The use of artificial roughness in movable-bed models

I -I , I Summary. roughne s s 'in movable-bed models

Tests have been done in a laboratory flume? to evaluate the in-fluence of vertical rods of 3 mm dia on the hydraulic and sedimentolo-gical characteristics of the flow.

The first report deals with the measurements with fine bakelite and waterdepths 10 and

5

centimeters.

The ~_':i_~~.~.E.<?.r_~ deals with the measurements with fine sand and the same waterdepths.

The results, must be carefully interpreted as follows 'from the two conclusions.

/ ' Note

-The tests have been carried out and evaluated by partipants of the International Course in Hydraulic Engineering as a practical groupwork in this course.

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4n---~ '/1-0:

,t'

go

.

~

t

~

{.

Cr

IJV~ ~

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./

Summary.

Tests with bakelite

CONTENTS

1. Introduction.

2. Description of Tests.

3. Tests results.

4.

Basic calculations.

5.

Calculations of the results.

6.

Conclusions and recommendations.

7. N~omenc1ature.

LIST OF FIGURES 1. Flume Delft Hydraulics Laboratory.

2. Frijlinks bedload formul~.

3

.

Calibration' for

70

0 V-notch.

4.

Calibration curve of current meter.

5.

Size distribution curves.

6. Ripple heights in IIdeep" vrater.

7.

II _{lengths in}

"

"

8.

_"

celerity in

_"

'I

PHOTOGRAPHS 1. Test flume.

2. Gauges for _{measuring the energy gradient.}

3.

_{Sediment feeding system.}

Ripple photo's, test no.

r.

Ripple photo's, test no. II.

REFERENCES

1. Gunther Ptoschek. Artificial roughness elements. Report no. W.L.V.₂, Delft Hydraulics Laboratory.

2. Ruwheden in vertrokken modellen.

Verslag over proeven betreffende staafjes en roosters. Delft Hydraulics Laboratory report, I Ed, 284.

3. Rouse, H. Engineering Hydraulics, 1958, pg. 122.

1 2 3 4 9

16

19

\

\

Summar.Y,

'l'ests with bakelite.

The use of artificial roughness in movable-bed models

Tests have been done in a laboratory flume, to evaluate the influence

of vertical rods of 3 mm .. dia. on the hydraulic and sedimentological

characteristics of the flow.

The first two tests have been done with some 10 cm waterdepth. In

both tests the same flow rate and sedi~ent transport was used, the only

difference between the tests ~eing the artificial roughness, which was

applied during the second test.

The following two tests were done in a similar way with a

water-depth of about ~ and with a reduqed flow rate and sediment transport.

For both 10 em and

5

om waterdepths, the bar resistance was then measured

in the flume without bakelite.

The influence of the rods on the ripple factor, ~, thus on the

bottom roughness, could be evaluated, after e1imination of the bar

resistance.

In the case of 10 em depth, the artificial roughness caused a

reduction"of bottom roughness, while with a depth of

5

cm an increased

bottom roughness with the bars was found.

By calculating the bed load from the product of the mean ripple

celerity and half the meru1 ripple height a very good agreement was found

\

\

Tests with bakelite

The use of artificial roughness in movable-bed models

1. Introduction.

Incompatable scale relationships for the several channels of a proposed hydraulic model, to be 'buil t with a movable bed, led to the conclusion that the roughness of one of the principal sections should be artificially increased. To the knowledge of the authors artificial roughness has never previously been applied to movable bed models. Thus, it was decided to conduct flume tests in an attempt to discover in what way the imposed roughness would influence the bed load movement; and in this way formulate recommendations for the application of this technique to hydraulic model studies.

The tests were conducted from March to June

1962

at the Hydraulics Laboratory, Delft. Testing was restricted to the only flume available in the laboratory which had dimensions:

Length~ Width~ Depthg 30 m. 0.30 m. 0.35 m.

Two materials, fine bakelite and sand, were tested. For each

material two phases of transport (according to the transport formula of Frijlink) were considered. The tests on each material were made by

different groups, and the following report deals solely with those tests using fine bakelite, The second part of the report contains the results obtained using sand.

The tests have been done under the guidance and with the assist~nce of Messrs. J~E. Prins and H.N.C. Breusers of the Hydraulics Laboratory, by:

J.A.T. Aspden I.J. Wainer D. R. Wells & J.A. Zwamborn,

2. Description of Tests.

~'he tests were performed in a 27"~ meter long, 30 cm vlide outdoor flume at the Delft facility of the Delft Hydraulics Laboratory. The pertinent dimension and configuration are shown in Fig. no. 1.

2

A constant discharge was maintained in the 30 x 35 cm channel by use of a 700 triangular weir (3):t. The discharged water was recirculated via a circular reservoir. Assurance of a constant discharge waS obtained by observations of the water level (2) in the stilling basin (11) from which water flowed to the triangular weir.

The dynamics of the water vroro measured in the middle of the flume as shovm in the diagram. The slope of the energy line was observed by two pitot tubes situated 10 meters apart (4)-(5) and the waterdepth and surface vrere observed by two point gauges (6)-(7) 9 meters apart and centered around the same point as the pitot tubes.

A, number of stream velocity measurements were made by means of the propellor velocity meter situated between the pitot tube gauges

(9).

Measurements were take~ at enough points vertically to obtain a velocity profile in all cases except those for which the waterdepth only allowed a few measurements. Bakelite was used as a substitute for natural sand.

It was necessary to enable the bakelite transport to come to

equilibrium over a period of some hours before tests could be performed. "

An automatic timer (1) regulated the input of bakelite into the head of the flume. '1.'h8 bakelite was packed in measured quanti ties into cells over the upstream end of the flume and the timer fed enough water into these cells, one at a time, periodically to wash the bakelite into the flume" The transported bakelite could again be collected and measured in a trap (10) at the downstream ond of the flume during a test.

Photo's were taken of the ripples at one p~rticular place, at five minutes intervals.

A few samples of the sediment were analysed by sieving in order to attain size distributions.

3. Test results

The average values are summarized in the table below.

Tests with movable bed.

Deep water Shallow water

Quanti ty (h .:, 10 ern, No rods

-Q (flow in 10-3

m

3

/s)

8.40

h

(waterdepth in 10-2 m) 12.1

-

_Ie

(energy slope) 0.76xlO-3

T t (total bedload in N/hr. ) 66.6

-V measured

(average vel.

in 10-2

m/s)

24.4

v=Q/bh

-2

I

10 m s 23.2

Bakelite

Roughness tests.

(vvithout movable bed).

Q ~8 l/seo) (h ~5 em,

With rods No rods

, , 8.47 3.10 11.9 6.2 1.34xlO-3 0.99xlO-3 -67.6 . 16.2 23.9 17.2

£.hI

1&!1

d

=

0054 x 10-3 m m d 90

=

0.75 x 10-3 " 6 s

=

-

1400 kg/m3 Q ~.3 I/see) With rods 3.10 7.4 1.37XIO-3 16.2 15.9

.l4.!.2

D eep wa er t Sh 11 a ow wa er t 10 ern _{5 em} . Quanti ty

No rods With rods No rods With rods

-

_{10-3 m3}

_I

_f::

_3\.10 Q in 8036 8.36 3.10

h

in 10- 2 m _{11.15 11. 72 6.22 6.49}

-

_-3 0.99xlO- 3 0.19xlO 3 0.55x10-3 Ie _0033xl0

-

_-2

_1/:

V in 10 m s _{25.2 21.2 16.5 12.8}

V=Q0

b _""IS .25.0 2)·

_

g

~

%'-3

l ()- _ I_ -;:;:-;=--;::

-.

The following additional remarks can be made.

Flow measurement was done with the 700 sharp edged V-notch for which the calibration is shovm in fig. 2. Both the relationship Q = 1.4xH2•5 tg cp/2

(Delft) and Q

=

1.34 H2•48 tg cp/2 (King's Handbook of Hydraulics) show an appreciable deviation for Q ( 1.5 lis and Q ,

7.5

lis. A much better fit of the points is obtained with a relation of the type Q

=

constant x H2 • 2 • Eecause the measured points, however, do not extend far enough

to warrent the acceptance of the power 2.2 the simpler formula

Q

= 1.4 H

2•

5

tg cp/2 has been used.

'l'his seemed aoceptable, beoause all tests were done with flow ratas of 3 lis or 8 lis.

For flow rates of 10 lis and over, the possible erro~r, however, may be large.

Velocity measurements were done with a propellor current meter. For the calibration, see fig.

4.

Size distribution ourves of the bed material and the bakelite taken from

the sediment trap at the low and of the flume are shown in fig.

5.

The two materials seem to be virtually the same, although the transported

material has a somewhat smaller standard devia~ion. No general oonclusions, however, can be drawn beoause only one set of ourves WaS obtained. The total transport for eaoh test was known from the feeding rate, which in itself was verified by measuring the sediment oaught at the end· of th6

flume.

Ripple dimensions and oelerities have been r~corded photographically and the results have been summarised in fig.'s

6, 7

and

8

for the 10 em depth.

4.

Basic oalculations

4.1. The trcmsport theory acoording to Frijlink can be plotted, as shown in figure 1, using the parameters:

Tb :=: d =: rn 6. =: 3/2 /-_. d \ 6g m and 6.d ' m IJ.hI

volume of bottom transport/unit width.

mean grain diameter. P s - Pw

P

=

denSity of bottom material

P_w s

P =: density of water.

jl ripple factor~ according to Frijlinks _jl

h

₌

depth of water.

I

₌

slope of energy line. C

₌

Chezy roughness coeff. C _gr

₌

C (grain roughnes s) •

d90

Approximately the two following phas91tl of transport were oonsidered:

T

(1) _...,;b:.-_

d 3/2

vI:,

m g

= 0.2 (2)

The depth of water taken for each phase of transport Was 0.1 m and 0.05 m respectively.

From the sieve _{analysis, figure 4,} d _m

₌

0.54 x 10-3 m.

-3 d

90

=

0.75.x 10 m.

Also Ps

=

1400 kg/m 3, giving ~ 0.4. The computed values are:

(1) h 10 em _{(2) h}

₌

₅

_cm jl _{0,44 jl}

₌

_0,52 I 0,61.10 -3 _{I 0,64.10}

-3

-

_{0,24 m/soc} v

₌

Q 7,8.10- 3 m3/sec v :::I 0,19 m/sec Q

=

2,85.10-3 m3/sec assumed ripple roughness: _{assumed ripple roughl"ess}

k

=

1/3 ripple height

=

k

=

1/3 ripple height

=

0.8 em 2 em

These values may be compared with the results of the measurements.

4.2. Side wall influence

In consideration of the limited width of the channel it was

necessary to take the roughness of the side-walls into account when cal

-culating the bottom roughness from the experimental results. This Was

clone in the following manner.

)

V velocity~ R

=

hydraulic radius~ I

=

slope of energy line,

C

=

a coefficient of roughness, ,based on the logarithmic velocity

dis-12 R tribution

=

18 log k + 6/4 1

K = a roughness factor for the material considered or the bed form,

6 = the thickness of the laminar sublayer (in case of movable bed

negligible).

(1) Assume first that the walls

of the channel are perfectly

smooth, i.e. there is no wall friction. Then thus hxB ~

=

13

=

h.

v

2 C 2 h b

'f

t

I

j---~

Subscript 'b' refers to conditions as result of bottom roughness only.

(II) Maintaining the same velocity, assume now that the bottom is completely frictionless. Then thus Also: C w hxB B Rw =

2h

=

2' •

I _w

=

2V2 C 2 B w ========== 6B 18 log k + 6/4 • w

Subscript 'Wi refers to conditions

as result of wall friction only.

Thus I _w is seen to be independent of the depth/ of water (h), and to tend to zero as

'B'

increases. Combining:

or

) C 2 B w Putting C t 2 + 2C_b2 h ..I

When Itotal is knovm,

we have

C 2

b _[

C2C2B

t w

The ""vall roughness C can be found by assuming a v'alue of k for the

w wall material.

4.3.

Bar resistance

I t vvas proposed that the artificial roughness should. take the form

of wire spokes suspended from a framework over de channel, and extending

into the bottom material.

Two reports (Ref. 1 + 2) were found to exist which investigate the

effect of such vertical roughness elements on the flow of water in fixed

bed channels. The latter of these reports w~s used to estimate the

necessary density of the roughness elements, and the results obtained

were compared with the graphs given in the former report. The agreement

was satisfactory.

Methodg

Consider a reach, length L, of a channel having depth h and breadth

B. The resistance to flow in this channel will beg

2

pgh BLI

=

pgh BL

-Y--e C2 R

(1)

Now imagine a bar, width b, to be immersed in the stream over a

depth h. The resistance offered to the flow by this bar will beg

CD

=

Drag coefficient,

and if there are In' such bars introduced, the total resistance offered

by the bars iss

n 2

Thus1 the total resistance to flow will now beg )

2 [1 n •

~

CD bh ] pg FLV

;r-

+ FL

C R g where F

=

hxB.

Alternatively, by assuming a new roughness coefficient C' for the channel with bars, the total resistance can be written:

Thus, or pg FL V 2 C,2 R pg FL V 2

2~

C,2 _R

=

pg FLV

_c

2 + R n

=

2g FLLL 1

1

CD bhI.C;2-~

-

C2 R

n.t

CD bh

1

g FL )

Further1 the number of bars per unit surface area

n'

4.4.

Bar spacing for a particular case.

The value of C for the stages of transport and material used is in

~

the region of 30 m2 /s. For the proposed model which brough about the ~ inception of these tests, it was required to reduce this value to

18

m2/s~

1-..

i.e. C

=

30 m:?'/s

The spokes used as roughness elements had a diameter of 3 mm (= d), and

the value of'C_D1 from graphs (Ref 3) for cylindricql bodies is 1.2

with h

=

0.1 m and B

=

0.30 m:

, '_ 2x9 0 81 \" 1

n - . 2

1.2x3xlO-3xO.l (18)

For practical reasons a density of

66.7

bars per square meter was

aclopted; the spacing being as shoym. ~<J (~·i4 " •

4.5. The slope (Ill) by only the bars.

The resistance to flow caused by the bars can be written either (I) As the force offered by the bars to the waters

n 2

2'

CD bh pV , or

(II) In terr.;s of the slope, I R, produced by the bars, (small slopes being

addative): Thus: or pg FLI R" n CD bh pV2 2 pg FL n CD b V2 L.B.2g n' C b V2 D 2g withs F

=

hxB

It is to be noted that the slope is independent of the water depth.

5.

Calculations of the results

5.1.

Determination of bar resistance for two waterdepths 0 Test no .. V.

No movable bed.

(1)

Deep water case No bars: Q 8.36xlO-3

m

3

/s.

h 11.15x10-2 m.

-3

Ie 0.33xlO • V :: Q/Bh :: 0.25 mist R :: 0.064 m. With bars (b

=

3

mm):

Q

~

8.36xlO-3

m

3

/s.

hI = 11.72x10-2 m.

-

3

I'=0.99x10. _e

-,

V

=

0.238 mist R'~ 0.066 m.

1],10 obtain the Itota1 which is the combined influence of bottom and walls,

for the case with bars, the measured slope Ie must be reduoed in the

following way: I total V,2/R1 -~=-xI. V2/R e

It is assumed that with the small change in R~ the C value is constant. One finds 8 '

Itotal = 0.88 Ie = 0.29xI0-3, thus IR

=

~'e

- Itotal

=

0.1xI0-3,

which is the slope due to the bar resistance only. The value of CJ) can now be found from:

n' C bV2

I _R = _2g J) _CJ) = 1.2l·

The assumed value of CJ)

=

1,2 is thus correct.

(2) Shallow water case. h

=

6.2 and 6.5xlO-2 m.

In

the same way as for (1), the following values, are foundt

I = 0.90 I 0.11xI0- 3 (II = 0.55xlO- 3 )

total e e

I _R

=

0.)8Xl0- 3 and _CJ) =

l.dl.

The graph from Rouse gives a value CJ)

=

1.3 for Re

=

480.

The above values for CJ) are very close to the values given by

Rouse for a cylindrical body.

5.2. Wall friction. Test no. V.

From the two tests without bars, the C value~ of the'channel can

be calculated and from this Ch~zy roughness value, the k value can be

found.

(1) Deep water case.

:L '

C

=

54.3 m2/s, giving k

=

5xlO-4 m. (2) Shallow water case. _,

C = 51.3 m

2

/s₉ giving k

=

0.6xI0-4 m.

In the latter case9 the laminar sublayer becomes important,

there-fore tho first value of k is more reliable./

5.3. Test no. I. J)eep water9 no bars.

- -3 3 Q 8 • 4 Oxl 0 m / s.

=

66.6 N/hr.

h

= 0.121 m. '" 4.5xI0-6'm2/s 0',232 m/s

-3

lEI = I

=

0.16x10 • total

Thus: )

=

0.182

d 3/2

I{6g

In

Assuming Frijlink transport formula₁ from graph, figure 1, which

gives

6.d

8

4

f.l.hIb

= •

t 60d h 1

In the parame er~, the slope is that one to the bottom s ear on y.

f.l. b

v

2

₌

C 2

h

I

=

C b 2

_h

_I b, t total and C 2 C ·2 ] 2 t w

~

=

C 2B _ 2C 2

h

2

V

2 C

=

--:...--t

h

I total Wall friction C • w w t ~ or C t = 24.2 m-fi/s.

Assume that the roughness factor1 k, for the walls

=

From Thusa or R B w

=

2

= R 0.15 w 600.

-

_a

=

=

2.5xlO-

4

R = V.R w

₌

0.232xO.15 e the C 2 b

-

v graph, 10-6 according to

=

3.5xlO •

4

Thijsseg =

676,

Energy slope due tolbottom friction onlys

-

3

=

0.66xlO I w

-3

=

O.lOxlO •

Now Il can be found from:

or

For the preliminary calculations, Il = 0.44 was found vdth the

assumption of k

=

~

ripple height. In reality, k is much bigger, even

~ then the ripple height, which results in a lower Il value for the

same transport conditions.

5.4.

Test no. II. Deep water, with bars.

-

_Q

₌

_8.47xlO

-

3 3/

_{m s. Tb}l

₌

_{67.6 .N/hr.} h = ,2.119 mo - Q . V

=

--

=

0.237 m/s. Eh -3 I E

=

1.34xlO • Thus: d 3/2

.

'{6g

m

-6

2/

4.56xlO m s.

Slope due to the artificial roughness (CD

=

1.21, see

Wi th C

₌

w nl _{C b V}2 Ii)

=

D 1\ 2gj _ 66.7xl.21x3xlO-3x(O.237)2 - 2x9.81 I total ( ) -3 -3

c It34-0.69 xlO

=

0.65xlO •

C 2 -2 V _727, 1. Ct

=

27 m2/s.

=

= or t

_h

I total 1. 60 m2/s8 2 1. C_b = 866, or C b

=

29.4 m2/s~

Slope due to bottom friction onlys

-2

Ib V Oo,2,2xlO- 3 I -3

C 2 _h = w

=

O.lOxlO •

Tb

From figure 1, when --~~---

-d 3/2

Vzg

-m

or

5.5. Interpretation of the results of test no.'s I and II.

Test I and II were done with virtually the same flow conditions

and the same rate of transport.

Nevertheless for test II a larger ripple factor must be introduced

to bring the transport in accordance with Frijlinks formulau This

in-crease in~ is caused by the reduction of Ib which was measured

(0.55xlO- 3 against 0.66xI0- 3 ). Thus the bars influence the bottom

roughness.

In the above case, the bottom roughness is reduced by the presence

of the bars. This is in accordance with the observation that the ripples

of :test no. II were somewhat smaller than for for test no. I.

In a practical case where one wants to increase a model slope, by

means of bars, from 11 to 12 (or increase the roughness from C_l to _{C2 )} the slope due to the bars should be IR

=

~ (1

2 - 11), where ~ is a

correction factor to introduce the change of bottom roughness due to the presence of the bars.

For the particular conditions of test I and I I is found from:

=

0.69

=

1. 24-0.66 1.19.

The required base spacing will then be (see 4.3)8

2g

[1

1

]

CD bR C,2 - C2 .

After elimination of the wall friction for test 11(1 - Iw

=

(1.34-0.10)xlO-3

=

1.24xlO-3 ) the

Ch~zy

roughness Gleis found frome

:L

or C'

=

19.5 m2

/sG

1 1

5.6. Test no. III. Shallow water, no bar3. Thus:

-

-

3 3/

Q : 3.1OxlO m s.

h :

0.062 m.

V :

h

En

:

0.167 m/s • .

-

3

IE: Itotal : 0.99xlO

0.044. d 3/2

\fig

m Tlb : 16.2 N/hr. T 16.2 1 09 10-6 2/ b : 360OxO.3x9.81x1400

=

. x m s.

From figure 1, when

d 3/2

V6g

=

m

In the same way as before, one finds a

&.:.L :

12.6

.-IJ.hlb

~

C

t

=

3103 m-2js.

As before C

=

60 (independent of depth),

w 1.. and Cb

=

21.8 m2_/s. Thus: and thus IJ. : 0.292.

5.7.

Test no.

IV.

Shallow water,

Thus:

-

_{Q : 3.1OxlO}

-

3

_m

3/

_s.

h :

0.:.074 m.

V

=

-9

=

0.140 m/s

bh

-

3

I E

=

1.37xlO • 0.°44. d

3/21.J(;g

=

m and I

=

0.05xlO- 3, w with bars. t 16.2 N/hr. Tb

=

Tb

=

1.11xlO . -6 m

2/

8.

Thusg and ~ C b

=

15.9 m

2

_/s.

-2 V C 2

Ii

b

=

66.7x.147xO.3xlO-3 (0.140)2

2z9.81

=

0.29

x

10-3

and 6d From fig. 1 ~ 1. Ilhlb Tb

12.6

when --~~--- -d

3/2

I/6g -

0.044,

Il

=

0.22.

m

5.8.

Interpretation of the results from test no.'s III and IV.

For the shallow water, the opposite influence of the bars and the

bottom roughness is found. The ripple factor is smaller in the case

with bars or in other word~ with the same flow- and transport 90nditions,

a greater bottom roughness (or a smaller C

b value) is obtained, when,

the bars are introduced.

A possible explanation for this unexpected increased bottom

rough-ness can perhaps be found from the fact that without bars, the flow was

slightly meandering, thus following a relatively deep channel. With bars,

the meandering was stopped~ and flow had to pass over more pronounced

ripples.

In this case, the ~ value as defined under

5.5

becomes~

~

=

0.29

=

thus smaller th~n onel

1.33-0.94

Vfuen the wal~ friction is eliminated again, the Chazy factor

Ct 2

_'V

2

_(I

_-

_I

_ii)

_{= 197}

e w

or

,

J.

d-_ ~

The overall roughness is thus increased from 21.8 m2/s to 14 m2/s.

5.9

Ripple sizes and celerities.

The photographically.recordG~ ripple dimentions for test no.'s I and II are summarized in fig.'s 6~ 7 and 8.

When the assumption is made that the shape of the ripples is triangular, the bedload can be calculated.

For test no. I.

-2

Mean ripple height 4.OxlO m. Width of channel B

=

0.3 m.

11 11 celerity 1.76 m/hr.

Tb'

=

ixO.04xO.3xl.76

=

10.5xlO-3 m3/hr (1 litre mixture contains 6.55 N dry material) = .§2 N/hr.

Feeding rate was 66.6 N/hr. For test no. II.

-2 Mean ripple height 3.7xlO m.

11 11 celerity 1.5 m/hr.

Tb I =

~-xO.

037xO.3xl.5 = 8035xlO- 3 m3/hr =

2i

N/hr ..

Feeding rate was 67.6 N/hr.

However, in the latter case more transport in suspension (due to the bars) took place, which of course is not included in the 54 N/hr.

,-6. Conclusi'.Jns and recommendations.

The following conclusions can be drawn as regards the influence of

artificial bar resistance in a model with movable bed.

a) The bars influence the bottom configuration, and thus the bottom roughness or ripple sizes also.

Using the same flow rate Q, waterdepth h and transport T, both in

the case with bars and without bars, for a waterdepth of approx .. 10 em

the bottom roughness was reduced by the bars and for approx. 5 em an increased bottom roughness was found.

b) A reduction of bottom roughness can partly be explained by the more

rectangular velocity distribut~on as a result of the bar resistance

and by the abi;Li ty of· the bars, to bring sediment in suspension in

)

c) In the case of the shallow water-depth, it was observed that a certain

amount of meandering. occurred in the case without bars1 thus on the

average a deeper channel with consequently lower resistance was

available.

By putting in rods, the meandering waS prevented and the flow was

forced to go straighter. The increased bottom roughness may be

ex-plainedby this phenomenon.

However1 insufficient test results are available to draw a definite conclusion as regards to this.

d) For the waterdepths tested, the channel roughness can be increased

by using bars •.

For deep water, the Chezy coefficient was reduced by 0.6 and for

shallow water by 0.64.

e) The method can be applied to models, provided the ~ value for the

major flow stages is known.

The required rod density is given by:

When the depth is.halved, nt will be double, but in that case ~ will

reduced up to

35%,

which for a great part compensates for the

re-duced _{depth 1 thus reducing the difference of n' for different depths}

a great deal.

In view of the above ·conclusions, the following recommendations can

be made:

a) More tests should be done, with different waterdepths, to ensure

that the obtained results ar~ representative.

Especially for shallow water, it should be tried to eliminate any

difference in flow conditions· (Le. meandering) which may affect the

results. For this purpose a thin model plate could subdivide the ohannel in the middle such as to reduce the channel width and any

possible meandering.

b) Because there are ·so many varibales, it seems better to test particular conditions for a certain model, rather then try to find a general

rule. For instance in the case of a Niger model, a certain increase of roughness of the Benue is necessary.

The bar spacings can be calculated, when a value for ~ is assumed, for each main river stage. When n' is found, each river stage should be tested in two flumes with different widths and the correct values for

n

determined from the test results.

If neoessary, n' can be adjusted untill the assumed value of

n

coincides with the value found from the tests.

B b C C' C gr CD d m d 90 g H h I e Ib = = =

=

= ::: ::: ::: ::: I = VI Itotal = .I R k = Q :;: )Nomenclature width of channel

diameter of roughness elements

12 R

Ch6zy resistance coefficient

=

18 log K +

'6/4

Resistance coefficient

d~fined

by C'

=

V2/RI _e

Chezy coefficient, assuming no wall friction

Chazy coefficient, assuming no bottom friction

a measure of combined wall and bottom resistance defined by

C

t

2

=

[:b:

:W:

:c

2

h

l

W b

j

18 1 _{og d90} 12h ( ' _{graln roug} h _{ness ac or} f t )

drag coefficient

mean diameter of the bed material

che diameter for which

90%

of the material is smaller

acceleration of gravity water depth (V-notoh)

water depth

slope of energy line

slope due to bottom roughness only

slope due to wall roughness only

Ib + I _vv

slope due to roughness. elements only

roughness factor (or a

=

~)

disoharge

R hydraulic radius of the channel

\ hydraulic radius assuming

no

wall friotion

n

'if R e T_' b Tb V !~ v ps r'" I"' .. = = :::

hydraulio radius assuming no bottom friction VR

Reynolds' no. v total transport

transport per m width

velooity of flow

thiokness 'of laminar sublayer

es ...

ew

pw

r

:-3/2

ripple fact or -.;'

%--

J

= Viscosity of wate~r

:::

denSity of bed material

\

I I \ Ad JlRI 25 20 15 10 5

a

0.001

\

1\

0.01 0.1

FR'JlINK'S BEDLOAD FORMULA

\

~

.

\

10

I

I

)

V

"

lI. TRANSPORTED MATERJAL

11

v-

I

.

u

v

'

1/

I. BASE MATERIAL 99 "

if

.

95

1/

~I

8£ __

_{- -}

_{- -}

-f - -l - i- -

- - - -

I - - -90 0:: 80 UJ -l -l <! 70 1: til ~ 60 50 40 ~ _IJ 0 ~

W.

LI'I

~~

vll'

/ /1 30 20

//j

D ,

rJ6 _

_

_{- -}

--~

~

f - I - ~

-

-_{1 - - - -'.- -~---}

~--VI

BAKELITE/,s = 1400 kg/m 3

/;

V

I. d₅₀

=

570 )oJ d m = 540 )oJ V-= 1.38

/

d gO =760JJ 10 5

LJ

[7

7

II. d 50 d m = 570}J = 540 JJ q-

=

1.30

V

d gO

=

740 jJ /J

V

0.1 o 0.1 0.15 0.2 0.3 0.4 0.5 0.6 O.B 1.0 2 3 5 GRAINSIZE IN mm B

SIZE DISTRIBUTION CURVES BAKELITE \1., .. ...,.. .... _ _ _ . •. . . . _ . _ . .. _ _ _ • ____ _ .~ .~ ..

I

( I ) NO ARTIFICIAL ROUGHNESS

I

-io

.45 --I )

!

"0 - -f I ₃₅

-I

I

30 1-. MEAN, HEIGHT. 4.0 ems

I

28 READINGS 25

t

-20 -I-,

I

I 15

-

-I I 10 - -: I I S

-0

I

1-1.5 2-2.5 3-3.5 4-4.5 5-5.5 6-6.5 I 7-7.5 I _ems ,

I

I I I

!

_{(II )}

WITH ARTIFICIAL ROUGHNESS

I

0;0

50

-: 1 4S l-I 40 -I-, I 30

30 I- MEAN HEiGHT

=

3.7 ems

, 33 READINGS

,

!

,

₂₅ ro ' I I ₂₀ -I-I 15 -, _, 10 l-S _\ 0 2-2.5 3-3.5 4-4.5 5-5.5 6-6.5 ems I -

a

HISTOGRAM

_O

_F

_{RIPPLE HEIGHTS "DEEp}H WATER . ... .l'

'hj

_b

, . B -

-r

( I ) NO ARTIFICIAL ROUGHNESS I

I

Yo

45 ,...

I

, 40 f- , 35 I-, 30 I-" "

MEAN LENGTH - 40,S em.

17 READINGS 25 I-20 I-15 I-10 f-5 I -0 15-25 25-35 35-'5 '5-55 55-65 65-75 ems

'-( rr) WITH ARTIFICIAL ROU GHNESS

.

io

50

-r-,

45

40

35

l-I

30 - MEAN LENGTH = 31.0 em.

34 READINGS 1

!

25 - " 20 - l-I I ₁₅ -I 10

I

5

l-I

0 15-25 25-35 35-45 '5 -55 ems I ! 8 I

HISTOGRAM

_O

_F

_{RIPPLE ,LENGTH "DEEP" WATER}

-

h

7

( I ·) _{NO ARTIFICIAL ROUGHNESS} 45

-r-%

40 - .. 35 f- _... 30 - MEAN CELERITY

=

1.76 m/hr 23 READINGS 25 -I 20 -I I 15 -l-I 10 5 -0 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 i m/hr

( IT) WITH ARTIFICIAL ROUGHNESS 50 1-.

10

45

-., 40 r

.

,

35 f--I I I J MEAN CELERITV ·1.50 m/hr I ₃₀ -33 READINGS 25 r-20- f--I 15 ~ 10 r 5 - I-a .0 -0.5 0.5-1.0 1.0-1.5 1.5 -2.0 2.0- 2.5 2.5-3.0 m/hr .

,

I

B

,

l

HISTOGRAM _{OF RIPPLE CELERITY "DEEP"WATER}

~

I

WATERLOOPKUNDIG LABORArORIUM 580

I

FIG. 8

\

-Tests with dune sand Contents ~ 1. Introduction ₁ 2. Test results ₂ 3. Calculations

₃

4. Conclusions ₁

5.

Estimate of _{error in /J. (test}

₄₎

₈

Figures

1. Size distribution ourves

Photographs

1. _{Ripple photots test no. 1}

2. Ripple photo's test no. ₃

movable bed models

Tests .~1th dune sand

1. Introduction

The tests desoribed in the following were the second in a series to find the effect of artificial roughness in movable bed models.

These tests were carried out in the same way as the first series except that in this case the bed material waS dune sand where-ns previously it was bake1iteQ A description of the apparatus and test procedure is given in the first report.

The test performed using sand as bed material were:

Test 1. Nominal 10 cm waterdepth without articificial roughness Test 2. Test 3~ Test

4.

II

"

II 10

5

5

em

_"

em II em 11

These were carried out by Messrs. S.R. GRAVELING A. O. MAY P. ROOVERS, with II 11 11 without 11

of the 1961/62 International Course in Hydraulic Engineeringe

II 11

"

/ , ,

I

I

I'

I

,

, I I' "

,

:1 II I, I I I I I' I

II

11 'I 1\ 1\ \1 ,\

2. 'l'est results

The average values are summarieed in the table below.

Deep water Shallow water

Quantity No rods With rods With rods No rods

test no.l test no.2 no.3 no.4

Q

(in 10-3 m3/s) 12.3 1203 4.87 4.87

b: (waterdepth 11.8 11.8

-2 ) in 10 m

I ( energyslope) 1. 7xlO-3

e 3.1xlO- 3 2.9xlO-3 4.1xlO- 3

T t (total bedloac 2.8 2.8 2·4 2.8 in l/hr)

v

measured ve- 34.2 29.2 2703 25 locity in 10 -2 m s

Ii

v

= 'Q

/b.b: 34.5 34.5 28 28 -2 / in 10 m s

Size distribution curves of the feeding matering and the transported material are shown in fig. 1.

Photographs were taken at periods of 5 and 10 min. to obtain some value of the ripple sizes and propagation. Unfortunately

photo-graphs were not taken during the second test owing to the heavy rain-fall at the-time.

3. Caloulations

The calculations are given in the table below. They were basic-ally the same as for tho first series of tests. 'llhe calculations for

test No.2 carry a small doubt because the -recorded readings for the

slope of the energy line were 1 em less than shown (see Appendix 2).

This original value, however, gave results which were highly improbable

and it was thus concludecl that an error of 1 em had been made. This can happen if one reads at the 'wrong' end of a vernier scale, which on a rainy day and with an instrument not clearly marked, is quite possible.

...

Calculation formula , Measurements

v

:

;

B~

1

Yvhere B=0.30 m I Q V

(,

"I

B. h vIlle =-

\(ffi"

i

('\A-; 18

109(11h \

tI' , d_{90 )} - 1 b .t f<. ~ 2TI CD B w-h-,re • v 2 g C)=1.20 for h=O.ll m c"/1.30 for h=0.06 m ~! =3xlO-3 m \

z:.

(

IR + Ib I

e

3/2

f:

'

\

e

b ) ,gives

grr

gives

Test No. 1 Nominal 10 cm no bars I Dune sandy p = 2650 kg/m 3 s \ d m Q I e h T' _b = = = = = = 210 ~, d 90 = 300 ~ 12.3 l/sec 1. 7xlO-3 11.8 em 4.4 l/hr (wet) 2.8 l/hr (dry)

Neglecting wall roughness _~

0.0123 / V = O.3xO.118 = 0.345 m s C'= 0.345 -24. 6m

ts

VO.1l8x1.7xlO-

3

C =18 log 12xO.118

=66m~}

/s gr 3x10-4 , ~ C_b=C_t=C'=24. 6 m2/s Test No. 2 Nominal 10 em with bars Dune sand, p _s = 2650 kg/m3 d m = 210 ~, d90 = 300 ~ Q

= 12.3 l/see

Ie = 3 .1xl 0-3 h

=

11.8 em

Tb

= 4.4 l/hr

(wet) = 2.8 l/hr (dry)

Neglecting wall roughness

0.0123 / V

=

0.3xO.118 = 0.345 m s :L C'= 0.345 = 18m2

/s

Vo.

118x3

.1~10-3

-3 2 I _1 2Ox1 2(}..{3x l O :x;0.345 R 2JC • 0.3 9.81 :L C =C

=

0.345 24 6

2/

b t --~ . 3 • m s

VO.118xl.65xlO-~

=

(2:6

6

)3/

2

"

0

.23

4.35x10:'

5

~ = - -... """--=----~ ::2 0.224 0.118x1.65xl0- 3

,

"

Calculation formula

-C :::18 log 12XI3/2 where

w K ~

~

Kis assumed = 5xl04 m

Test No. I - (con.)

Consi'dering wall roughness

C =18 log 12xO.3/2 = w 5x10-4

v

2 2 I = = 0.345 x2 ::: W C w 2 B/2 642xO.30 , = 0.2xI0-3 I =I -I

=

(1.7-0.2)xI0-3 b e w = 1.5xI0-3 1 C b = 26.2

'

m

2/s 0.25

-5

I.! = 4.35x10

=

0.25 0.118xl.5xIO- 3

Calculations of ripple Neglecting wall roughness

heights C x C C I _ b gr ripple

-\/0

2 -:

c2 ' gr b ( _v-ipple = , 18 1 og -121 _K j(' ripple height Q,alculation of y) rR giving k = 5.4 cm

Considering wall roughness

c

-

26.2x66 =

28.5m

i

p

ripple-V662_26:22

giving K = 3.7 cm

Test No.2 - (con.)

Considering wall roughness

I = 0.2xI0- 3

VI

,,__ 4035xI0-5 6

~ = 0.2

0.118xl.45xI0- 3

Negleoting wall roughness

giving k = ~.4 om

Considering wall roughness

C = 26.3x66 =28e5mi/s

ripple

V662

-

26:)2

-Calculation formula Formula as given in

{

Appendix 10.

_I

i \ Measurements

(

~

l

Test No. 3 Nominal 5 cm with bars Dune sand 1 _Ps : ; 2650 kg/m3 d : ; 210 111 d 90= 300 Il m Q : ; 4.87 l/sec I : ; 2.9xlO- 3 e h : ; 5.76 cm TI : ; 3.8 l/hr (wet) b : ; 2.4 l/hr (dry)

Neglecting wall roughness

v - 0.00487 :; 0.28 m/s

- O. 3xO. 0576

Test No. 4 Nominal 5 cm without bar Dune sand 1 P :; 2650 kg/m3 s d : ; 210 111 d 90= 300 Il m Q : ; 4.87 l/sec I : ; 4.lxlO- 3 e h = 5.83 cm T' = 4.4 l/hr (wet) b : ; 2.8 l/hr (dry)

Neglecting wall roughness v - 0.00487

=

0.28 m/s

- 0.3xO.0583

C =18 log 12xO.0576 60.5mi/s C

gr 3xlO-4 gr -3 2 I _R-2X -~ 2~nl.30x3xlO _{vx 0.3 x 4.81} 0.28 :; lxlO-3 C b= . _._ .. O.

2~

27 mils VO.0576xl.9XlO-3

_

1..1L)3/2

_

Il - ~ 60.5 - 0.)0 Il

=

4.l5xlO-5 0.0576x1.9xlO-3 :; 0.38 ~ C b :; Ct

=

0' :; 18 m2/s I

181

3/ 2 Il :; ( 60.5! :; 0.~6 4.35xlO-5

Calculation formula Formula as given in Appendix 11 Calculations of ripple heights Calculation of

n

'[ =: '=--_ _

1

.;;.;

R

~

__ -Ib + I - I TTT R bTU

Test

No.3 -

(con.) Considering wall roughness

v

2 I -

=

w C 2 B w '2

-3

= 0.2xlO

=

1b=1e-1w-1R=(2.9- 0.2-l)Xl0-3

-

3

= 1.7xlO

c

0.28

b

=Vo-:

0576~i.

;ixlO- 3 .. 28 \ 3/2 II - /~, - 0 32 f'" -

n

,

0

o. 5/

- .

-5

I.l. = 4.15xlO

=

0.43 O. 0576xl. 7xlO- 5

Neglecting wall roughness

giving K

=

1.65 em

Considering wall roughness C. 1 - 60.5x28 =31.5mi/s

rlpp

e-V60:52_282

giving K

=

1.2 em

1

n

=

2.7-3.9

= -

0.83

Test

No.4

-

(con.) Considering wall roughness

1 C t

=

18

m

2

_/s

182x642X302 I = 0.2xl03 w Ib=1 -I =(4.l- 0 .2)xlO-3 e w = 3.9xlO-3

(

~\3/2 I.l. = '. 60.5) = 0.17

-5

4.35xl0 = 0.19 O. 0583x3 .9xlO-3 I.l.

=

Neglecting wall roughness

giving K

=

6.2 em

giving K

=

6 em

4.

Conclusions and recommendations

From the results of the tests the following can be said.

a) There is a good agreement of the average velocity, fourid by

measure-ment of discharge and waterdepth~ with the velocity measured by the

current meter, except in test No.2, where the difference is about

15%.

b) The measured Quantity of the material leaving the flume and that

in-troduced to the flume were practically the same.

c) Comparison of photographs those fo~ tests 3 and 4 (5 cm depth) shows

that~ without artificial roughness~ the ripples are very unregular

and high9 but that with artificial roughness they are much more

regular and lower.

d) The influence of the wall roughness of the flume is small, having

about

5%

effeot on C values and

5-10%

on ~ values.

e) Introducing artificial roughness by bars does not necessarily increase the total roughness because the bars cause much more regular and

lower ripples.

For the

10

cm testss

1

The Chezy coefficient C'(=

-1-)

changes from

24.6

to

18

m2 /sec when

RIe 1

bars are introduced~

C

_b changes only from

26.2

to

26.3

m2/s9c.

For the

5

em tests~

1

Here C' increases from

18

to

21.7

m2/sec, C

t increases from

18

to

1 1

26.7

m2/sec and

C

_b increases from

18.3

to

28

m2/eec.

The above results suggest that the artificial roughness has more effect on the bed formation at small water depths than at large ones. f) Introduction of artificial roughness causes the following effects on

the ripple factorg

For

5

oms There is an increase from

0.19

to

0.430

For lOcm: There is little change i.e.

0.25

to

0.26.

g) ~ good agreement exists between values Of/~ calculated from Frijlinkts

Ct 3 2

transport formula and values of Il = (·0) ~

gr

For the

5

cm test with artificial roughness the difference was about

25%.

For the rest, differences were within

10%.

h) An estimate of the 'probable error' involved in making the calculations

5.

Estimate of error in ~ (test 4)

The value of ~ was determined from

where

7V

is determined from Frijlinks

In the neighbourhood of the test values of ~ ~ ~ varies with the

1/3 power of

p.

Thus

The error ins T waS estimated to be 10%, that in ~ 2% and the

error in d

5%.

The error in h and I could be estimated from the measurements. The standard error in the mean value is

s '

V'<th-h~2

n n-l

Where h is the individual reading,

h

is the mean depth and n is the number of observations. s has been found for both upstream and down-stream measurements. For upstream e(h-h)2

=

19.8 s

=

0.15 em. For downstream e (h-h)

=

29.3 s = 0.18 em 2 em 2 em n

=

30 n

=

30

h

= 6.08

h

=

5.83 em

So the standard error in the mean depth from both upstream and

down-stream measurements together amounts to s

=

0.2 erne

Standard error with slope I

orientation.

- 2 8

8 (I-I)

=

48xlO- n

=

10 · I =; 4.1xlO

-3

s

=

0.07xlO-3 • Together with an error in the pitot tube

-3

01 = O.lOxlO •

I,

I Ii

II

II

I'

II

II

'I

II

,I

I

Summarized T = 2.8 l/hr _°T = 0.28 l/hr 6 =

1.65

°6 = 0.03

d

= 210 /J. °d

=

10 /J.

h

=

5.95

em °h = 0.2 em

r

= 4.1x10- 3

or

= 0.lOxlO- 3

The maximum error is given by.

2.t!.=1~+2M+*M+.§1l+g

=8 ct!

/J. 3 T 6 6. " d h

r

.5

1°

For the test with bars the error in /J. will be larger as a

-

, ) 99.9 99

V

0:: ₉₅

/

UJ

1/ .

..J ..J <l: ₉₀ .. :L

V

VI

;:

~. 80

/1

0 70

I

60

/

50 40

I

30 20

fI

It

-10 .. 5 I.

I

1

If'

~

~ 0.1 . / V 0.05 0.07 0.1 0.15 0.2 0.3 . 00.4 _{0.5 1.0} GRAIN SIZE IN mm BOTTOM MATERIAL

- - - -

SAND TRAP MATERIAL

B

SIZE DISTRIBUTION CURVES DUNE SAND

o .