() . . WEIGHT () 1. RIGHT TRIANGLE WITH 2 45 ANGLE ( )1. PLATE ()2. EQUILATERAL TRIANGLE ( )2. PIPE & CYLINDER ()3. TRAPEZOID ()3. CONE (REDUCER)4. CIRCLE ()4. SPHERE ()5. CIRCULAR SECTOR ()5. ROUND BAR ()6. CIRCULAR SEGMENT ( )6. ROUND PLATE ()7. REGULAR POLYGON ()8. REGULAR HEXAGON (). 9. ELLIPS 11. THICKNESS for SHELL & HEAD ( )10. ELLIPS 22. VOLUME ()3. PRESSURE LOSS (). VOLUME () & SURFACE () . 1. CUBE ()1. FLOW RATE ()2. SQUARE PRISM ()2. PIPE INSIDE DIA. ()3. SPHERE ()3. VELOCITY ()4. SPHERICAL ZONE ()4. DENSITY ()5. PIPE & CYLINDER ()5. VISCOSITY ()6. ELBOW ()6. KINEMATIC VISCOSITY ()7. CONCENTRIC REDUCER ( )7. STUD BOLT LENGTH ( )8. CONE ()8. HEX BOLT LENGTH ( )9. PRESSURE LOSS for PIPE ( )

1. RIGHT TRIANGLE WITH 2 45 ANGLE ( )3. TRAPEZOID ()5. CIRCULAR SECTOR ()7. REGULAR POLYGON ()9. ELLIPS 110. ELLIPS 28. REGULAR HEXAGON ()6. CIRCULAR SEGMENT ( )4. CIRCLE ()2. EQUILATERAL TRIANGLE ( )8. CONE ()7. CONCENTRIC REDUCER ( )6. ELBOW ()5. PIPE & CYLINDER ()4. SPHERICAL ZONE ()3. SPHERE ()2. SQUARE PRISM ()1. CUBE ()1. PLATE ()2. PIPE & CYLINDER ()4. SPHERE ()3. CONE (REDUCER)6. ROUND PLATE ()5. ROUND BAR ()1. THICKNESS for SHELL & HEAD ( )2. VOLUME ()3. PRESSURE LOSS ()1. FLOW RATE ()7. STUD BOLT LENGTH ( )8. HEX BOLT LENGTH ( )9. PRESSURE LOSS for PIPE ( )3. VELOCITY ()2. PIPE INSIDE DIA. ()7. STUD BOLT LENGTH ( )8. HEX BOLT LENGTH ( )9. PRESSURE LOSS for PIPE ( )4. DENSITY ()5. VISCOSITY ()6. KINEMATIC VISCOSITY ()

-AREA CALCULATION RIGHT TRIANGLE WITH 2 45 ANGLESA = AreaA = a2 /2C = 1.4142 * aH = 0.7071 * aa = 1.4142 * H* ACTUAL CALCULATIONLengtha=50mmA=0.0013m2=1250.0mm2C=70.7mmH=35.4mm---------------------------------------------------------------------------------------- EQUILATERAL TRIANGLEA = AreaA = a * H / 2H = 0.866 * aC = 1.155 * H* ACTUAL CALCULATIONLengtha=50mmHeighH=70mmA=0.00175m2=1750.0mm2C=80.9mm

-AREA CALCULATION TRAPEZOIDA = AreaA = (a + b) * H /2* ACTUAL CALCULATIONLength for Uppera=120mmLength for Bottomb=100mmHeightH=80mmA=0.0088m2=88.00cm2=8800.0mm2---------------------------------------------------------------------------------------- CIRCLEA = AreaC = CircumferenceA = * d2 / 4C = * d* ACTUAL CALCULATIONDiameterd=50mmA=0.00196m2=19.63cm2=1963.5mm2C=157.1mm

-AREA CALCULATION CIRCULAR SECTORA = AreaL = ArcR = RadiusA = R2 * * / 360L = R * * / 180R = 2 * A / L* ACTUAL CALCULATIONRadiusR=150mmAngle=25degreeA=0.0049m2=49.09cm2=4908.7mm2L=65.4mm---------------------------------------------------------------------------------------- CIRCULAR SEGMENTA = AreaC = CordA = (R2 * * / 360) - C (R - h) / 2h = R - ( 4 R2 - C2 )/ 2C = 2 h (2 R - h)* ACTUAL CALCULATIONRadiusR=50mmAngle=60degreeC=50.0mmh=6.7mmA=0.00023m2=226.5mm2

h

-AREA CALCULATION REGULAR POLYGONA = Arean = Number of Sidesr = Radius of Inscribed CircleA = n * r * H / 2r = (R2 - H2/4)H = 2 * (R2 - r2)R = (r2 + H2/4) = 180 - * ACTUAL CALCULATIONCircum. Circle RadiusR=150mmLength for SideH=176.3356mmNumber of sidesn=5r=121.35mmA=0.05350m2=53496.9mm2---------------------------------------------------------------------------------------- REGULAR HEXAGONA = AreaR = Radius of Circumscribed CircleA = 2.598 * H2 = 3.464 * r2R = H = 1.155 * r* ACTUAL CALCULATIONRadius of Circum.R=500mmA=0.64950m2=649500.0mm2r=433.0mm

-EllipsAREA CALCULATION ELLIPSE 1A = AreaP = PerimeterA = * a * bP = * {2 * (a2 + b2)}* ACTUAL CALCULATIONLengtha=100mmLengthb=50mmA=0.0157m2=157.08cm2=15708.0mm2P=496.7mm---------------------------------------------------------------------------------------- ELLIPSE 2C = Ratio of Minor Axis to Major AxisC = a / bX = {a2 - (2 * C * Y2)}Y = (a2 - X2) / C* ACTUAL CALCULATIONLehgtha=100mmLehgthb=50mmHeighX=50mmC=2.00000Y=43.3mm

-VOLUME & SURFACE AREA CALCULATION CUBEV = VolumeS = Surface AreaV = A3S = 6 * A2* ACTUAL CALCULATIONLengthA=200mmV=0.0080m3S=0.2400m2---------------------------------------------------------------------------------------- SQUARE PRISMV = VolumeS = Surface AreaV = A * B * CS = 2 * (A*B + B*C + A*C)* ACTUAL CALCULATIONLengthA=200mmHeightB=150mmWidthC=100mmV=0.0030m3S=0.1300m2

-VOLUME & SURFACE AREA CALCULATION SPHEREV = VolumeS = Surface AreaV = ( * d3) / 6S = * d2* ACTUAL CALCULATIONOutside Dia.d=1000mmV=0.5236m3S=3.1416m2---------------------------------------------------------------------------------------- SPHERICAL ZONEV = VolumeS = Surface AreaV = 0.5236 * H * (3*C12/4 + 3*C22/4 + H2)S = * D * H* ACTUAL CALCULATIONOutside Dia.D=200mmHeigh for ZoneH=20mmLength 1C1=50Length 2C2=150mmV=0.0002m3S=0.0126m2

-Pipe&CylinderVOLUME & SURFACE AREA CALCULATION PIPE & CYLINDERV = VolumeS = Surface AreaV = * d2 * L / 4S = * D * L* ACTUAL CALCULATIONOutside Dia.D=3000mmUsed Thicknesst=6mmInside Dia.d=2988mmLengthL=2000mmV=14.02429m3S=18.84955m2---------------------------------------------------------------------------------------- ELBOWV = VolumeS = Surface AreaV = 19.739 * R * d2 / 16S = 39.478 * R * D / 8* ACTUAL CALCULATIONOutside Dia.D=114.3mmUsed Thicknesst=6mmInside Dia.d=102.3mmLengthR=152.4mmV=0.00197m3S=0.08596m2

-ReducerVOLUME & SURFACE AREA CALCULATION CONCENTRIC REDUCERV = VolumeS = Surface AreaV = * H * (d12 + d1 * d2 + d22) / 12C = {(D1 - D2)/2}2 + H2S = * C * (D1 + D2) / 2* ACTUAL CALCULATIONOutside Dia.D1=508mmInside Dia.d1477.8mmOutside Dia.D2355.6mmInside Dia.d2333.4mmLengthH=508mmV=0.0663m3C=513.68mmS=0.6968m2---------------------------------------------------------------------------------------- CONEV = VolumeS = Surface AreaV = * d2 * L / 12C = (D / 2)2 + L2S = * D * C / 2* ACTUAL CALCULATIONOutside Dia.D=114.3mmInside Dia.d=102.3mmLengthL=152.4mmV=0.00042m3C=0.16276mmS=0.02922m2

-&WEIGHT CALCULATION PLATEW = WeightL = Lengthw = Widtht = ThicknessSg = Specific GravityW = L * w * t * Sg* ACTUAL CALCULATIONLengthL=100mmWidthw=70mmThicknesst=6mmSpecific GravitySg=7.85W=0.33kg=0.73lb---------------------------------------------------------------------------------------- PIPE & CYLINDERW = Weightt = ThicknessD = Outside Dia.Sg = Specific GravityL = LengthW = * t * (D - t) * Sg * L* ACTUAL CALCULATIONThicknesst=6mmOutside Dia.D=114.3mmLengthL=1000mmSpecific GravitySg=7.85W=16.03kg=35.33lb

# Specific Gravity (Sg) Carbon Steel : 7.85 Stainless Steel (304) : 7.93 Stainless Steel (316) : 7.98

-ConeWEIGHT CALCULATION CONEW = Weightt = ThicknessSg = Specific GravityW = /2 * t * C * (D1 + D2 - 2t) * Sg* ACTUAL CALCULATIONOutside Dia.D1=508mmOutside Dia.D2=219.1mmLengthH=508mmThicknesst=6mmSpecific GravitySg=7.85C=528.14mmW=27.94kg=61.60lb---------------------------------------------------------------------------------------- SPHEREW = Weightd = Dia.Sg = Specific GravityW = /6 * d3 * Sg* ACTUAL CALCULATIONDia.d=100mmSpecific GravitySg=7.85W=4.1102kg=9.0615lb

# Specific Gravity (Sg) Carbon Steel : 7.85 Stainless Steel (304) : 7.93 Stainless Steel (316) : 7.98

-WEIGHT CALCULATION ROUND BARW = WeightL = LengthSg = Specific GravityW = /4 * L * D2 *Sg* ACTUAL CALCULATIONOutside Dia.D=20mmLengthL=1000mmSpecific GravitySg=7.85W=2.47kg=5.44lb---------------------------------------------------------------------------------------- ROUND PLATEW = Weightd = Dia.Sg = Specific GravityW = /4 * d2 * t * Sg* ACTUAL CALCULATIONDia.d=100mmThicknesst=10mmSpecific GravitySg=7.85W=0.62kg=1.36lb

# Specific Gravity (Sg) Carbon Steel : 7.85 Stainless Steel (304) : 7.93 Stainless Steel (316) : 7.98

FLOW RATE CALCULATION FLOW RATEQ = Flow Rate ()A = Section Area ()V = Velocity ()Q = A * V* ACTUAL CALCULATIONInside Dia.d=100mmVelocityV=3m/secA=0.0079m2Q=84.82m3/h=1413.7L/min.=2995.7ft3/h=373.5gal/min (US) Calculation for Unit Conversiona. Inside Dia. (d)b. Velocity (V)1cm=10mm1m/h=2.778E-04m/sec1m=1000mm1km/h=0.2778m/sec1in=0.0254mm1in/sec=0.0254m/sec1ft=0.3048mm1ft/sec=0.3048m/sec1mile=1609.34mm1ft/min=0.00508m/sec1yd=0.9144mm1mile/h=0.047m/sec

INSIDE DIA. CALCULATION INSIDE DIA. (PIPE SIZE)d = Inside Dia ()Q = Flow Rate ()V = Velocity ()d = (4 Q) / ( * V)* ACTUAL CALCULATIONFlow RateQ=75m3/hVelocityV=3m/secA=0.0069m2d=94.0mm=9.4cm=3.7020in=0.3084ft Calculation for Unit Conversiona. Flow Rate (Q)b. Velocity (V)1L/min.=0.06m3/h1m/h=2.778E-04m/sec1ft3/h=0.02832m3/h1km/h=0.2778m/sec1ft3/sec=101.935m3/h1in/sec=0.0254m/sec1gal/min=0.02271m3/h1ft/sec=0.3048m/sec(US)1ft/min=0.00508m/sec1mile/h=0.047m/sec

VELOCITY CALCULATION VELOCITYV = Velocity ()Q = Flow Rate ()A = Section Area ()V = Q / A* ACTUAL CALCULATIONFlow RateQ=200m3/hInside Dia.d=150mmA=0.0177m2V=3.14m/sec=11317.7m/h=123.77in/sec=10.31ft/sec=7.033mile/h Calculation for Unit Conversiona. Flow Rate (Q)b. Inside Dia. (d)1L/min.=0.06m3/h1cm=10mm1ft3/h=0.02832m3/h1m=1000mm1ft3/sec=101.935m3/h1in=0.0254mm1gal/min=0.02271m3/h1ft=0.3048mm(US)1mile=1609.34mm1yd=0.9144mm

DENSITY CALCULATION DENSITY = Density () = Viscosity () = Kinematic Viscosity () = / * ACTUAL CALCULATIONViscosity=1CPKinematic Viscosity=1.2cSt=833.3kg/m3=0.8333g/cm3=52.03lb/ft3=0.0301lb/in3 Calculation for Unit Conversiona. Viscosity ()b. Kinematic Viscosity ()1PaS=1000CP1m2/s=1.0E+6cSt1kg/mS=1000CP1St=100cSt1P=100CP1m2/h=277.8cSt1kgfS/m2=9806.65CP1ft2/s=92903.0cSt1in2/s=645.16cSt

VISCOSITY CALCULATION VISCOSITY = Viscosity () = Density () = Kinematic Viscosity () = * * ACTUAL CALCULATIONDensity=1000kg/m3Kinematic Viscosity=1cSt=1.0CP=0.0010PaS=0.0010kg/mS=0.0100P (= g/cmsec)=0.00010kgfS/m2 Calculation for Unit Conversiona. Density ()b. Kinematic Viscosity ()1g/cm3=1000kg/m31m2/s=1.0E+6cSt1g/m3=0.001kg/m31St=100cSt1lb/ft3=16.019kg/m31m2/h=277.8cSt1lb/in3=27680kg/m31ft2/s=92903.0cSt1in2/s=645.16cSt

KINEMATIC VISCOSITY CALCULATION KINEMATIC VISCOSITY = Kinematic Viscosity () = Viscosity () = Density () = / * ACTUAL CALCULATIONViscosity=5CPDensity=955kg/m3=5.2356cSt=5.24E-06m2/s(ex. 1.23E-06 = 1.23 * 10-6)=0.0524St=0.0188m2/h=0.0001ft2/s=0.0081in2/s Calculation for Unit Conversiona. Viscosity ()b. Density ()1PaS=1000CP1g/cm3=1000CP1kg/mS=1000CP1g/m3=0.001CP1P=100CP1lb/ft3=16.019CP1kgfS/m2=9806.65CP1lb/in3=27680CP

PRESSURE VESSEL CALCULATION THICKNESS for SHELL & 2:1 ELLIPSOIDAL HEADSts = Required Thickness for Shellth = Required Thickness for 2:1 Ellips. HeadP = Design PressureR = Inside RadiusS = Allowable StressE = Joint EfficiencyC = Corrosion Allowancets = P * R / (S * E - 0.6 P) + Cth = P * D / (2 S * E - 0.2 P) + CPer ASME Sec. Div.1 UG-27(c)(1),(2)Per ASME Sec. Div.1 UG-32(d)* ACTUAL CALCULATIONDesign PressureP=15kgf/cm2Inside Dia.D=400mmAllowable StressS=1202.3kgf/cm2Joint EfficiencyE=0.85Corrosion AllowanceC=3mmtS=5.962mmth=5.498mm (= Required min. Th'k after forming) Used min. Th'k for Head=6.323mm VOLUME for PRESSURE VESSELLength for End to EndL=1000mmHeigh for T.L. to T.L.H=700mmInsdie Dia for Nozzled=381mmV0.175m3

DLH

-STUDBOLT LENGTH CALCULATION STUD BOLT FOR RAISED FACE FLANGE (ANSI)A = Stud Bolt Length Exclusive of Negative Tolerance nL = Length for Stud BoltC = Min. Flange Thicknesst = Plus Tolerance for Flange Thicknessd = Heavy Nut ThicknessF = Total Height of Facing of DepthG = Gasket Thicknessn = Negative Tolerance on Bolt LengthA = 2 * (C + t + d) + G + FL = A + nPer ANSI B16.5 para 6.10.2, Bolt Lengths (ANNEX F)* ACTUAL CALCULATIONMin. Flange ThicknessC=25mmPlus Tolerance for Flange Thicknesst=3mmBolt SizeD=3/4inchHeavy Nut Thicknessd=19.05mmTotal Height of Facing of DepthF=0mmGasket ThicknessG=4.5mmNegative Tolerance on Bolt Lengthn=1.6mmA=98.6mmL=100.2mm

ex) 1 1/2 , 3/4,..

-HEXBOLT LENGTH CALCULATION HEX BOLTL = Length for Stud Boltt = Min. Base Thicknessd = Hex Nut ThicknessL = t + d + 0.8 D* ACTUAL CALCULATIONMin. Base Thicknesst=24mmBolt SizeD=16mmHex Nut Thicknessd=13mmL=49.8mm

-PRESSURE LOSSES CALCULATION STRAIGHT PIPE (CYLINDER)P = Pressure LossR = Reynolds No.f = Friction Cofficient = DensityV = Velocityg = Gravity Velocity = ViscosityP = f * L/d * * V2 / 2 gR = V * d * / * ACTUAL CALCULATIONInside Dia.d=52.5mmLengthL=1000mmFlow RateQ=30m3/hDensity=880kg/m3Viscosity=2.4CPV=3.850m/secR=74103.9/d=0.0048f=0.0312P=0.0396kgf/cm2 Calculation for Unit Conversiona. Density ()b. Viscosity ()1g/cm3=1000kg/m31PaS=1000CP1g/m3=0.001kg/m31kg/mS=1000CP1lb/ft3=16.019kg/m31P=100CP1lb/in3=27680kg/m31kgfS/m2=9806.65CPc. Flow Rate (Q)d. Velocity (V)1L/min.0.06m3/h1m/h2.78E-04m/sec1ft3/h0.02832m3/h1in/sec0.02541ft3/sec101.935m3/h1ft/sec0.3048

(by Moody Curve)( Steel )

-PRESSURE LOSSES CALCULATION PRESSURE VESSELP = Pressure LossR = Reynolds No.f = Friction CofficientLn = Length for Nozzle = DensityV = Velocityg = Gravity Velocity = ViscosityP = (f * Ln/d * * V2 / 2 g)+ ( * K * V2 / 2 g)R = V * d * / * ACTUAL CALCULATIONInside Dia. for Nozzled=100mmInside Dia. for VesselD=750mmLength for face to faceL=1200mmFlow RateQ=100m3/hDensity=880kg/m3Viscosity=2.4CPV=3.537m/secR=129681.8/d=0.0025f=0.0263P=0.0914kgf/cm2 Calculation for Unit Conversiona. Density ()b. Viscosity ()1g/cm3=1000kg/m31PaS=1000CP1g/m3=0.001kg/m31kg/mS=1000CP1lb/ft3=16.019kg/m31P=100CP1lb/in3=27680kg/m31kgfS/m2=9806.65CP

(by Moody Curve)DL( Steel )d

: 1999 10 5 : 2002 11 3VER. NO. : CAL-2002 : http://pipeline.wo.to) 1. , . ( )2. .

Sheet21. PIPERe =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re =74103.9Re/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/D0.00010.00020.00040.00060.00080.0010.0020.0040.0060.0080.010.01500000000000000000000000030000.04430000.04430000.04430000.04430000.04430000.04430000.04630000.04830000.04930000.05130000.05230000.05500000000000000000000000040000.040640000.040640000.040740000.040840000.040940000.04140000.04240000.04440000.04640000.047840000.049540000.05300000000000000000000000050000.03850000.038250000.038450000.038650000.038750000.038850000.0450000.04250000.04450000.04650000.047650000.05100000000000000000000000060000.035860000.03660000.036260000.036560000.036860000.03760000.03860000.0460000.042360000.044260000.04660000.0500000000000000000000000070000.033170000.033570000.033870000.034270000.034570000.035270000.036770000.03970000.041770000.043270000.04570000.049500000000000000000000000080000.03380000.033380000.033580000.03780000.03480000.034280000.035880000.03880000.040880000.042280000.04480000.048700000000000000000000000090000.03290000.032390000.032590000.032790000.032990000.033290000.034590000.037290000.039990000.041890000.043590000.0481000000000000000000000000100000.0313100000.0315100000.0317100000.032100000.0322100000.0325100000.0338100000.0365100000.0395100000.0143100000.0432100000.0479000000000000000000000000200000.0267200000.0268200000.0269200000.0275200000.0277200000.028200000.0298200000.033200000.036200000.0385200000.0418200000.046000000000000000000000000300000.0235300000.0243300000.0248300000.0255300000.0257300000.0262300000.028300000.0318300000.0349300000.0377300000.04300000.0455000000000000000000000000400000.0225400000.0228400000.0235400000.024400000.0246400000.025400000.0272400000.031400000.034400000.0372400000.0396400000.0451000000000000000000000000500000.0213500000.0219500000.0225500000.023500000.0237500000.0242500000.0268500000.0304500000.0339500000.0368500000.0393500000.045000000000000000000000000600000.0205600000.021600000.0215600000.0225600000.023600000.0237600000.0263600000.0301600000.0336600000.0365600000.0391600000.0448000000000000000000000000700000.0198700000.0205700000.0212700000.0219700000.0227700000.023700000.026700000.03700000.0334700000.0363700000.0389700000.04450.01967688290.01967688290.02029480480.02029480480.02103584380.02103584380.02173584380.02173584380.02249480480.02249480480.02291792190.02291792190.02591792190.02591792190.0299589610.0299589610.03331792190.03331792190.0362589610.0362589610.03881792190.03881792190.04437688290.0443768829800000.0195800000.02800000.0208800000.0215800000.0222800000.0228800000.0258800000.0299800000.0332800000.0362800000.0387800000.0442000000000000000000000000900000.019900000.0195900000.0204900000.021900000.0219900000.0225900000.0256900000.02985900000.033900000.0361900000.0385900000.04410000000000000000000000001000000.01871000000.01931000000.021000000.02091000000.02171000000.02221000000.02541000000.02981000000.03281000000.0361000000.03831000000.0440000000000000000000000002000000.01662000000.01722000000.01842000000.01932000000.02052000000.02112000000.02472000000.0292000000.03222000000.03582000000.0380200000000000000000000003000000.01573000000.01623000000.01783000000.01873000000.01983000000.02083000000.02433000000.02893000000.0323000000.03563000000.03800000000000000000000004000000.01494000000.01584000000.01724000000.01844000000.01954000000.02054000000.024064000000.02870600000000000000005000000.01455000000.01545000000.0175000000.01825000000.01935000000.02035000000.024045000000.02870400000000000000006000000.01426000000.01526000000.01696000000.018056000000.01926000000.02016000000.024026000000.02870200000000000000007000000.01397000000.0157000000.01687000000.018037000000.01917000000.027000000.0247000000.028700000000000000008000000.01378000000.01498000000.016828000000.018028000000.019068000000.020028000000.02398000000.028600000000000000009000000.01369000000.014859000000.016759000000.018019000000.019039000000.020019000000.023859000000.0285000000000000000010000000.013510000000.014810000000.016710000000.01810000000.01910000000.0210000000.0238210000000.0284000000000000000020000000.012820000000.014420000000.016220000000.017820000000.018920000000.019820000000.02380000000000000030000000.012630000000.014230000000.0160530000000.01880000000040000000.012440000000.014140000000.01600000050000000.012350000000.0140000100000000.0122100000000.013960000200000000.012200000000.0139 f :0.019680.020290.021040.021740.022490.022920.025920.029960.033320.036260.038820.04438/D =0.004760.004760.004760.004760.004760.004760.004760.004760.004760.004760.00476f =0.000000.000000.000000.000000.000000.000000.000000.031240.000000.000000.000000.031242. PRESSURE VESSELRe =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re =129681.8Re/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/DRe/D0.00010.00020.00040.00060.00080.0010.0020.0040.0060.0080.010.01500000000000000000000000030000.04430000.04430000.04430000.04430000.04430000.04430000.04630000.04830000.04930000.05130000.05230000.05500000000000000000000000040000.040640000.040640000.040740000.040840000.040940000.04140000.04240000.04440000.04640000.047840000.049540000.05300000000000000000000000050000.03850000.038250000.038450000.038650000.038750000.038850000.0450000.04250000.04450000.04650000.047650000.05100000000000000000000000060000.035860000.03660000.036260000.036560000.036860000.03760000.03860000.0460000.042360000.044260000.04660000.0500000000000000000000000070000.033170000.033570000.033870000.034270000.034570000.035270000.036770000.03970000.041770000.043270000.04570000.049500000000000000000000000080000.03380000.033380000.033580000.03780000.03480000.034280000.035880000.03880000.040880000.042280000.04480000.048700000000000000000000000090000.03290000.032390000.032590000.032790000.032990000.033290000.034590000.037290000.039990000.041890000.043590000.0481000000000000000000000000100000.0313100000.0315100000.0317100000.032100000.0322100000.0325100000.0338100000.0365100000.0395100000.0143100000.0432100000.0479000000000000000000000000200000.0267200000.0268200000.0269200000.0275200000.0277200000.028200000.0298200000.033200000.036200000.0385200000.0418200000.046000000000000000000000000300000.0235300000.0243300000.0248300000.0255300000.0257300000.0262300000.028300000.0318300000.0349300000.0377300000.04300000.0455000000000000000000000000400000.0225400000.0228400000.0235400000.024400000.0246400000.025400000.0272400000.031400000.034400000.0372400000.0396400000.0451000000000000000000000000500000.0213500000.0219500000.0225500000.023500000.0237500000.0242500000.0268500000.0304500000.0339500000.0368500000.0393500000.045000000000000000000000000600000.0205600000.021600000.0215600000.0225600000.023600000.0237600000.0263600000.0301600000.0336600000.0365600000.0391600000.0448000000000000000000000000700000.0198700000.0205700000.0212700000.0219700000.0227700000.023700000.026700000.03700000.0334700000.0363700000.0389700000.0445000000000000000000000000800000.0195800000.02800000.0208800000.0215800000.0222800000.0228800000.0258800000.0299800000.0332800000.0362800000.0387800000.0442000000000000000000000000900000.019900000.0195900000.0204900000.021900000.0219900000.0225900000.0256900000.02985900000.033900000.0361900000.0385900000.04410000000000000000000000001000000.01871000000.01931000000.021000000.02091000000.02171000000.02221000000.02541000000.02981000000.03281000000.0361000000.03831000000.0440.01807668150.01807668150.01867668150.01867668150.01952509070.01952509070.02042509070.02042509070.0213438180.0213438180.02187349980.02187349980.02519222720.02519222720.02956254530.02956254530.0326219090.0326219090.03594063630.03594063630.03821689090.03821689090.0440.0442000000.01662000000.01722000000.01842000000.01932000000.02052000000.02112000000.02472000000.0292000000.03222000000.03582000000.0380200000000000000000000003000000.01573000000.01623000000.01783000000.01873000000.01983000000.02083000000.02433000000.02893000000.0323000000.03563000000.03800000000000000000000004000000.01494000000.01584000000.01724000000.01844000000.01954000000.02054000000.024064000000.02870600000000000000005000000.01455000000.01545000000.0175000000.01825000000.01935000000.02035000000.024045000000.02870400000000000000006000000.01426000000.01526000000.01696000000.018056000000.01926000000.02016000000.024026000000.02870200000000000000007000000.01397000000.0157000000.01687000000.018037000000.01917000000.027000000.0247000000.028700000000000000008000000.01378000000.01498000000.016828000000.018028000000.019068000000.020028000000.02398000000.028600000000000000009000000.01369000000.014859000000.016759000000.018019000000.019039000000.020019000000.023859000000.0285000000000000000010000000.013510000000.014810000000.016710000000.01810000000.01910000000.0210000000.0238210000000.0284000000000000000020000000.012820000000.014420000000.016220000000.017820000000.018920000000.019820000000.02380000000000000030000000.012630000000.014230000000.0160530000000.01880000000040000000.012440000000.014140000000.01600000050000000.012350000000.0140000100000000.0122100000000.013960000200000000.012200000000.0139 f :0.018080.018680.019530.020430.021340.021870.025190.029560.032620.035940.038220.04400/D =0.002500.002500.002500.002500.002500.002500.002500.002500.002500.002500.00250f =0.000000.000000.000000.000000.000000.000000.026280.000000.000000.000000.000000.02628