metodos nr tirante normal y critico

CALCULO DEL TIRANTE NORMALN Error0 1 0.3267437544639 5.18979768 0.02746181 0.93704114 0.1403790179812 5.11179209 0.01186672 0.90957934 0.0602294964648 5.07550467 0.005103543 0.89771264 0.0258206658973 5.05936745 0.002190094 0.8926091 0.0110650840511 5.05233976 0.000938935 0.89041901 0.0047409402026 5.04930758 0.000402376 0.88948008 0.0020311416471 5.04800461 0.00017247 0.88907771 0.0008701642066 5.04744568 7.38592E-058 0.88890532 0.0003727828125 5.0472061 3.16421E-059 0.88883146 0.0001597010698 5.04710344 1.35556E-05

10 0.88879982 6.841614569E-05 5.04705945 5.80727E-0611 0.88878626 2.930953191E-05 5.04704061 2.48784E-0612 0.88878045 1.255622089E-05 5.04703253 1.06579E-0613 0.88877797 5.379091351E-06 5.04702908 0.888776914 0.8887769 2.304405235E-06 5.04702759 0

CALCULO DEL TIRANTE CRÍTICON Error0 1 6.4489795918367 27 0.090632471 0.7611489 1.4177080792387 15.6423867 0.013354552 0.67051644 0.162110799741 12.1389919 0.000275063 0.65716189 0.0032072955168 11.6602671 1.1521E-074 0.65688682 1.342259515E-06 11.6505081 2.02061E-145 0.65688671 2.353672812E-13 11.650504 06 0.65688671 0 11.650504 07 0.65688671 0 11.650504 08 0.65688671 0 11.650504 09 0.65688671 0 11.650504 0

10 0.65688671 0 11.650504 011 0.65688671 0 11.650504 012 0.65688671 0 11.650504 013 0.65688671 0 11.650504 0.6568867114 0.65688671 0 11.650504 0

𝑦_(+1𝑘

)

𝑓(𝑦_𝑘 ) 𝑓′(𝑦_𝑘 )

𝑦_(𝑘+1) 𝑓(𝑦_𝑘 ) 𝑓′(𝑦_𝑘 )

Introducir los Datosb g

5 0.014 0.0015 3 9.8 No b1 32 33 34 35 36 37 38 39 3

10 311 312 313 314 3

TIRANTE NORMAL

TIRANTE CRÍTICO

𝐴=𝑏𝑦𝑃=𝑏+2𝑦

𝑦_(𝑘+1)=𝑦_𝑘−((𝑏𝑦)^(5/3)/(𝑏+2𝑦)^(2/3) −𝑄𝑛/( 〖𝑆 ^□(64&1/2)〗 _0^ ))/((𝑏𝑦/(𝑏+2𝑦))^□(64&1/2) [5/2 𝑏−2/3 𝑏𝑦/(𝑏+2𝑦) 2] )

𝑛 𝑆_0̂ 𝑄

𝑦_(𝑘+1)=𝑦_𝑘−(𝑏^2 𝑦^3−𝑄^2/𝑔)/(3(𝑏𝑦)^3 )

A P v TIPO DE REGIMEN0.93704114 3.20156701 0.7611489 0.87804609 4.87408228 3.41667712 Subcritico Lento0.90957934 3.29822796 0.67051644 0.85231326 4.81915867 3.51983261 Subcritico Lento0.89771264 3.34182664 0.65716189 0.84119367 4.79542527 3.56636064 Subcritico Lento

0.8926091 3.3609337 0.65688682 0.83641145 4.7852182 3.58675149 Subcritico Lento0.89041901 3.36920031 0.65688671 0.83435924 4.78083802 3.59557353 Subcritico Lento0.88948008 3.37275681 0.65688671 0.83347943 4.77896016 3.59936899 Subcritico Lento0.88907771 3.3742832 0.65688671 0.83310239 4.77815543 3.60099794 Subcritico Lento0.88890532 3.37493762 0.65688671 0.83294085 4.77781064 3.60169632 Subcritico Lento0.88883146 3.37521807 0.65688671 0.83287164 4.77766292 3.60199561 Subcritico Lento0.88879982 3.37533823 0.65688671 0.83284199 4.77759963 3.60212385 Subcritico Lento0.88878626 3.37538971 0.65688671 0.83282929 4.77757252 3.60217879 Subcritico Lento0.88878045 3.37541177 0.65688671 0.83282385 4.77756091 3.60220232 Subcritico Lento0.88877797 3.37542121 0.65688671 0.83282152 4.77755593 3.60221241 Subcritico Lento

0.8887769 3.37542526 0.65688671 0.83282052 4.7775538 3.60221673 Subcritico Lento

TIRANTE NORMAL

TIRANTE CRÍTICO

𝑦_𝑛 𝑏∕𝑦_𝑛 𝑦_𝑐

OBS.

CALCULO DEL TIRANTE NORMALN Error0 1 0.24593729 6.14569608 0.040017811 0.95998219 0.01461661 5.89741657 0.002478482 0.95750372 0.00065162 5.88213662 0.000110783 0.95739294 2.84116E-05 5.88145392 4.83071E-064 0.95738811 1.23754E-06 5.88142415 2.10415E-075 0.9573879 5.39018E-08 5.88142285 9.16476E-096 0.95738789 2.34773E-09 5.8814228 3.99176E-107 0.95738789 1.02257E-10 5.88142279 1.73864E-118 0.95738789 4.45466E-12 5.88142279 7.57394E-139 0.95738789 1.92735E-13 5.88142279 3.27516E-14

10 0.95738789 0 5.88142279 011 0.95738789 0 5.88142279 012 0.95738789 0 5.88142279 013 0.95738789 0 5.88142279 014 0.95738789 0 5.88142279 0.95738789

CALCULO DEL TIRANTE CRITICON Error0 1 6.99319728 40.8888889 0.171029281 0.82897072 1.57161419 23.6382829 0.066485972 0.76248475 0.17132784 18.6263453 0.009198153 0.7532866 0.0028994 17.9984651 0.000161094 0.75312551 8.74816E-07 17.9876048 4.86344E-085 0.75312546 7.9492E-14 17.9876015 4.44089E-156 0.75312546 0 17.9876015 07 0.75312546 0 17.9876015 08 0.75312546 0 17.9876015 09 0.75312546 0 17.9876015 0

10 0.75312546 0 17.9876015 011 0.75312546 0 17.9876015 012 0.75312546 0 17.9876015 013 0.75312546 0 17.9876015 014 0.75312546 0 17.9876015 0.75312546

𝑦_(+1𝑘

)

𝑓(𝑦_𝑘 ) 𝑓′(𝑦_𝑘 )

𝑦_(𝑘+1) 𝑓(𝑦_𝑘 ) 𝑓′(𝑦_𝑘 )

𝑦_(𝑘+1)=𝑦_𝑘−(((𝑏+𝑘𝑦)𝑦)^□(64&3)/((𝑏+2𝑘𝑦) )−𝑄^2/𝑔)/(((𝑏+𝑘𝑦)𝑦)^□(64&2)/((𝑏+2𝑘𝑦) ) [3(𝑏+2𝑘𝑦)−((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦𝑘))2𝑘] )

Introducir los DatosQ So n b K g No6 0.001 0.014 2 2 9.8 1

23456789

1011121314

𝑦_(𝑘+1)=𝑦_𝑘−(((𝑏+𝑘𝑦)𝑦)^□(64&5/3)/((𝑏+2𝑦(1+𝑘^2 )^□(64&1/2) ))^□(64&2/3) −𝑄𝑛/𝑆^□(64&1/2) )/(((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦(1+𝑘^2 )^□(64&1/2) ))^□(64&1/2) [5/3 (𝑏+2𝑘𝑦)−3/2 ((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦(1+𝑘)^□(64&1/2) ))2√(1+𝑘^2 )] )

𝑦_(𝑘+1)=𝑦_𝑘−(((𝑏+𝑘𝑦)𝑦)^□(64&3)/((𝑏+2𝑘𝑦) )−𝑄^2/𝑔)/(((𝑏+𝑘𝑦)𝑦)^□(64&2)/((𝑏+2𝑘𝑦) ) [3(𝑏+2𝑘𝑦)−((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦𝑘))2𝑘] )

𝐴=(𝑏+𝑘𝑦)𝑦𝑃=b+2y√(1+𝑘^2 )

b A P v2 0.95998219 2.08337198 0.82897072 3.763096 6.47213595 1.594431822 0.95750372 2.08876474 0.76248475 3.74863416 6.29317088 1.600582972 0.95739294 2.08900643 0.7532866 3.74798834 6.28208679 1.600858772 0.95738811 2.08901697 0.75312551 3.74796018 6.28159137 1.60087082 0.9573879 2.08901743 0.75312546 3.74795895 6.28156977 1.600871322 0.95738789 2.08901745 0.75312546 3.7479589 6.28156883 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.600871342 0.95738789 2.08901745 0.75312546 3.7479589 6.28156879 1.60087134

TIRANTE NORMAL

TIRANTE CRÍTICO

𝑦_(𝑘+1)=𝑦_𝑘−(((𝑏+𝑘𝑦)𝑦)^□(64&5/3)/((𝑏+2𝑦(1+𝑘^2 )^□(64&1/2) ))^□(64&2/3) −𝑄𝑛/𝑆^□(64&1/2) )/(((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦(1+𝑘^2 )^□(64&1/2) ))^□(64&1/2) [5/3 (𝑏+2𝑘𝑦)−3/2 ((𝑏+𝑘𝑦)𝑦/(𝑏+2𝑦(1+𝑘)^□(64&1/2) ))2√(1+𝑘^2 )] )

𝑦_𝑛 𝑏∕𝑦_𝑛 𝑦_𝑐

TIPO DE REGIMEN OBS.Subcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico Lento

Introducir los Datos

Q 0.567 N A

n 0.015 0 0.5 -0.07017557 0.36742553D 0.9144 1 0.61962042 -0.01580016 0.47367782So 0.0016 2 0.64890397 -0.00339458 0.4983593g 9.8 3 0.65551799 -0.00067957 0.50382935

4 0.65686003 -0.00013303 0.504934195 0.65712349 -2.5912E-05 0.505150876 0.65717484 -5.0425E-06 0.50519317 0.65718483 -9.8108E-07 0.505201318 0.65718678 -1.9087E-07 0.505202919 0.65718715 -3.7135E-08 0.50520322

10 0.65718723 -7.2248E-09 0.5052032811 0.65718724 -1.4056E-09 0.505203312 0.65718725 -2.7346E-10 0.505203313 0.65718725 -5.3203E-11 0.505203314 0.65718725 -1.0351E-11 0.5052033

N A0 0.5 0.02168077 0.367425531 0.44791523 0.00298989 0.319857032 0.43812305 9.04607E-05 0.310907553 0.43780784 9.11833E-08 0.310619574 0.43780752 9.29604E-14 0.310619285 0.43780752 0 0.310619286 0.43780752 0 0.310619287 0.43780752 0 0.310619288 0.43780752 0 0.310619289 0.43780752 0 0.31061928

10 0.43780752 0 0.3106192811 0.43780752 0 0.3106192812 0.43780752 0 0.3106192813 0.43780752 0 0.3106192814 0.43780752 0 0.31061928

𝑦_(+1𝑘

)

𝑓(𝑦_𝑘 )

𝑦_(𝑘+1) 𝑓(𝑦_𝑘 )

CALCULO DEL TIRANTE NORMAL

P

1.52206168 0.18848735 1.32318784 0.24139989 0.586652107 0.49132463 0.91038453 2.008821471.76842958 0.28783156 1.46237419 0.26785224 0.539557613 0.51754443 0.85475481 2.139560931.83197341 0.31325952 1.49719871 0.27203413 0.513239553 0.52156892 0.83013596 2.203012631.84659882 0.31901108 1.50515665 0.2728418 0.506365503 0.52234261 0.8238976 2.219693311.84958009 0.32017786 1.50677623 0.27299936 0.504926977 0.52249341 0.82260005 2.223194611.8501659 0.32040689 1.50709437 0.27303004 0.50464283 0.52252277 0.82234406 2.22388668

1.85028009 0.32045153 1.50715638 0.27303601 0.504587382 0.52252848 0.82229412 2.224021751.85030232 0.32046021 1.50716845 0.27303717 0.504576589 0.52252959 0.8222844 2.224048041.85030664 0.3204619 1.5071708 0.2730374 0.504574488 0.52252981 0.8222825 2.224053161.85030748 0.32046223 1.50717126 0.27303744 0.50457408 0.52252985 0.82228214 2.224054151.85030765 0.3204623 1.50717135 0.27303745 0.504574 0.52252986 0.82228206 2.224054351.85030768 0.32046231 1.50717136 0.27303745 0.504573985 0.52252986 0.82228205 2.224054381.85030769 0.32046231 1.50717137 0.27303745 0.504573982 0.52252986 0.82228205 2.224054391.85030769 0.32046231 1.50717137 0.27303745 0.504573981 0.52252986 0.82228205 2.224054391.85030769 0.32046231 1.50717137 0.27303745 0.504573981 0.52252986 0.82228205 2.22405439

CALCULO DEL TIRANTE CRÍTICOT

0.91038453 0.13500152 0.049603 0.40359377 0.416259342 0.14829066 0.91038453 -0.18805240.91421143 0.10230852 0.0327241 0.34987206 0.305334975 0.11190904 0.91421143 0.040624180.91360366 0.0966635 0.03005341 0.340309 0.286983127 0.10580464 0.91360366 0.083523950.91357711 0.09648452 0.02996998 0.34000367 0.286404703 0.1056118 0.91357711 0.08490650.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.08490790.91357708 0.09648434 0.0299699 0.34000337 0.286404119 0.1056116 0.91357708 0.0849079

𝐴^□(64&5/3)��□̂(64&2/3)

𝐴⁄𝑃 𝑓′(𝑦_𝑘 )𝑑𝐴⁄𝑑𝑦 𝑑𝑃⁄𝑑𝑦√(𝐴⁄𝑃)

𝐴^□(64&3)𝐴⁄𝑇 𝑓′(𝑦_𝑘 )

𝑑𝐴⁄𝑑𝑦 𝑑𝑇⁄𝑑𝑦𝐴^2⁄𝑇𝐴^□(64&2)

Error No

0.11962042 10.02928355 20.00661402 30.00134205 40.00026346 55.13478E-05 69.99335E-06 71.94437E-06 83.78287E-07 97.3597E-08 10

1.43185E-08 112.78571E-09 125.41968E-10 131.05441E-10 140.65718725

Error0.052084770.009792180.000315213.18372E-073.24574E-13

000000000

0.43780752

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&5/3)/(cos^(−1) (1−2𝑦/𝐷)"D " )^□(64&2/3) −𝑄𝑛/( 〖𝑆 ^□(64&1/2)〗 _0^ ))/(((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" ))^□(64&1/2) [5/3 ((𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) ))−2/3 ((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" )) 2/√(1−(1−2𝑦/𝐷)^2 )] )

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

D A P v

0.9144 0.61962042 1.4757422 0.44791523 0.36742553 1.52206168 1.543169850.9144 0.64890397 1.40914533 0.43812305 0.47367782 1.76842958 1.197016150.9144 0.65551799 1.3949274 0.43780784 0.4983593 1.83197341 1.137733360.9144 0.65686003 1.39207739 0.43780752 0.50382935 1.84659882 1.125381050.9144 0.65712349 1.39151927 0.43780752 0.50493419 1.84958009 1.122918620.9144 0.65717484 1.39141054 0.43780752 0.50515087 1.8501659 1.122436940.9144 0.65718483 1.39138939 0.43780752 0.5051931 1.85028009 1.122343130.9144 0.65718678 1.39138527 0.43780752 0.50520131 1.85030232 1.122324870.9144 0.65718715 1.39138447 0.43780752 0.50520291 1.85030664 1.122321320.9144 0.65718723 1.39138431 0.43780752 0.50520322 1.85030748 1.122320630.9144 0.65718724 1.39138428 0.43780752 0.50520328 1.85030765 1.12232050.9144 0.65718725 1.39138428 0.43780752 0.5052033 1.85030768 1.122320470.9144 0.65718725 1.39138428 0.43780752 0.5052033 1.85030769 1.122320470.9144 0.65718725 1.39138428 0.43780752 0.5052033 1.85030769 1.12232046

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&5/3)/(cos^(−1) (1−2𝑦/𝐷)"D " )^□(64&2/3) −𝑄𝑛/( 〖𝑆 ^□(64&1/2)〗 _0^ ))/(((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" ))^□(64&1/2) [5/3 ((𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) ))−2/3 ((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" )) 2/√(1−(1−2𝑦/𝐷)^2 )] )

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

𝑦_𝑛 𝐷∕𝑦_𝑛 𝑦_𝑐

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

TIPO DE REGIMEN OBS.

Subcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico LentoSubcritico Lento

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&5/3)/(cos^(−1) (1−2𝑦/𝐷)"D " )^□(64&2/3) −𝑄𝑛/( 〖𝑆 ^□(64&1/2)〗 _0^ ))/(((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" ))^□(64&1/2) [5/3 ((𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) ))−2/3 ((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(cos^(−1) (1−2𝑦/𝐷)"D" )) 2/√(1−(1−2𝑦/𝐷)^2 )] )

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

𝑦_(𝑘+1)=𝑦_𝑘−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&3)/(2√(𝑦(𝐷−𝑦) ))−𝑄^2/𝑔)/((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )^□(64&2)/(2√(𝑦(𝐷−𝑦) )) [3(𝐷/(2√(1−(1−2𝑦/𝐷)^2 )))(1−cos ( 〖 2cos〗^(−1) (1−2𝑦/𝐷) ) )−((𝐷^2/4 (cos^(−1) (1−2𝑦/𝐷)−1/2 sin (2 cos^(−1) (1−2𝑦/𝐷) ) )" " )/(2√(𝑦(𝐷−𝑦) ))) (𝐷−2𝑦)/√(𝑦(𝐷−𝑦) )] )

TIRANTE NORMAL

TIRANTE CRÍTICO