Andres Felipe Echeverria 1 Trabajo.docx
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2m
2m
D/2
escala numΓ©rica 1:25 escala grΓ‘fica:
0
0.25 0.5 0.75 1
1.5
DATOS: π· = β2 2 π· = 2β2 SoluciΓ³n DeducciΓ³n de formulas π·πππ π(π) β€ βπ π π«βπ Γrea HidrΓ‘ulica: ππ₯β π¦2 π΄β = 2 ( ) = 2 ( ) = π¦2 2 2 PerΓmetro Mojado: ππ = 2(βπ¦ 2 + π¦ 2 = 2β2π¦ 2 = 2π¦β2 Radio HidrΓ‘ulico:
2
2.5m
π β =
π¦2 2π¦β2
=
π¦ 2β2
Espesor de espejo:π = 2π¦ π·πππ π(π) > βπ π π«βπ Γrea HidrΓ‘ulica: π· π· (π¦ β 2 ) (π¦ β 2 ) π· 2 π· π΄β = ( ) + π· (π¦ β ) β 2 ( ) 2 2 2 π· 2 π· π· 2 π΄β = ( ) + π· (π¦ β ) β (π β ) 2 2 2 π· 2 π· π· π΄β = ( ) + (π β ) [π· β (π β )] 2 2 2 PerΓmetro Mojado: π· 2 π· 2 π· 2 π· 2 ππ = 2 (β( ) + ( ) ) + 2 (β(π¦ β ) + (π¦ β ) ) 2 2 2 2 π· 2 π· 2 π· 2 π· 2 ππ = 2 [β( ) + ( ) + β(π¦ β ) + (π¦ β ) ] 2 2 2 2 π· 2 π· 2 ππ = 2 [β2 ( ) + β2 (π¦ β ) ] 2 2 π· π· ππ = 2 [( ) β2 + (π¦ β ) β2] 2 2 π· π· ππ = 2(β2) [( ) + (π¦ β )] 2 2 Radio HidrΓ‘ulico: π· 2 π· π· ( 2 ) + (π β 2 ) [π· β (π β 2 )] π· π· 2(β2) [( 2 ) + (π¦ β 2 )] Espesor de Espejo: π· π = π· β 2 (π¦ β ) 2
CΓ‘lculos: CALCULOS Y(m)
Ah(m^2)
Pm(m)
Rh(m2/m)
T(m)
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4
0 0,01 0,04 0,09 0,16 0,25 0,36 0,49 0,64 0,81 1 1,21 1,44 1,69 1,96
0 0,28284271 0,56568542 0,84852814 1,13137085 1,41421356 1,69705627 1,97989899 2,2627417 2,54558441 2,82842712 3,11126984 3,39411255 3,67695526 3,95979797
0 0,03535534 0,07071068 0,10606602 0,14142136 0,1767767 0,21213203 0,24748737 0,28284271 0,31819805 0,35355339 0,38890873 0,42426407 0,45961941 0,49497475
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6 2,8
1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,82842712
2,23528137 2,4909668 2,72665222 2,94233765 3,13802307 3,3137085 3,46939392 3,60507935 3,72076477 3,8164502 3,89213562 3,94782105 3,98350647 3,9991919 4
4,24264069 4,5254834 4,80832611 5,09116882 5,37401154 5,65685425 5,93969696 6,22253967 6,50538239 6,7882251 7,07106781 7,35391052 7,63675324 7,91959595 8
0,52686087 0,5504311 0,56706891 0,5779297 0,58392563 0,58578644 0,58410285 0,57935819 0,57195174 0,56221621 0,5504311 0,53683289 0,52162304 0,50497423 0,5
2,65685425 2,45685425 2,25685425 2,05685425 1,85685425 1,65685425 1,45685425 1,25685425 1,05685425 0,85685425 0,65685425 0,45685425 0,25685425 0,05685425 0
π·πππ π(π) β€ βπ
π·πππ π(π) > βπ
Ejercicio N-1
1
z y 0,5m
ESCALA NUMERICA: 1:10 ESCALA GRAFICA: 0
0.1
0.2
0.3
0.4
0.5
0.75
1m
Datos π=π ππ° = π. ππ SOLUCION: Γrea HidrΓ‘ulica: ππ₯β ) 2 (π§π¦)(π¦) π΄β = (π)(π¦) + 2 ( ) 2 π΄β = ππ¦ + π§π¦ 2 π΄β = π¦(π + π§π¦) π§π¦ 2 + ππ¦ β π΄β = 0 2π¦ 2 + 0.5π¦ β π΄β = 0 π΄β = (π)(π¦) + 2 (
PerΓmetro Mojado: ππ = π + 2β(π§π¦)2 + π¦ 2 ππ = π + 2βπ§ 2 π¦ 2 + π¦ 2 ππ = π + 2βπ¦ 2 (π§ 2 + 1) ππ = π + 2π¦βπ§ 2 + 1 Radio HidrΓ‘ulico: π β =
π¦(π + π§π¦) π + 2π¦βπ§ 2 + 1
Espesor de Espejo: π + π + 2π§π¦
CALCULOS: CALCULOS Y(m)
Ah(m^2)
Pm(m)
0 0,01861407 0,06374586 0,12122145 0,18423292 0,25 0,31729515 0,38551445 0,45433151 0,52355609 0,59307033 0,66279756 0,73268584 0,80269877 0,8728101 0,93954952 0,99799083 1,04928749 1,09434155 1,13382347 1,16824369 1,19799734 1,22339337 1,24467419 1,26202924 1,27560445 1,28550896 1,29181976 1,29458478 1,29472709
0 0,01 0,04 0,09 0,16 0,25 0,36 0,49 0,64 0,81 1 1,21 1,44 1,69 1,96 2,23528137 2,4909668 2,72665222 2,94233765 3,13802307 3,3137085 3,46939392 3,60507935 3,72076477 3,8164502 3,89213562 3,94782105 3,98350647 3,9991919 4
0 0,58324463 0,78508016 1,04211878 1,32391467 1,61803399 1,91898705 2,22407302 2,53183229 2,84141401 3,15229115 3,46412081 3,77667069 4,08977801 4,40332544 4,7017932 4,96315066 5,19255632 5,39404421 5,57061272 5,72454462 5,85760698 5,97118147 6,0663522 6,14396632 6,2046765 6,24897084 6,2771936 6,28955914 6,29019556
Rh(m2/m) 0 0,01714546 0,05095021 0,08636252 0,12085371 0,1545085 0,18759897 0,22031651 0,25278136 0,28506933 0,31722958 0,34929498 0,38128821 0,41322536 0,44511813 0,4754104 0,50189224 0,52510788 0,54547896 0,5633174 0,57885976 0,59228861 0,60374641 0,61334467 0,62117043 0,62729066 0,6317554 0,63459991 0,63584614 0,63591028
T(m) 0 0,57445626 0,75498344 0,98488578 1,23693169 1,5 1,7691806 2,04205779 2,31732605 2,59422435 2,87228132 3,15119025 3,43074336 3,71079506 3,99124041 4,25819809 4,49196331 4,69714996 4,87736621 5,03529389 5,17297477 5,29198936 5,39357347 5,47869676 5,54811694 5,60241778 5,64203584 5,66727905 5,67833912 5,67890835
2m
D/2
escala numΓ©rica 1:25 escala grΓ‘fica:
0
0.25 0.5 0.75 1
1.5
DATOS: π· = β2 2 π· = 2β2 SoluciΓ³n DeducciΓ³n de formulas π·πππ π(π) β€ βπ π π«βπ Γrea HidrΓ‘ulica: ππ₯β π¦2 π΄β = 2 ( ) = 2 ( ) = π¦2 2 2 PerΓmetro Mojado: ππ = 2(βπ¦ 2 + π¦ 2 = 2β2π¦ 2 = 2π¦β2 Radio HidrΓ‘ulico:
2
2.5m
π β =
π¦2 2π¦β2
=
π¦ 2β2
Espesor de espejo:π = 2π¦ π·πππ π(π) > βπ π π«βπ Γrea HidrΓ‘ulica: π· π· (π¦ β 2 ) (π¦ β 2 ) π· 2 π· π΄β = ( ) + π· (π¦ β ) β 2 ( ) 2 2 2 π· 2 π· π· 2 π΄β = ( ) + π· (π¦ β ) β (π β ) 2 2 2 π· 2 π· π· π΄β = ( ) + (π β ) [π· β (π β )] 2 2 2 PerΓmetro Mojado: π· 2 π· 2 π· 2 π· 2 ππ = 2 (β( ) + ( ) ) + 2 (β(π¦ β ) + (π¦ β ) ) 2 2 2 2 π· 2 π· 2 π· 2 π· 2 ππ = 2 [β( ) + ( ) + β(π¦ β ) + (π¦ β ) ] 2 2 2 2 π· 2 π· 2 ππ = 2 [β2 ( ) + β2 (π¦ β ) ] 2 2 π· π· ππ = 2 [( ) β2 + (π¦ β ) β2] 2 2 π· π· ππ = 2(β2) [( ) + (π¦ β )] 2 2 Radio HidrΓ‘ulico: π· 2 π· π· ( 2 ) + (π β 2 ) [π· β (π β 2 )] π· π· 2(β2) [( 2 ) + (π¦ β 2 )] Espesor de Espejo: π· π = π· β 2 (π¦ β ) 2
CΓ‘lculos: CALCULOS Y(m)
Ah(m^2)
Pm(m)
Rh(m2/m)
T(m)
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4
0 0,01 0,04 0,09 0,16 0,25 0,36 0,49 0,64 0,81 1 1,21 1,44 1,69 1,96
0 0,28284271 0,56568542 0,84852814 1,13137085 1,41421356 1,69705627 1,97989899 2,2627417 2,54558441 2,82842712 3,11126984 3,39411255 3,67695526 3,95979797
0 0,03535534 0,07071068 0,10606602 0,14142136 0,1767767 0,21213203 0,24748737 0,28284271 0,31819805 0,35355339 0,38890873 0,42426407 0,45961941 0,49497475
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6 2,8
1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,82842712
2,23528137 2,4909668 2,72665222 2,94233765 3,13802307 3,3137085 3,46939392 3,60507935 3,72076477 3,8164502 3,89213562 3,94782105 3,98350647 3,9991919 4
4,24264069 4,5254834 4,80832611 5,09116882 5,37401154 5,65685425 5,93969696 6,22253967 6,50538239 6,7882251 7,07106781 7,35391052 7,63675324 7,91959595 8
0,52686087 0,5504311 0,56706891 0,5779297 0,58392563 0,58578644 0,58410285 0,57935819 0,57195174 0,56221621 0,5504311 0,53683289 0,52162304 0,50497423 0,5
2,65685425 2,45685425 2,25685425 2,05685425 1,85685425 1,65685425 1,45685425 1,25685425 1,05685425 0,85685425 0,65685425 0,45685425 0,25685425 0,05685425 0
π·πππ π(π) β€ βπ
π·πππ π(π) > βπ
Ejercicio N-1
1
z y 0,5m
ESCALA NUMERICA: 1:10 ESCALA GRAFICA: 0
0.1
0.2
0.3
0.4
0.5
0.75
1m
Datos π=π ππ° = π. ππ SOLUCION: Γrea HidrΓ‘ulica: ππ₯β ) 2 (π§π¦)(π¦) π΄β = (π)(π¦) + 2 ( ) 2 π΄β = ππ¦ + π§π¦ 2 π΄β = π¦(π + π§π¦) π§π¦ 2 + ππ¦ β π΄β = 0 2π¦ 2 + 0.5π¦ β π΄β = 0 π΄β = (π)(π¦) + 2 (
PerΓmetro Mojado: ππ = π + 2β(π§π¦)2 + π¦ 2 ππ = π + 2βπ§ 2 π¦ 2 + π¦ 2 ππ = π + 2βπ¦ 2 (π§ 2 + 1) ππ = π + 2π¦βπ§ 2 + 1 Radio HidrΓ‘ulico: π β =
π¦(π + π§π¦) π + 2π¦βπ§ 2 + 1
Espesor de Espejo: π + π + 2π§π¦
CALCULOS: CALCULOS Y(m)
Ah(m^2)
Pm(m)
0 0,01861407 0,06374586 0,12122145 0,18423292 0,25 0,31729515 0,38551445 0,45433151 0,52355609 0,59307033 0,66279756 0,73268584 0,80269877 0,8728101 0,93954952 0,99799083 1,04928749 1,09434155 1,13382347 1,16824369 1,19799734 1,22339337 1,24467419 1,26202924 1,27560445 1,28550896 1,29181976 1,29458478 1,29472709
0 0,01 0,04 0,09 0,16 0,25 0,36 0,49 0,64 0,81 1 1,21 1,44 1,69 1,96 2,23528137 2,4909668 2,72665222 2,94233765 3,13802307 3,3137085 3,46939392 3,60507935 3,72076477 3,8164502 3,89213562 3,94782105 3,98350647 3,9991919 4
0 0,58324463 0,78508016 1,04211878 1,32391467 1,61803399 1,91898705 2,22407302 2,53183229 2,84141401 3,15229115 3,46412081 3,77667069 4,08977801 4,40332544 4,7017932 4,96315066 5,19255632 5,39404421 5,57061272 5,72454462 5,85760698 5,97118147 6,0663522 6,14396632 6,2046765 6,24897084 6,2771936 6,28955914 6,29019556
Rh(m2/m) 0 0,01714546 0,05095021 0,08636252 0,12085371 0,1545085 0,18759897 0,22031651 0,25278136 0,28506933 0,31722958 0,34929498 0,38128821 0,41322536 0,44511813 0,4754104 0,50189224 0,52510788 0,54547896 0,5633174 0,57885976 0,59228861 0,60374641 0,61334467 0,62117043 0,62729066 0,6317554 0,63459991 0,63584614 0,63591028
T(m) 0 0,57445626 0,75498344 0,98488578 1,23693169 1,5 1,7691806 2,04205779 2,31732605 2,59422435 2,87228132 3,15119025 3,43074336 3,71079506 3,99124041 4,25819809 4,49196331 4,69714996 4,87736621 5,03529389 5,17297477 5,29198936 5,39357347 5,47869676 5,54811694 5,60241778 5,64203584 5,66727905 5,67833912 5,67890835
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