B. T. 1980 flood studies

i "' "' ::> 0 ' "' ~ ~ .:; c ~ -.f .~ "t; ~ ~ ~ u III-40 10000 8 000 I, I I oOOO ~000 2000 1000 800 600 400 200 100

_ Trdctovt Font (lb/ Fl1)-i Ooamet~r (ln.) or Vj

-1

rractive Force (l<s/M1J·Dlameter (Cm) ~ (N~~~

-

rT-f-+-t-r- . 7. ~ ~

Cdnals Woth 2 5'70, Colloids on WatQr1 Ru~~od

1

/ '/' j

I I I II' '

H

II'

1

\

~I'

l

f -Recommended for Canal~ W1th Hoah .- 1 -1--f . i _ ~

Content of Font Stdlmenlln Water ..;;:::: I I I j~ ~

!

1

Recommended for c.anals With lOWII [ \ (NI<) / !

II

'

Content of Fone Sedomtnt on Wdt.er -~ ~· 1 I

1 -Recommomded By S Fortier and 12' L C~nals Woth o 1'7c,t

~oboy With Water ' " Containing ' ' " ''" ' Co'llo'' ' ids 5,od , ~ / / Collood. s 1n W.rter, Ru• s!>ld

Recommended B)l A. Schol<lll~ch H

for Canal$ in 5and . / ~ <" [...;' I I I

I L _uz::+ .___(NK)./ ~ ~

Recommended for Canals

Nu ;~g Kulturaml (NI<l j.,. ...:;::::::::.. ~ ....,...v ' in Coarse, Noncohesive ~ ...

4

v

v M~teroal-S1ze 25,-0 larger tNK)

v

" j j l I I

~~

~~ ~ ( _ _'-- Recommended for C~nals Wolh Clear ~ater

-= I-':~

!""""~ ~ .... ~ ~ _Force Value_Oetermons of the CritiCa_ed By Ll Tra. Stcotive aub

80

60

. L.

"

Canal!> With Clear Wdttr, Rus!>od

v !:><

/ Recommended Sy S. for1ier and F. C. Scobey

~ / for Canals m Fme Sand With Clear Water

v

I I I I I 0.8 0.6 0.4 0 2 0.1 v.os 0.06 0.04 0 02 0 01 0 008 0007 ~ "'

..

§; "' 0. "' § 0 ~ .!: ~T ~ ~ .= -;;; .~ u 30 O.l 02 0.4 0..6 0.8 1 20 40 60 80100

Fig. 3.9.1 Recommended limiting shear stress for

canals. (/) ..0

-..c. Ol (1) 3: (1) c 0

-(f) 1000 100 10 0.1 0.01

Note: Specific weight of

stone=l651b/ft3 2

--

_.... I (1)

-0.8 (1) E 0 0.6 0 (1) c 0.4 0 if>

-

c (1) 0.2 0 > :J o-w 0.1 '/' I V

Fig. 3.9.2 Critical velocity as a function of stone size.

Table 3.7.1 Sediment grade scale.

Approximate Sieve Mesh

Size Openings per Inch

u.s.

Millimeters Microns Inches Tyler Standard Class

4000-2000 160-80 Very large boulders

2000-1000 80-40 Large boulders 1000-500 40-20 Medium boulders 500-250 20-10 Small boulders 250-130 10-5 Large cobbles 130-64 5-2.5 Small cobbles H

64-32 2.5-1.3 Very coarse gravel H

H

32-16 1.3-0.6 Coarse gravel I

N

16-8 0.6-0.3 2 1/2 Medium gravel ~

8-4 0.3-0.16 5 5 Fine gravel

4-2 0.16-0.08 9 10 Very fine gravel

2-1 2.00-1.00 2000-1000 16 18 Very coarse sand 1-1 1/2 1.00-0.50 1000-500 32 35 Coarse sand 1/2-1/4 0.50-0.25 500-250 60 60 Medium sand 1/4-1/8 0.25-0.125 250-125 115 120 Fine sand 1/8-1/16 0.125-0.062 125-62 250 230 Very fine sand

1/16-1/32 0.062-0.031 62-31 Coarse silt

1/32-1/64 0.031-0.016 31-16 Medium silt

1/64-1/128 0.016-0.008 16-8 Fine silt

1/128-1/256 . 0.008-0.004 8-4 Very fine silt

1/256-1/512 0.004-0.0020 4-2 Coarse clay

1/521-1/1024 0.0020-0.0010 2-1 Medium clay 1/1024-1/2048 0.0010-0.0005 1-0.5 Fine clay 1/2018-1/4096 0.0005-0.00024 0.5-0.24 Very fine clay

Table 3.7.1 Sediment grade scale.

Approximate Sieve Mesh

Size Openings per Inch

u.s.

Millimeters Microns Inches Tyler Standard Class

4000-2000 160-80 Very large boulders

2000-1000 80-40 Large boulders 1000-500 40-20 Medium boulders 500-250 20-10 Small bo1.,1lders 250-130 10-5 Large cobbles 130-64 5-2.5 Small cobbles H

64-32 2.5-1.3 Very coarse gravel H

H

32-16 1.3-0.6 Coarse gravel t

N

16-8 0.6-0.3 2 1/2 Medium gravel ~

8-4 0.3-0.16 5 5 Fine gravel

4-2 0.16-0.08 9 10 Very fine gravel

2-1 2.00-1.00 2000-1000 16 18 Very coarse sand

1-1 1/2 1.00-0.50 1000-500 32 35 Coarse sand

1/2-1/4 0.50-0.25 500-250 60 60 Medium sand

1/4-1/8 0.25-0.125 250-125 115 120 Fine sand

1/8-1/16 0.125-0.062 125-62 250 230 Very fine sand

1/16-1/32 0.062-0.031 62-31 Coarse silt

1/32-1/64 0.031-0.016 31-16

.

Medium silt

1/64-1/128 0.016-0.008 16-8 Fine silt

1/128-1/256 . 0.008-0.004 8-4 Very fine silt

1/256-1/512 0.004-0.0020 4-2 Coarse clay

1/521-1/1024 0.0020-0.0010 2-1 Medium clay

1/1024-1/2048 0.0010-0.0005 1-0.5 Fine clay

1/2018-1/4096 0.0005-0.00024 0.5-0.24 Very fine clay

IV-11

Tl. Uniform Width, Sinuous; T2. Wider ot Bends, Sinuous·, T3. Wider ot Bends,Stnuous T4. Vorioble Width, Braided

~~~ntN~~~w'' Present Point Bors Conspicuous b~~~~~~~sB~~~o~~sB~~d;emi- ~r~~~~~e Course of Low

S1nuous (or Slraigllf) Undorm Chonnel

Sinuous Point Bor Channel

Point Bar Braided Channel

Bar Braided or Island Braided Oramagte Co/JfSlJ

(a) Variability of unvegetated channel width: channel pattern at normal discharge

(b) Braiding patterns

51 Low(l-1.3) 52 Moderote ( 1.3-2.0) 53. High(>2.0)

(c) Types of sinuosities

I

Fig. 4.3.5 Classification of river channels (after Culbertson et al.,

-

.~

-·

..

-

~l

Somiarc\

r • -

,

~em

-

E?4f-~

-(AJ leU'-'\ ~ hlc.til~y te."~~~.

----··

(L24')(3')

(sb·y

·

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7ri

~d~

·

·.

-z?

-- -

fo~t

__.,..___._.._,.__.,,...;.,..

_

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.

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~rn.

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---~ ;:s:0/---~3

.

'"

IIA-1

2.Al.O BRIDGE CONSTRICTIONS WITH NO BACKWATER (Neglecting energy losses)

A stream is rectangular in shape and 100 ft wide. The design

discharge is 5000 cfs and the uniform depth for this discharge is 10 ft.

Ne.gle.c.ting e.neJLgy lo~~ eA wha;t -L6 :the. maxhnum amount on c.o~t!Uc.tion :tha;t

c.an be. hnpo~ e.d wLthou:t c.au~ing bac.lwJa:teJL a:t :the. de.llig n fu c.haJtg e.?

The upstream flow rate per unit width is

Q

5000

q =

W

=

₁₀₀

= SO cfs/ ft the average velocity is

- Q -

5000

-v

-

A. -

_{1 0 0 0} -

s . o o

fp s and the specific h~ad is (from Eq. 2.5.3)

v2 . s2

H = 2g + y =

64.4 + 10 = 10.39 ft

According to Section 2.5.3, the maximum unit with this specific head is (from Eq. 2.5.16)

discharge that can oc~~~

~' ~ ~

# :

Jt

~?&{

=

103.4 cfs/ft

Therefore, the width of channel which will accommodate this unit discharge is

5000

103.4 - 48.3 ft.

and the amount of the constriction is 100- 48.3

=

51.7 ft.

:t

Note, as discussed on page II-41, this contraction could cause an

undulating hydraulic jump downstream. When energy losses are considered

----

--

--

____

..

----·

there will be some backwater at this constriction. This backwater is evaluated by conventional methods such as those given in "Hydraulics of Bridge Waterways" (Federal Highway Administration, 1970).

IIA-2

2.A2.0 BACKWATER FROM A DOWNSTREAM DIVERSION DAM

A small diversion dam is to be placed across a stream downstream of a highway bridge. The purpose of the dam is to head up water for diversion into a canal. At the bridgey the design flood discharge was 5000 cfs. The river is 100 ft wide and has a uniform flow depth of 10 ft for the design discharge.

What

L6

the maM.mwn hught

ofi

the dam

that wJ.Lt not c.au.6

e

bac.k.wateJt

at

the bfr..idge?

The unit discharge in the river at design flood discharge is

Q

5000 q = -

_w

= - - = 50 cfs/ ft 100 the velocity is V

=

L

=

~~

= 5. 00 fps . yo

and the specific head is (from Eq. 2.5.3)

v2

52

H = -_2g + y

=

Zg + 10 = 10.39 ft 0

As a first approximation assume no energy loss in the reach. Then at the dam, the elevation of the total energy line is 10.39 ft above the bed (see Fig. 2.A2.1). At the dam,

H . + ~z

=

10.39 ft

m1n max

that is, the dam can be built to a height of ~Z which decreases the max

specific head at the dam to H . . From Eq. 2.5.11 mln

H .

mln

and from Eq. 2.5.7 so Thus IIA-3

2

~

y = (L) 1/3 c g 2 = (~)1/3 = 32.2 4.27 ft 3 H . _m1n

= -

₂ (4.27)

=

6.40 ft ~z

=

10.39 - 6.40

=

4.0 ft m

If the dam is built to a crest elevation 4.0 ft above the bed, critical flow will occur at the dam for a flow of 5000 cfs and the dam will cause no backwater.

How much backwater will the dam cause for a flow of 1000 cfs if the normal depth for this discharge is 5 ft and the dam height is 4.0 ft?

Upstream of the dam,

and

q

=

~

=

i~~o

-

10 cfs/ft

v

=

s_

=

_!_Q_

=

2 fp s

o Yo 5

At the dam the flow is critical so from Eq. 2.5.7

2

Y =

cL)

1/3

and from Eq. 2.5.11

c g 2 = (.!..Q_)l/ 3 = 1.46 ft 32.2 H . m1n 3

=

2

(1.46)

=

2.19 ft

The specific head upstream of the dam is then (assuming no energy loss)

H

=

H .

+ ~Z m1n

IIA-4 or

H = 2.19 + 4.00 = 6.19 ft

Also, the specific head upstream of the dam is (from Eq. 2.5.4)

2 Therefore or The solution is H=_g__+y 2 2gy 2 _g__2 + y = 6.19 2gy 3 2 102 y 6.19 y + 64.4 = 0 y = 6.14 ft

As the normal depth is only 5 ft, the backwater is ~y = 6.14 - 5.00

=

1.14 ft

That is, the depth upstream of the dam is increased 1.14 ft by the 4.0-ft high dam when the flow is 1000 cfs.

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