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FLUJO RÁPIDAMENTE VARIADORESALTO HIDRÁULICO

ESTRUCTURAS HIDRÁULICASING. VÍCTOR GARZÓN

AUTORES

 Natalia C. Petencpetev@unal.edu.co

 Edward E. Muñozemunozba@unal.edu.c

o

 Juan S. Acosta jsacostam@unal.edu.c

o

Yeison E. Benítez yebenitezi@unal.edu.c

o

 Sebastián García sebgarciavas@unal.edu.c

o

RESUMENConsidé!ns! "#s si$%i!n&!s 'i()&!sis* Un +#n#" +on (!ndi!n&! "on$i&%din#" 'oi,on&#"- sin !!+&os d! i++i)n- dond!no !/is&! #"$%n# !s&%+&%# !n #"$0n &#1o d!" 2o"%1!n d! +on&o" 3 !" +o!i+i!n&! d! Coio"is 3 4o%ssin!s5 i$%#" # "#%nid#d. 4#6o !s&#s +ondi+ion!s s! (%!d! (od%+i %n R!s#"&o 'id7%"i+o !n !" 5%! "# %!,# !s(!+8i+# s! 1#n&i!n!+ons&#n&! #n&!s 3 d!s(%és d! 5%! s! (!s!n&! !s&! !n)1!no !n !" "%6o. O+%! +%#ndo %n "%6o s%(!+8&i+o +#19i#

 (o #"$%n# +ondi+i)n i1(%!s&#- s% é$i1!n 7(ido # %n é$i1!n "!n&o :s%9+8&i+o;- $!n!#ndo !n&on+!s %n s#"&o!"#&i2#1!n&! #9%(&o d! "# s%(!i+i! d!" #$%# # +os&# d! 5%! !" "%6o disi(# (#&! d! s% !n!$8#. :DUARTE - <=>>;

ABSTRACTConsider the following scenario: A channel with horizontal longitudinal slope, without friction effects, where there is

no structure in some section of the control volum. and Coriolis and Boussines coefficient eual to one. !nder these

conditions can produce a hydraulic jump where the specific strength is maintained constant before and after this

 phenomenon is present in the flow. "ccurs when a supercritical flow changes by any condition imposed from a rapid 

change to a slow rate regime #subcritical$, generating a relatively abrupt jump in the water surface at the e%pense of 

the flow of their energy dissipates.

Palabras clave: S#"&o- R!s#"&o Hid7%"i+o- N01!o d! Fo%d!- C#n#" !+&#n$%"#.

INTRODUCCIÓN

?C%#ndo !" +#19io 7(ido !n "# (o%ndid#d d! "%6o!s d!sd! %n ni2!" 9#6o # %n ni2!" #"&o- # 1!n%do !"!s%"&#do !s %n# s%9id# #9%(&# d! "# s%(!i+i! d!"#$%#. Es&! !n)1!no "o+#" s! +ono+! +o1o !s#"&o'id7%"i+o.@ :CHO- <==B; Es&os o+%!n +%#ndo'#3 %n +on"i+&o !n&! "os +on&o"!s 5%! s! !n+%!n&#n#$%#s #i9# 3 #$%#s #9#6o- "os +%#"!s in"%3!n !n "#1is1# !/&!nsi)n d!" +#n#". Los !s#"&os (%!d!n

 (od%+is! !n +%#"5%i! +#n#"- (!o !n "# (7+&i+# "os

!s#"&os s! (od%+!n !n +#n#"!s d! ondo 'oi,on&#"-3# 5%! !" !s&%dio d! %n !s#"&o !n %n +#n#" +on

 (!ndi!n&! !s %n (o9"!1# +o1("!6o 3 di8+i" d!#n#"i,# &!)i+#1!n&!. :EIA- <==;

P## !!+&os d! !s&! !s+i&o- 3 +on !" in d!+o1(!nd! !" +o1(o&#1i!n&o d! di+'o !n)1!nos! #n#"i,) !n !" "#9o#&oio- !" "%6o d! %n +#n#"

!+&#n$%"# 'oi,on&#" 5%! +%!n&# +on !s&%+&%#s d!!n&#d# :&i(o +o1(%!&#; 3 s#"id# 5%! (!1i&!n$!n!# !s#"&os 'id7%"i+os.

E" o96!&i2o d! !s&# !/(!i!n+i# !s +o1(## !"+o1(o&#1i!n&o !#" 3 &!)i+o d! "os !s#"&os'id7%"i+os- 1os&#ndo "# !"#+i)n !/is&!n&! !n&! "#

 (o%ndid#d ini+i#" d!" 1is1o 3 s% +o!s(ondi!n&! (o%ndid#d s!+%!n&!- &!ni!ndo (!s!n&! !" n01!o d!Fo%d!. Adi+ion#"1!n&!- !"#+ion# "# "on$i&%d d!"!s#"&o +on !" n01!o d! Fo%d! +on 9#s! !n "#s

in2!s&i$#+ion!s d! Si"2!s&! :>B;.

METODOLOGIA

En !" "#9o#&oio s! !s&%di# %n !s#"&o 'id7%"i+o !n%n +#n#" !+&#n$%"#- (## !""o s! '#+! +i+%"# #$%# #di!!n&!s +#%d#"!s- (## s% !!+&o s! 1id!n "#s

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#"&%#s d! "# "71in# d! #$%# :#$%#s #9#6o > 3 #$%#s#i9# <; d!" !s#"&o 'id7%"i+o.En +#d# !ns#3o s! d!9! 1!di "# "on$i&%d ini+i#" 3in#" :+1; d! "# +in&# indi+#do# !n !" &#n5%! d!#"1#+!n#1i!n&o 3 s% !s(!+&i2o &i!1(o :s; (## "%!$o!n+on&# !" 2#"o d!" +#%d#".

 &magen ' Canal (ectangular 

• S! d!6) "%i (o !" +#n#" !" (i1! +#%d#".

•

• S! #9i) "# +o1(%!&# ("#n#.

• Un# 2!, !s&#9i"i,#do !" "%6o s! !#"i,#on

1!di+ion!s d! "# #"&%# d! "71in# d! #$%# 6%s&o#n&!s 3 d!s(%és d!" !s#"&o (## +ono+! "#"on$i&%d d!" 1is1o.

•

•  S! 1idi) !" d!s("#,#1i!n&o d! "# +in&# #+o("#do

# %n "o&#do !n !" &#n5%! 2o"%1é&i+o- 1idi!ndo!" &i!1(o d! !s&! d!s("#,#1i!n&o

• S! +!) %n (o+o "# +o1(%!&# ("#n# +on !" in

d! $##n&i,# %n +#%d#" di!!n&! #" (i1!o

• S! !(i&! !" (o+!di1i!n&o (## +%#&o +#%d#"!s

di!!n&!s.

RESULTADOS

A (#&i d! "# $%8# d! "#9o#&oio !n&!$#d# s! 9%s+#!so"2! "#s si$%i!n&!s #+&i2id#d!s ("#n!#d#s*

>. Con 9#s! !n "# !/(!si)n .O9&!n$# !" $#i+o &!)i+o 3 "# !"#+i)n !/(!i1!n&#"

d! .

<. Con 9#s! !n "# !/(!si)nO9&!n$# !" $#i+o .

. O9&!n$# %n $7i+o 5%! !"#+ion! "# "on$i&%d d!"!s#"&o +on !" n01!o d! Fo%d!.B. E/("i5%! !n &odos "os +#sos !" (o5%é d! "#sdi!!n+i#s !n&! "#s !+%#+ion!s &!)i+#s 3 "#s

 (o(%!s&#s !/(!i1!n&#"1!n&!.

Los d#&os o9&!nidos !n "# (7+&i+# (## B +#%d#"!sdi!!n&!s !s&7n !s%1idos !n "# &#9"# >*

CAUDAL PUNTO X (m) (m)L!"#$%&'Resal (m)

DELTA L(cm)

TIEMP(s)

>> =-== =-=<B

=-<= -= -=B< <-B= =-=KB

<> >-B== =-=<

=-= -= -K<< ->== =->>B

> =-= =-=>

=-B= -= <<-<< <-K== =->=

B> =-<> =-=K

>->= -= >B-<< ->= =->

)abla ': *atos de la pr+ctica

Con "os d#&os o9&!nidos !n "# (7+&i+# d! "#9o#&oio (o+!d!1os # +#"+%"# !" +#%d#" +on "# !+%#+i)n :>;.

Q=∆ L

t   ∗200

:>;

L%!$o s! +#"+%"# "# 2!"o+id#d #n&!s 3 d!s(%és d!"!s#"&o 'id7%"i+o- +on "# !+%#+i)n :<;.

V =Q

 A=  Q

 y∗b :<;

Con 3 #"&%# d! "# "71in# d! #$%# 3 9 9#s! d!"+#n#" !+&#n$%"#. O9&!ni!ndo "# &#9"# <.

CAUDAL

PUNTOCAUDAL

(Ls)CAUDAL

(m*s)

+EL,-

(ms)

+EL,.

(ms)

>>

-=KB =-== >->> =->K<

<>

>-K =-=> <-=< =-B=<

>

<-= =-=< >-B =-B<

B>

B<-=K =-=B< >-B< =-KK<

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)abla : Calculo caudales y velocidades.

S! +#"+%"# !" n01!o d! Fo%d! :F; #$%#s #i9# d!"!s#"&o 'id7%"i+o +on "# !+%#+i)n *

 Fr=  V 

2√ g∗ y

=  Q

 A∗2√ g∗ y

:;

M!di#n&! "# !/(!si)n s!

o9&i!n! "# !"#+i)n

Y 2

Y 1  &!)i+# 3 s! !#"i,# "#

+o1(##+i)n $#i+# +on "# !"#+i)n

Y 2

Y 1

!/(!i1!n&#"- o9&!ni!ndo "# &#9"# 3 "# $7i+# >.

Ca&'al /r - .- e01 .- %e!

> <-<BB -=== <-K>

< B-<= B- -=<

<-> -<B <-BB

B >-B=> - >-B

)abla -: (elacin /0/' 1s 2umero de 3roude

1 2 2 3 3 4 4 50

1

2

3

4

5

6

 Y2/Y1 vs Fr

Expe Linear (Expe) Teor

Fr 1

 Y2/y1

4rafica ': /0/' 1s 25mero de 3roude

A +on&in%#+i)n s! +#"+%"# "# !n!$8# !s(!+8i+# #$%#s#i9# 3 #$%#s #9#6o d!" !s#"&o 'id7%"i+o +on "#

!+%#+i)n B- s! '#""# "# di!!n+i# !n&! !s&#s !n!$8#s :

∆ E ¿  (## !n+on&# "# !"#+i)n∆ E

 E1

.

 E= z+  v2

2g :B;

S! $#i+# "# !"#+i)n &!)i+#

3 "# !"#+i)n !/(!i1!n&#"∆ E

 E1

  +#"+%"#d#

#n&!io1!n&! Vs !" N01!o d! Fo%d!*

Ca&'al /r - E- (m) E. (m) 2E (m) 2EE- E01 2EE- %

> <-<BB =-=K< =-=K< =-==<= =-=<<K =->B=<

< B-<= =-<< =-><< =->>=< =-B =-B<>B

<-> =->B> =->K= =-==K =-== =-><

B >-B=> =->=< =-< =-> =->K =-=<>

)abla6: (elacin∆ E

 0   E

1  e%perimental y

terica.

1 2 2 3 3 4 4 50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ΔE/E1 vs Fr

Expe Teor

Fr 1

ΔE/E1

4rafica :∆ E

 0   E

1  1s 25mero de 3roude

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Po 0"&i1o s! +#"+%"# "# "on$i&%d d!" !s#"&o 'id7%"i+o&!)i+o +on "# !+%#+i)n 3 s! +o1(## +on "#"on$i&%d d!" !s#"&o 'id7%"i+o !/(!i1!n&#" 1!dido!n "# (7+&i+#.

 L RH 

 y1

=9,75∗( Fr−1)1,01   :;

Ca&'al L!"# e01 (m) L!"# %e! (m) /r -

> =-<== =-= <-<BB

< =-== =-B<< B-<=

=-B== =-B <->

B >->== =-B >-B=>

)abla7: 8ongitud del resalto hidr+ulico e%p y terica.

1 2 2 3 3 4 4 50.0

0.5

1.0

1.5

Loni!"# vs Fr

Expe Teor

Fr 1

Lon ($)

4rafica -: 8ongitud (esalto 9. 1s 25mero de 3roude

RESULTADOS

En "# G7i+# > s! !2id!n+i# +o1o "# !"#+i)n d!#"&%#s d! "71in# d! #$%# !/(!i1!n&#"!s s! +o1(o&#d! o1# di!!n&! # "# &!)i+#- &#n&o #s8 5%! %n#

 (osi9"! "8n!# d! &!nd!n+i# !/(!i1!n&#" no &!nd8#s!n&ido 8si+o ni &!)i+o. Pod!1os #&i9%i !s&! !o #5%! %&i"i,#1os (o+os +#%d#"!s (## +ons&%i "#

$7i+# d! !"#+i)n d! #"&%#s !/(!i1!n&#"1!n&!- !sd!+i- s! !s(!#8# %n# 1!6o #(o/i1#+i)n #" %&i"i,# %n# 1#3o +#n&id#d d! +#%d#"!s !n !s&! #n7"isis.Adi+ion#"1!n&! !s&o 9ind#8# 1#3o +i&!io (##d!s+#&# d#&os #&8(i+os- 3# 5%! "#s "!+&%#s !n

 (7+&i+# son 9#s&#n&! in!/#+&#s.

En "# G7i+# < d! i$%#" o1# no s! (%!d! id!n&ii+# 

%n +o1(o&#1i!n&o !n "# !i+i!n+i# :   ∆ E 0   E

1

 $ d!" !s#"&o 'id7%"i+o #" +o1(##"o +on "# &!o8#- (%!s !n d! "os B +#%d#"!s s! 2!n !s%"&#dos d! !o #+!(&#9"!s. En "#s $#i+#s d! !s%"&#dos d! !"!6#5%! "os 2#"o!s o9&!nidos !/(!i1!n&#"1!n&! (## !"+#%d#" n%1!o B !s&7n 1%3 #"!6#d#s d! "# &!o8#- (o "o 5%! s! (od8# d!+i 5%! !n "# &o1# d! d#&os !n !s&#+ondi+i)n d! +#%d#" '%9o #"$0n !o '%1#no 3o d!ins&%1!n&#+i)n.

L# +o1(##+i)n d! "on$i&%d d!" !s#"&o 'id7%"i+o!/(!i1!n&#" +on !s(!+&o # "# &!o8# $!n!o 1!6o!s!s%"&#dos- "o 5%! !s d! $#n i1(o&#n+i# !n "# 2id#

 (o!sion#" 3# 5%! (od!1os (!d!+i +on +oni#n,#so9! "# &!o8# "# "on$i&%d d! %n !s#"&o 'id7%"i+o # "#

'o# d! dis!#- +on in!s +o1o disi(#+i)n d! !n!$8#-$!n!#+i)n d! &%9%"!n+i# o #%1!n&o d!" ni2!" d! "#"71in# d! #$%#.

CONCLUSIONES

D! #+%!do # "os +7"+%"os 3 !s%"&#dos!#"i,#dos !n "# (7+&i+# d! "#9o#&oio- 3 #"os +ono+i1i!n&os (!2ios 3 !+o"!+&#dos

 (## "# !#"i,#+i)n d! !s&! ino1! s! (%do""!$# # "#s si$%i!n&!s +on+"%sion!s*

A 1#3o +#%d#" !" !s#"&o &i!nd! # s! 17s "!6os d! "# +o1(%!&# 3 !" 3<#%1!n&#.

Los !s%"&#dos o9&!nidos no son 2!#+!s#" s! +o1(##dos +on "# !"#+i)n

- (osi9"!1!n&! (o !"n01!o d! d#&os 5%! s! &o1#on.

L# !"#+i)n d! #"&%#s dii!!+onsid!#9"!1!n&! !n +o1(##+i)n # "#!"#+i)n &!)i+#. A%n5%! si s! '#+i!ndo

"# !"#+i)n (o 18ni1os +%#d#dos "#$7i+# o9&i!n! "# 1is1# di!++i)n (!o+on %n# (!ndi!n&! in!io # "# &!)i+#.

A" o+%i %n !s#"&o 'id7%"i+o !" &i#n&!s!7 1!no #" +8&i+o (o "o 5%!!s&#!1os &#9#6#ndo !n "%6os%(!+8&i+o.

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L# dis1in%+i)n d! "# 2!"o+id#d 3 !"#%1!n&o !n "# (o%ndid#d !s !s%"&#dod! %n# disi(#+i)n d! !n!$8#.

RE/ERENCIAS

%&' *. T. (2004). HIDRÁULICA DECANALES ABIERTOS.  +oo!,-

&LL.

TE %. . (2011). Introducción ala Hídraulica de Canales.+oo!,- niversi#a# aiona #e

%oo$9:a.

E E. (; #e iie$9re #e 200;).

ec!nica de "luidos # RecursosHidr!ulicos. e"pera#o e 12

#e ar<o #e 2016 #e

="i#os.eia.e#".o/in#ex.>!$-

>!!p-//="i#os.eia.e#".o/>i#ra"i

a/ar!i"oses/="?oenanaes/res

a!o>i#ra"io/resa!o>i#ra"io.>

!$