Maximo Villon Ejercicios

n cana) rectan)ar de 1 m de ancoF se "n"c"a a) #"e de n c"manc"o Ke t"ene na #"so a )a cresta como se mestra en )a 5ra. 9"co c"manc"o t"ene )a m"sma )on"t de) cana) B con na cara de  = 2F43 m sobre )a m"smaF debera descarar n cada) ) cana) sera eYcaPado en t"erra con n coe5c"ente de ros"dad n = 0F02 B e) re" debe ser sbcr"t"co. 9eterm"nar )a #end"ente necesar"a en e) cana) #ara Ke e) resa)to "dra)"co se "n"c"e as" como )a )on"td  sando )a Horm)a de S"enc"n de )a *ona Ke debe rePest"rse. #erd"da de ener"a #or Hr"cc"on sobre e) c"manc"o 0F1 M 12/2.

-S! b= = = Q= n=

1 4.2 2.43 112. 0.02

H =

0.1

[m] [m] [m] [m3/s] [ad"m] M12/2

CC-*S-CS * C! _=(.G

o =

100.% 7m2

;o =

1.116 7m/s

9C  *CC * **>! *o =

$.?$4 7m

(∗+ W,WW1 +2 W1 0F1∗(∗ +2/,2 W +2/,2W,WW1 +2 

S": t = o

o =

Reem#)a*ando e "terando:

6.64 [m]

51 = 0.?23 7m

CC * --* C>!

 〗+3=W +2/,W+2 ∗ W ∗+∗W2+2W2W1+2 /2 〗+3=,W1

Reem#)a*ando B reso)P"endo:

5c = 1.?60


52 = 3.$36

CC *  >- * *S,Se;n S"enc"n < =0 Ls

=

(

A * Y 2

−

A = 

,Cana)es rectan

)

Y 1

s = 14.%8 m s E 1%.00 m CC *  9**-* "So#! =,(∗/ 〖 ∗�_ 〗+,23 +2

=∗_

&n = &2

.= 〖2∗ 〗_


A = 4.8 [m2]  = 22.2 [m]

So = 0.0008 7m/m

a)tra de 4F2 m ,de) d de cresta Ke e) anco ) Q = 112F m3/s. en en ZDo n"Horme Dsto a) #"e de )a ca"daF ,Cons"derar como

6.64 0.23

=

6.64 0.000

.34 3.63(

=

.33 0.001

7m

7m

)ares

n n cana) tra#e*o"da) Ke condce 1F3 m3/sF con n anco de so)era de b = 1 mF ta) ros"dad 0F014F se #rodce n K"ebre en s #end"ente camb"ando desde 0F008 sobr a 0F0004 en e) )ado aas abaDo como se mestra en )a 5ra.

Ca)c)ar e) #er5) de ZDo en e) tramo aas arr"ba desde e) K"ebre asta na secc"on conDado maBor &2 de) resa)to "dra)"coF sando:

*l metodo de tramos ('os -S! Q= b= *= n= So1 =

1.3 1 1 0.014

[m3/s] [m] [ad"m] [ad"m]

0.008 [m/m]

So2 =

0.0004 [m/m]

CC * S --*S +*S! -ramo 1! W /∗∗∗ =1/WWW+,2-3 W+,1-2 1WW1+2 ,,,W W1 /,W2W1 O,1W+2 +,2-3W+,1-2 ( ∗+ ∗WW1+2  (∗+∗


5n1 = 0.3?4 7m W= = W //W

-ramo 2! W /∗∗∗ =1/WWW+,2-3W+,1-2 

; =

2.%32 7m/s

(∗ + W ∗ (∗+∗ W2 O,1W+2 +,2-3W+,1-2 WW2+2 ,,,W W 2 W 2+2 /,W2

5n2 = 0.83$ 7m


CC * --* C-C!

+2/=+3/ 〖(∗+) 〖�� 〗+2 〗+3/(2∗)∗

5c =


CC *  9**-* C-C! _=∗+ WWWW  〖��〗+2

Ac = 0.6(4 [m2]

._=∗+ W2WWO,1W+2 

c = 2.334 [m]

_=_/._

Rc = 0.2( [m]

_∗_ 〗+,23 +2 =,(∗/ 〖

Sc = 0.003% 7m/m

-9 * 9*:!

&



0.003



0.008

!"#o $%$

0.42



0.34

!"#o $1$

CC * --* C> +5 * * *S- @C "52#! ,cac"on enera) #ara cana)es tra#e*o"da)es ! +4,,"#2 !+3/2,,$# 2(#1 ! +2/2%# +2/2(# >&' (# 1! >&'(# 1+2=0

! = 〖 2/ 〖�〗 1 �〗 ' =+2/,21  # =1/(∗ 1 

X =

&n2/0F34

r=

0.8

t=

2.66

Reem#)a*ando en )a ecac"on enera) e "terando:

52 = 0.%83 7m

S*CC * C-! &2 = 0.83 [m]

asta

0.%83

&n2 = 0.836 [m]

F

CC * 9*: +1!  =,(∗/ 〖 �_ 〗+,23 +2  _ (2−1 @ =(1+2/2=

Y

A

P

R

V

0.5833

0.924

2.650

0.349

1.408

0.6339

1.036

2.793

0.371

0.6845

1.153

2.936

0.7350

1.275

0.7856 0.8362

V 2

E

Se

SEm

So - SE

0.101

0.684

0.0016

---

---

1.255

0.080

0.714

0.0012

0.0014

0.0066

0.393

1.128

0.065

0.749

0.0009

0.0010

0.0070

3.079

0.414

1.019

0.053

0.788

0.0007

0.0008

0.0072

1.403

3.222

0.435

0.927

0.044

0.829

0.0005

0.0006

0.0074

1.535

3.365

0.456

0.847

0.037

0.873

0.0004

0.0005

0.0075

2 g

p = 2$.206 7m

ongitud del 9er(l!

C03;. ,*/ 9*3:2/ 0.(00 -23.4-*S 0.800 0.00 0.600 0.=00 0.400 0.300 0.200 0.100 0.000 0

=

10

1=

20

2= /14

S" e) K"ebre en )a #end"ente camb"a desde 0F008 sobre e) )ado aas arr"ba a 0F004 e ca)c)ar e) #er5) de) ZDo en e) tramo aas abaDoF desde e) K"ebre asta na secc"on sea e) t"rante norma) en esta tramoF sando:

*l metodo por -ramos ('os !"rante #ara )a secc"on aas arr"ba:

5n1 = 0.3?4 7m

!"rante #ara )a secc"on aas abaDo:

So2 =

0.004 [m/m]

W /∗∗∗ =1/WWW+,2-3W+,1-2 (∗ + W ∗ (∗+∗ W2 O,1W+2 +,2-3W+,1-2 2WW2+2 ,,,W W 2 W 2+2 /,W2

5n2 = 0.4%3 7m


S*CC * C-! 2  2=0F(( 〖�〗 Como:

&c  &

52 = 0.446 7m

Eo se #rodce resa)to en e) K"ebre de )a #end"enteF entonce n RemansoF donde: &1 = &n1

CC * 9*:! 0.34

'

&

'

0.44(

 =,(∗/ 〖 �_ 〗+,23 +2  _ (2−1 @ =(1+2/2=

Y

A

P

R

V

0.3737

0.513

2.057

0.250

2.532

0.3887

0.540

2.099

0.257

0.4037

0.567

2.142

0.4187

0.594

0.4338 0.4488

V

2

E

Se

SEm

So - SE

0.327

0.701

0.0080

---

---

2.408

0.296

0.684

0.0070

0.0075

-0.0035

0.265

2.294

0.268

0.672

0.0061

0.0065

-0.0025

2.184

0.272

2.188

0.244

0.663

0.0053

0.0057

-0.0017

0.622

2.227

0.279

2.090

0.223

0.656

0.0047

0.0050

-0.0010

0.650

2.269

0.287

1.999

0.204

0.653

0.0041

0.0044

-0.0004

2 g

ongitud del emanso!

r = 30.$13 7m

C03;. ,*/ 9*3:2/ 0.=00 -23.4-*S 0.4=0 0.400 0.3=0 0.300 0.2=0 0.200 0.1=0 0.100 0.0=0 0.000 0

=

10

1=

20

2=

30 /14>2-

)d * = 1F coe5c"ente de e) )ado aas arr"ba

Bo t"rante sea e)

1.300 0.34

=

1.300 0.000

0.4?2 7m

1.300 0.836

=

1.300 0.000

0.12 0.42

=

0.12 0.000

0.000 0.83

=

0.000 0.000

CrPa %1

5

F

0.83$

(_>(_  @ 

ΔE

ΔX

∑Δx=X

---

---

0

0.030

4.50950982

4.510

0.035

5.01984399

9.529

0.039

5 .352952 63

14.882

0.041

5 .581712 33

20.464

0.043

5 .744750 16

26.209

30 2-0,

e) )ado aas abaDoF donde )a #roHnd"dad

1.300

=

1.300

0.43

s se #rodce

(_>(_  @ 

ΔE

ΔX

∑Δx=X

---

---

0

-0.016

4 .674628 89

4.675

-0.012

4 .934883 27

9.610

- 0. 00 9

5 .3 70 94 41 5

1 4.9 80

- 0. 00 6

6 .2 74 39 24 7

2 1.2 55

- 0. 00 4

9 .3 57 67 69 3

3 0.6 13

3= 0,

0.000

Se t"ene n cana) de secc"on rectan)arF cBo anco de so)era es b = 2mF coe5c"ent B condce n cada) de 2F m3/s. n este cana) eY"ste na com#erta cBa abertra es a = 0F3 m B t"ene e) #er5) de H )a 5ra.

Cons"derando Ke )a abertra de )a Pena contra"da en )a com#erta es: B=CcVa dond na d"stanc"a 1FVa aas debaDo de )a com#ertaF se #"de: a Rea)"*ar e) estd"o de )os #er5)es de ZDo. b Ca)c)ar B d"bDar )as #er5)es.

-S! b= 2 n= 0.01 Q= 2. a= 0.3 Cc = 0.61 d= 1. a*S- *

[m] [ad"m] [m3/s] [m] Va

S 9*:*S * ::

CC * S --*S +*S! W /∗∗∗ =1/WWW+,2-3 W+,1-2

S1 = 0.001 [m/m]

W,WW,,,W ( W/,W2 (∗∗ W+,2-3W+,1-2 Reem#)a*ando e "terando:

W /∗∗∗ =1/WWW+,2-3 W+,1-2

S2 =

0.01

5n1 =

[m/m]

W,WW,,,W ( W/,W2 (∗∗ W+,2-3W+,1-2 Reem#)a*ando e "terando:

CC * --* C-C! 1 2

5n2 =

q =  g     -+ 1!

5c =

Yc

0.%42 7m

&n2 = &1  2=1F01 〖�〗

52 = 0.6$%3

*CC >** 9 *-*+ * --* -*   C+9  2=O,2,G1>G2

〖  :

 〗 2=/(∗

=∗

: =∗ : 2=/2 : 2=G2 :

G2=∗

9es#eDamos e) t"rante anter"or 1:

G1=+2/,2∗+2 +2 〖 � 〗+2 +∗

reem#)a*ando:

h1 =

1.6$1 7m

) #er5) ser7: 0.(6

'

&

'

1.(61

CC *  9**-* C-C! _=∗+) 〖 ��〗+2

Ac = 1.084 [m2]

._=2∗O,1+)+2 

c = 3.084 [m]

_=_/._

=,(∗/ 〖 _∗_ 〗+,23 +2

Rc = 0.32 [m]

Sc = 0.0048 7m/m

Cc =

-9 * 9*:! 0.42

'

0.00 0.(6

 '

0.001 &

!"#o $%$ !"#o $1$

-+ 2! CC =∗ @= CC  =1F

d=

CC * --* C> +*! 2/2O,,2∗+2/(∗2 ( 2+2/4 〖 −�〗

,Cana)es Rectan)ares


=/

51 = 0.2?2 7m

) #er5) ser7: 0.214

'

0.00 0.42

 

&

'

0.22

-9 * 9*:! 0.(6



0.001 &

!"#o $%$ !"#o $3$

-+ 3!

51 =

0.(46



&



0.42

-9 * 9*:! 0.22

'

0.00 &

 '

0.001 0.42

!"#o $%$ !"#o $2$

-+ 4!

52 =

0.42



0.00 &

' '

&



0.426

-9 * 9*:! 0.426

'

0.01 0.42

!"#o $S$ !"#o $2$

CC * 9*: +1 "-ramo 1#! Y

A

P

R

V

0.9653

1.931

3.931

0.491

1.295

V

2

2 g 0.085

E

Se

SEm

So - SE

1.051

0.0010

---

---

1.1643

2.329

4.329

0.538

1.074

0.059

1.223

0.0006

0.0008

0.0002

1.3634

2.727

4.727

0.577

0.917

0.043

1.406

0.0004

0.0005

0.0005

1.5625

3.125

5.125

0.610

0.800

0.033

1.595

0.0003

0.0003

0.0007

1.7616

3.523

5.523

0.638

0.710

0.026

1.787

0.0002

0.0002

0.0008

1.9606

3.921

5.921

0.662

0.638

0.021

1.981

0.0002

0.0002

0.0008

C03;. ,*/ 9*3:2/ 2.=00 -23.4-*S 2.000

1.=00

1.000

0.=00

0.000 0

=00

1000

1=00

2000 /1

CC * 9*: +3 "-ramo 2#! Y

A

P

R

V

0.2135

0.427

2.427

0.176

5.855

0.2251

0.450

2.450

0.184

0.2367

0.473

2.473

0.2484

0.497

0.2600 0.2716

V 2

E

Se

SEm

So - SE

1.747

1.961

0.0782

---

---

5.553

1.571

1.797

0.0664

0.0723

-0.0713

0.191

5.280

1.421

1.658

0.0569

0.0616

-0.0606

2.497

0.199

5.033

1.291

1.540

0.0491

0.0530

-0.0520

0.520

2.520

0.206

4.808

1.178

1.438

0.0427

0.0459

-0.0449

0.543

2.543

0.214

4.603

1.080

1.351

0.0373

0.0400

-0.0390

2 g

p = 11.3%2 7m

ongitud del 9er(l! CC *  >- * *S ,Se;n S"enc"n < =0 Ls

=

s =

(

A * Y 2

−

)

Y 1

3.421 m

>- -- * -+ 2!

A = 

,Cana)es rectan

s = 3.421 [m]

on"td de) resa)to

# = 11.32 [m] d = 0.2 [m]

on"td de) #er5) ,Remanso on"td de )a Pena contra"da

t = 1%.268 7m

on. !ota) de) tramo 2

>- *S--* 9 * -+ 3! rest. = eGist. H t

eY"st. =

2(4

E

Se

SEm

So - SE

[m]

rest. =2?8.?0 7m V 2

Y

A

P

R

V

0.5421

1.084

3.084

0.352

2.306

0.271

0.813

0.0048

---

---

0.6229

1.246

3.246

0.384

2.007

0.205

0.828

0.0032

0.0040

-0.0030

0.7037

1.407

3.407

0.413

1.776

0.161

0.865

0.0023

0.0028

-0.0018

0.7845

1.569

3.569

0.440

1.593

0.129

0.914

0.0017

0.0020

-0.0010

0.8653

1.731

3.731

0.464

1.445

0.106

0.972

0.0013

0.0015

-0.0005

0.9461

1.892

3.892

0.486

1.321

0.089

1.035

0.0010

0.0012

-0.0002

2 g

de ros"dad n = 0F01 ndo como se mestra en

Cc = 0F61 B s"tado a

=

0.6%$ 7m

2.00 0.(6

2.00 0.000

=

0.422 7m

2.00 0.422

2.00 0.000

2 7m

-! O,2,G1>G2

0.61

CrPa %1

 * B@B!

0.214 7m  * BdB! ∗

0.%2% 7m

CrPa %3

0.64$ 7m

CrPa %2

0.42$ 7m

CrPa S2

ΔE

ΔX

∑Δx=X

---

---

0

0.172

794.94 3991

794.9 44

0 .1 83

3 61 .4 77 90 7

11 56 .4 22

0 .1 89

2 84 .4 87 95 5

1 44 0. 91 0

0 .1 92

2 53 .5 93 16 1

1 69 4. 50 3

0 .1 94

2 37 .4 30 58 7

1 93 1. 93 4

2=00 4>2-0,

ΔE

ΔX

∑Δx=X

---

---

0

-0.164

2.30033013

2.300

-0.139

2.28972412

4.590

-0 .11 8

2.2747 5257

6.86 5

-0.101

2.25545011

9.120

-0.087

2.2318 2184

11.35 2

)ares

ΔE

ΔX

∑Δx=X

---

---

0

0.015

-4.9569366

-4.957

0 .03 6

-20 .45 5056

-25 .412

0 .04 9

-48 .97 5393

-74 .387

0 .05 8

-11 3.70 566

-18 8.09 3

0 .06 3

-37 8.9 4653

-56 7.04 0

n cana) tra#e*o"da) con ta)d * = 1.F anco de so)era b = 1. mF coe5c"ente de ro #end"ente de 0F( o/ooF condce n cada) de 1.8 m3/s. n na c"erta secc"on deb"do a ) ado#ta na #end"ente de) 1\. Ca)c)ar e) #er5) de ZDo en e) tramo de menor #end"en donde se #rodce e) camb"o de #end"ente asta na secc"on aas arr"ba donde e) t"r )a #roHnd"dad norma)F sando:

*l metodo de tramos ('os

-S! b= n= Q= S1 = *= S2 =

1. 0.014 1.8 0.000( 1. 0.01

[m] [ad"m] [m3/s] [m/m] [ad"m] [m/m]

CC * --* +! =1/∗∗+,2-3∗+,1-2 +)∗_+2 ,,(∗_+)∗_+2 /(2∗_ O,1+)+2 +,2-3 ∗+,1-2


5n = 0.$2? 7m

CC * --* C-C!

+2/=+3/ 〖(∗+) 〖〗〗+3/(2∗)∗ WWW〖+2


CC *  9**-* C-C! _=∗+) 〖 ��〗+2

Ac = 0.(80 [m2]

._=2∗O,1+)+2 

c = 3.124 [m]

5c =

_=_/._

Rc = 0.314 [m]

=,(∗/ 〖 _∗_ 〗+,23 +2

Sc = 0.0031 7m/m

-9 * 9*:! 0.003 0.62

'

&

'

0.000(

!"#o $%$

'

0.41

!"#o $2$

S*CC * C-!  1=0F((∗_

51 = 0.$21 7m

) #er5) ser7: 0.41

'

&

'

0.621

CC * 9*:!  =,(∗/ 〖 �_ 〗+,23 +2  _ (2−1 @ =(1+2/2=

Y

A

P

R

V

0.4505

0.980

3.124

0.314

1.836

0.4845

1.079

3.247

0.332

0.5186

1.181

3.370

0.5526

1.287

0.5866 0.6206

V 2

E

Se

SEm

So - SE

0.172

0.622

0.0031

---

---

1.668

0.142

0.626

0.0024

0.0027

-0.0018

0.351

1.524

0.118

0.637

0.0018

0.0021

-0.0012

3.492

0.368

1.399

0.100

0.652

0.0015

0.0016

-0.0007

1.396

3.615

0.386

1.289

0.085

0.671

0.0012

0.0013

-0.0004

1.509

3.738

0.404

1.193

0.073

0.693

0.0009

0.0010

-0.0001

2 g

p = 22?.30 7m


C03;. ,*/ 9*3:2/ 0.

-23.4-*S

0. 0. 0. 0. 0. 0. 0. S2=0

S200

S1=0

S100

S=0 /14

9*: * : * * -+ * +5 9**-* *S*  S*CC  9**-* @S-  S*CC >S A * * --* *S 1I + CC * --* +ara na #end"ente de :

S2 =

0.01

[m/m]

=1/∗∗+,2-3∗+,1-2 +)∗_+2 ,,(∗_+)∗_+2 /(2∗_ O,1+)+2 +,2-3 ∗+,1-2

5n = 0.32$ 7m


-9 * 9*:! 0.003 0.41



&



0.01

!"#o $S$



0.326

!"#o $2$

CC * 9*:!  =,(∗/ 〖 �_ 〗+,23 +2  _ (2−1 @ =(1+2/2=

Y

A

P

R

V

0.3260

0.648

2.675

0.242

2.776

0.3509

0.711

2.765

0.257

0.3758

0.775

2.855

0.4007

0.842

0.4256 0.4505

V 2

E

Se

SEm

So - SE

0.393

0.719

0.0100

---

---

2.532

0.327

0.678

0.0077

0.0088

0.0012

0.272

2.321

0.275

0.650

0.0060

0.0068

0.0032

2.945

0.286

2.138

0.233

0.634

0.0048

0.0054

0.0046

0.910

3.035

0.300

1.978

0.199

0.625

0.0038

0.0043

0.0057

0.980

3.124

0.314

1.836

0.172

0.622

0.0031

0.0035

0.0065

2 g

p = 46.?6 7m


C03;. ,*/ 9*3:2/ 0.

-23.4-*S

0. 0. 0. 0. 0. 0. 0. 0. 0. S=0

S4=

S40

S3=

S30

S2=

S20

S1=

S10

0. S=

/14

s"dad n = 0.014 B con na to#ora5a de) terreno eF desde )a secc"on nte es 1\ menor Ke

0.4%1 7m

1.800 0.62

=

1.800 0.000

0.330 0.41

=

0.330 0.000

CrPa %2

(_>(_  @ 

ΔE

ΔX

∑Δx=X

---

---

0

0.004

-2.1802692

-2.180

0.011

-8.736176

-10.916

0.015

-20.60392

-31.520

0.019

-47 .013164

-78.534

0 .0 22

- 14 8.7 63 05

- 22 7.2 97

00 600 =00 400 300 200 100 000 0 2-0,

* S* 9C* * C+A * 5 J* * --* +.

1.800 0.326

CrPa S2

(_>(_  @ 

ΔE

ΔX

∑Δx=X

---

---

0

- 0. 04 1

- 35 .6 48 78 7

- 35 .6 49

- 0. 02 7

-8 .6 12 11 68

- 44 .2 61

- 0. 01 7

-3 .6 11 44 95

- 47 .8 72

- 0. 00 9

- 1. 52 68 32 9

- 49 .3 99

- 0. 00 3

- 0. 39 55 28 7

- 49 .7 95

=00 4=0 400 3=0 300 2=0 200 1=0 100 0=0 000 0

=

1.800 0.000

2-0,

n cana) tra#e*o"da) de anco de so)era b = 1. mF ta)d * = 1F t"ene na #end"ente coe5c"ente de ros"dad de 0.02. S" )a #roHnd"dad en )a secc"on  es 1.2 m B en ) aas abaDo es 1.68 m. 9eterm"nar e) cada) en e) cana).

atos! b= n= S= &1 = &2 = *= Y =

1. 0.02 0.0004 1.2 1.68 1 (2

[m] [m/m] [m] [m] [m]

S*>K * +*- * S -+S :S! *n la seccion 1!  1=∗ 1+)∗ 1+2

A1 = 4.(0 [m2]

. 1=2∗1 O,1 +)+2 

1 = .(( [m]

Reem#)a*ando en )a ecac"on:

*n la seccion 2!  2=∗ 2+)∗ 2+2

A2 = .342 [m2]

. 2=2∗2 O,1+)+2 

2 = 6.22 [m]

Reem#)a*ando en )a ecac"on:

Cond"c"on:

C1 = C2

e 0.4 o/ ooF B n a secc"on ^ (2.0 m

) t"rante norma) de n cana) tra#e*o"da) #ara )as stes caracter"st"cas: b = 1 mF * = es 1 m. Y"ste na #resa Ke #rodce na crPa de remanso de a)tra 0. mF como s

Se K"ere determ"nar )a a)tra de) remanso en )a secc"on F s"tado a na d"stanc"a a #resaF sab"endo Ke esta s"tado 00 m aas arr"ba de )a secc"on ^F )a ca) t"ene  de 0.3 m.

-S! b= n= & = *= So =

1 0.02 1 2 0.000

[m] [ad"m] [m] [m/m]

CC * C! =1/∗∗+,2-3∗+,1-2

=∗+)∗ +2

Ac = 3.000 [m2]

.=2∗O,1 +)+2  _=_/._

CC * --* 51!

c = .42 [m] Rc = 0.48 [m]

,Se;n e) metodo de )os tramos 5Dos

Maximo Villon Ejercicios

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