficient of the parachute\n",
+ "\n",
+ "#calculations\n",
+ "A=W/(Cd*d*((C**2)/2))#The area of cross section in m**2\n",
+ "D=((A*4)/(3.14))**(1/2)#Diameter of the parachute in m\n",
+ "\n",
+ "#output\n",
+ "print 'The required diameter of the parachute is %3.2f m'%(D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required diameter of the parachute is 7.94 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.3 page 54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "A=10*1.2#Area of the airplane wing in m**2\n",
+ "C=((240*10**3)/3600)#Velocity of the wing in m/s\n",
+ "F=20#Total aerodynamic force acting on the wing in kN\n",
+ "LD=10#Lift-drag ratio\n",
+ "d=1.2#Density of the air in kg/m**3\n",
+ "\n",
+ "#calculations\n",
+ "L=(F)/(1.01)**(1/2)#The weight that the plane can carry in kN\n",
+ "Cl=(L*10**3)/(d*A*((C**2)/2))#Coefficient of the lift\n",
+ "\n",
+ "#output\n",
+ "print '(1)The coefficient of lift is %3.3f\\n(2)The total weight the palne can carry is %3.1f kN'%(Cl,L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(1)The coefficient of lift is 0.622\n",
+ "(2)The total weight the palne can carry is 19.9 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.4 page 54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "m=25#Mass flow rate of the air in kg/s\n",
+ "d=1.1#Density of the air in kg/m**3\n",
+ "Ca=157#Axial flow velocity of the air in m/s\n",
+ "N=150#Rotational speed of the air in rev/s\n",
+ "U=200#Mean blade speed in m/s\n",
+ "lc=3#Rotor blade aspect ratio \n",
+ "sc=0.8#Pitch chord ratio\n",
+ "\n",
+ "#calculations\n",
+ "rm=(U)/(2*3.145*N)#Mean radius of the blades in m\n",
+ "A=(m)/(d*Ca)#The annulus area of flow in m**2\n",
+ "l=(A)/(2*3.1*rm)#The blade height in m\n",
+ "C=l/lc#The chord of the blades in m\n",
+ "S=sc*C#The blade pitch in m\n",
+ "n=(2*3.141*rm)/(S)#Number of blades \n",
+ "\n",
+ "#output\n",
+ "\n",
+ "print '''(a)The mean radius of the blades is %3.3f m\n",
+ "(b)The blade height is %3.2f m\\n(c) (1)The pitch of the blades is %3.4f m\n",
+ "(2)The chord of the blades is %3.3f m\\n(d)The number of the blades are %3.f'''%(rm,l,S,C,n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The mean radius of the blades is 0.212 m\n",
+ "(b)The blade height is 0.11 m\n",
+ "(c) (1)The pitch of the blades is 0.0294 m\n",
+ "(2)The chord of the blades is 0.037 m\n",
+ "(d)The number of the blades are 45\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.5 page 56"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "sc=0.8#Pitch-chord ratio of compressor blade\n",
+ "b1=45#Relative air angle at inlet in degree\n",
+ "b2=15#Relative air angle at oulet in degree\n",
+ "a1=b1#Cascade air angle at inlet in degree\n",
+ "a2=b2#Cascade air angle at outlet in degree\n",
+ "\n",
+ "#calculations \n",
+ "en=a1-a2#Nominal deflection angle of the blade in degree\n",
+ "m=((0.23*(1)**2))+(0.1*a2/50)#An emperical constant for a circular arc camber where (2*a/c)=1\n",
+ "t=(a1-a2)/(1-0.233)#Blade camber angle in degree\n",
+ "d=(m*(sc)**(1/2))*t#The deviation angle of the blade in terms of (degree*t)\n",
+ "ps=a1-(t/2)#The blade stagger for a given circular arc cascade in degree\n",
+ "\n",
+ "#output\n",
+ "print '''(a)The nominal deflection angle is %i degree\n",
+ "(b)The blade camber angle is %3.2f degree\n",
+ "(c)The deviation angle is %3.2f degree\n",
+ "(d)The blade stagger is %3.2f degree'''%(en,t,d,ps)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The nominal deflection angle is 30 degree\n",
+ "(b)The blade camber angle is 39.11 degree\n",
+ "(c)The deviation angle is 9.10 degree\n",
+ "(d)The blade stagger is 25.44 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.6 page 57"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import atan, degrees, tan\n",
+ "#input data\n",
+ "t=25#The camber angle of aero foil blades in degree\n",
+ "ps=30#The blade stagger angle in degree\n",
+ "sc=1#The pitch-chord ratio of the blades\n",
+ "In=5#The nominal value of incidence in degree\n",
+ "\n",
+ "#calculations\n",
+ "a1=ps+(t/2)#The cascade blade angle at inlet in degree\n",
+ "a2=a1-t#The cascade blade angle at outlet in degree\n",
+ "a1n=In+a1#The nominal entry air angle in degree\n",
+ "a2n=degrees(atan((tan(a1n))-(1.55/(1.0+(1.5*sc)))))#The nominal exit air angle in degree\n",
+ "\n",
+ "#output\n",
+ "print '''(1)The cascade blade angles at -\n",
+ "(a)inlet is %3.1f degree\n",
+ "(b)exit is %3.1f degree\n",
+ "(2)The nominal air angles at -\n",
+ "(a)inlet is %3.1f degree\n",
+ "(b)exit is %3.2f degree'''%(a1,a2,a1n,a2n)\n",
+ "# the answer in the textbook is not correct."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(1)The cascade blade angles at -\n",
+ "(a)inlet is 42.5 degree\n",
+ "(b)exit is 17.5 degree\n",
+ "(2)The nominal air angles at -\n",
+ "(a)inlet is 47.5 degree\n",
+ "(b)exit is -12.69 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.7 page 58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import atan, cos, tan, pi\n",
+ "#input data\n",
+ "C1=75#Velocity of air entry in m/s\n",
+ "a1=48#Air angle at entry in degree\n",
+ "a2=25#Air angle at exit in degree\n",
+ "cs=0.91#The chord-pitch ratio \n",
+ "P0m=(11*9.81*10**3)/10**3#The stagnation pressure loss in N/m**2\n",
+ "d=1.25#The density of the sair in kg/m**3\n",
+ "\n",
+ "#calculations\n",
+ "Cp=(P0m/(0.5*d*C1**2))#The pressure loss coefficient \n",
+ "am=degrees(atan((tan(a1)+tan(a2))/2))#The mean air angle in degree\n",
+ "Cd=2*(1/cs)*(P0m/(d*C1**2))*((cos(pi/180*am))**3/(cos(pi/180*a1))**2)#The drag coefficient \n",
+ "Cl=(2*(1/cs)*cos(pi/180*am)*(tan(pi/180*a1)-tan(pi/180*a2)))-(Cd*tan(pi/180*am))#THe lift coefficient\n",
+ "\n",
+ "#output\n",
+ "print '''(a)The pressure loss coefficient is %3.4f\n",
+ "(b)The drag coefficient is %3.4f\\n(c)The lift coefficient is %3.3f'''%(Cp,Cd,Cl)\n",
+ "# the answer in the textbook is not correct."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The pressure loss coefficient is 0.0307\n",
+ "(b)The drag coefficient is 0.0518\n",
+ "(c)The lift coefficient is 1.222\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.8 page 59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "a1=40#The cascade air angle at entry in degree\n",
+ "a2=65#The cascade air angle at exit in degree\n",
+ "C1=100#Air entry velocity in m/s\n",
+ "d=1.25#The density of the air in kg/m**3\n",
+ "sc=0.91#The pitch-chord ratio of the cascade\n",
+ "P0m=(17.5*9.81*10**3)/10**3#The average loss in stagnation pressure across cascade in N/m**2\n",
+ "\n",
+ "#calculations\n",
+ "Cp=(P0m/(0.5*d*C1**2))#The pressure loss coefficient in the cascade\n",
+ "am=atan((tan(a2)-tan(a1))/2)#The mean air angle in degree\n",
+ "Cd=2*(sc)*(P0m/(d*C1**2))*((cos(pi/180*am))**3/(cos(pi/180*a2))**2)#The drag coefficient \n",
+ "Cl=(2*(sc)*cos(pi/180*am)*(tan(pi/180*a1)+tan(pi/180*a2)))+(Cd*tan(pi/180*am))#THe lift coefficient\n",
+ "\n",
+ "#output\n",
+ "print '(a)The pressure loss coefficient is %3.4f\\n(b)The drag coefficient is %3.4f\\n(c)The lift coefficient is %3.3f'%(Cp,Cd,Cl)\n",
+ "# the answer in the textbook is not correct."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The pressure loss coefficient is 0.0275\n",
+ "(b)The drag coefficient is 0.1399\n",
+ "(c)The lift coefficient is 5.430\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex 2.9 page 60"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#input data\n",
+ "W=30000#The weight of the jet plane in N\n",
+ "A=20#The area of the wing in m**2\n",
+ "C=250*5/18#The speed of the jet plane in m/s\n",
+ "P=750#The power delivered by the engine in kW\n",
+ "d=1.21#Density of the air in kg/m**3\n",
+ "\n",
+ "#calculations\n",
+ "L=W#The lift force on the plane is equal to the weight of the plane in N\n",
+ "Pd=0.65*P#The power required to overcome the drag resistance in kW\n",
+ "D=(Pd/C)*10**3#The drag force on the wing in N\n",
+ "Cd=D/(0.5*d*A*C**2)#The coefficient of drag for the wing \n",
+ "Cl=L/(0.5*d*A*C**2)#The coefficient of lift for the wing \n",
+ "\n",
+ "#output\n",
+ "print '(a)The coefficient of lift on the wing is %3.3f\\n(b)The coefficient of drag on the wing is %3.3f'%(Cl,Cd)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The coefficient of lift on the wing is 0.514\n",
+ "(b)The coefficient of drag on the wing is 0.120\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-05-29 01:41:11 +0000