Researctt
fnttOrattlcs
\Ahllurgrford
SELF-CLEAIIS
ING CONDITIONS
FOR SEWERSCARRYTNGSEDIMENT
by
R W P May, P M Brown, G R Hare and K D Jones
Report SR 221
December1989
Registered Office: Hydraulics Research Limited,
lirallingford, Oxfordshire OX10 8BA.
Telephone: 0491 35381. Telex: 848552
This report describes work funded by the Department of the Environment under
Research Contract No DGRPECD7/6/82. It is published on behalf of the
Department of the Environment, but any opinions eqlressed in this report are
not necessarily those of the funding Departruent. The work nas carried out
in the River Engineering Department of Hydraulics Research, Wallingford
headed by Dr W R White. Ttre nominated project officers were Dr R P
ltrorogood for DoE and Dr W R White for HR.
@
Crovn Copyright
Published
Office.
1989
by perrnission
of the Controller
of Her Majesty's
Stationery
ABSTRACT
An ocperinental study, funded by the Department of the Environment, was made
of the factors governLng the deposltion- of non-cohesive sedj.ment ln a 300rrn
dlameter concrete pipe. Tests were carried out with 0.72m:r sand uslng f1t;
velocities between 0.5mls and 1.5mls, proportlonal depths of flow between
3/8-fu11 end pipe-full
and volumetric lediment eoncenlratLons between 0.3ppm
and 440ppm. TLre-20nlength of concrete pipe was installed in a tlltlng
flume equlppgd with separate re-circulation
systens for water and sediient.
A 19* optical device was developed for contlnuously measuring the rate of
sediment transport in the system.
Data for the linit of deposition in the concrete pipe \rere conpared wlth
previous HR results for smooth 77mn and 158rundiameier pipes .ird orittt
several available formulae. Analysi.s showed that the timiting sedlnent
concentrations in the concrete pipe were approximately half tfiose erqlected
in a smooth pipe of equal diamelei.
ghe reiuction in trensporting cipaclty
was e:<plained in terme of an increase in the threshold veloiity
oi tfrl
sedirnent in the rougher pipe. A forrnuLa for predicting the limit or
deposition in both rough and smooth pipes was-developel using all the HR
data. This can be used to estimate mrnirum flow velocities ior
self-cleanling
sewets based on pipe size, sediment size, depth of fLow and
rate of sediment transport.
Tests were also carried out with smal1 depths of sedlment deposition.
These showed that a mean sediment depth oi fZ of the pipe di-ameier enableE a
flow to transport significantly
more sedifient than at the limit of
deposition with
noincrease
in head loEs. Self-cleansing sewers
-effectively
designed for a lX sedjrnent depth could therefore be laid at fLatter minirnr:n
gradlents than those designed accordlng to a ,no-depos{tr criterion.
SYMBOLS
A
Cross-sectional
C
v
D
Volumetric
D-gr
d
Non-dimensional
d
mm
E
Sediment size
g
Acceleration
i
Hydraulic
k
Size of bed roughness
ks
k-ss's
L
Hydraulic
m
Gradient
n
Manning's roughness coefficient
P
Wetted perimeter
a
l{ater
a_
-s
R
Volumetric
Re
So
V
Reynolds number of flow
VL^
Ds
area of flow
sediment concentraLion
Pipe diameter (internal)
grain
(L2))
in nrn
energy of flow
due to gravity
gradient
of flow
roughness in Colebrook-White
formrla
Composite value of k_ for pipe with sedirnent
Laursenfs paraneter (Equation (18))
of specific
energy line
of flow
discharge
Hydraulic
Gradient
sediment discharge
radius
of flow
(= A/P)
(= 4VR/u)
of pipe invert
Mean flow velocity
Flow velocity
bed-load
at transition
from sediment movement as
to suspended-load
V.
Flow velocity
Vm
Minfunurn flow velocity
L
(Equation
(dro)
Mean sediment size
Specific
parameter
at limit
of deposition
corresponding
to specified
depth
of sediment deposit
V-
Ttrreshold velocity
V-_
Ert
V-_
Pipe
Value of V- for rough pipe
Value of V- for smooth pipe
w
FaIl
E
ESt
of isolated
sediment particle
X
of sediment particle
Parameter defined by Equation (30)
Y
Parameter defined by Equation
y
Depth of flow
O
Angle of pipe to horizontal
I
Darcy-Weisbach friction
u
Kinematic viscosity
of water
u m
p
Kinematic
of water-sediment
o
Standard deviation
r
s
o
velocity
Density
viscosity
(positive
upwards)
factor
of water
Mean shear stress
(32)
in pipe
mixture
in
CONTEMTS
Page
INTRODUCTION
1
SCOPEOF ST"I]DY
5
PREVIOUSSTUDIES
5
3.1
3.2
3.3
3.4
Definitions
Threshold of movement
Transport without movement
Transport with deposition
TEST ARRANGEUEM
4. I
4.2
10
General layout
Sedfunent concentration
5
7
B
13
15
measurement
15
18
EXPERIMENTALPROCEDURE
24
5. I
5.2
5.3
5.4
24
25
26
29
Clear-water roughness
Ttrreshold of movement
Limit of deposition
Deposited bed
EXPERIUENTALPGSULTS
30
6.1
6.2
6.3
6.4
6.5
30
35
36
42
43
Pipe friction
Threshold of movement
Lfunit of deposition
Unsteady flow conditions
Deposited bed
DISCUSSION
47
7.I
7.2
47
5L
Liait of deposition
Deposited bed
CONCLUSIONS
53
ACKNOWLEDGEUENTS
56
REFERENCES
57
TABLES
1
2
3
4
5
6
7
8
9
E:cperimental results
for 299run pipe - clear water resistance
Experimental results
for 299run pipe - limit
of deposition
E:qrerimental results
for 299nrn pipe - deposited bed
Values of ko for clear water in 299rrn pipe
Values of n-for clear water in 299nrn pipe
Values of tr for clear water in 299nunpipe
Measured and predicted
threshold velocities
in 299rnn pipe
Measured and predicted
at limit
of deposition
concentrations
HR data
Analysis of data for limit of deposition
- all
CONTENTS(CONTID)
FIGURES
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
L7
t8
19
20
2l
22
23
24
25
26
27
28
29
30
Layout of test rig
Detail of concrete pipe section showing slots and removable lids
Cross-section through sediment sensor
Schematic layout of sensor equipment
Sensor calibration
at 1.39 m/s
Sand grading
k" versus Reynolds nrxnber for clear water in 299mn pipe
Manning's n versus clear-water velocity
in 299rrn pipe
Lanbda versus Reynolds number for clear water in 299mmpipe
Head loss at limit of deposition - orperimental data for 299mm
pipe
Sediment concentration
at limit of deposition - errperimental data
for 299rrn pipe
Limit of deposj.tion - comparison of experimental data for 299rwrt
pipe with May's equations (pipe-fu11)
- comparison of experimental data for 299nm
Limit of deposition
pipe with May's equation (pipe 3/4-full)
- comparison of orperimental
Limit of deposition
data for 299nrn
pipe with Mayrs equations (pipe L/2-f.ull)
- comparison of experimental data for 299nrn
Limit of deposition
pipe with May's equations (pipe 3/8-full)
- comparison of experimental data for 299m
Lirnit of deposition
pipe with other equations (pipe-ful1)
- conparison of oqperimental data for 299nrn
Linit
of deposition
pipe with other equations (pipe 3/4-fu11)
- comparison of experimental data for 299rnn
Lfunit of deposition
pipe wi.th other equations (pipe !/2-f,u,ll)
- conparison of oqperimental data for 299nrn
Lfunit of deposition
pipe with other equations (pipe 3/8 full)
- HR data for 299nrn, 158nrn and 77wn pipes in
Lfunit of deposition
May's format
- HR data for 299rmn, L58mmand 77rrn pipes in
Lirnit of deposition
I
l{acke s format
- HR data for 299nm, l58nm and 77rmnpipes in
of deposition
Linit
llayerle & Nallurirs
format
Deposited bed * effect of deposited bed on sediment transport rate
in 299rrn pipe (pipe-full)
Deposited bed - effect of deposited bed on sediment transport rate
in 299nrn pipe (pipe 1/2-fu11)
Comparison of rneasured and predieted sediment concentrations
with
deposited beds in 299nrn pipe
Proportionate
change in friction
factor due to deposited beds in
299mmpipe
Change in koo roughness due to deposited beds in 299rrn pipe
- X versus d/R
Limit of delSsition
Linit of deposition - Y versus d/R
Limit of deposition - all HR data compared with Equation {32)
APPENDIX
A
Formulae for
fall
velocity
and kinernatic
viscosity
INTRODUCTION
It
has long been recognised
that
sediment deposits
sewers cause loss of flow capacity
surchargi.ng
and sometimes surface
problems were often
were usually
dealt
maintenance.
considered
with
television
to be localised
and
developments have
the adverse effects
the increased
Ttre
by means of routine
sewers are more serious
Firstly,
and can lead to
flooding.
However, two recent
demonstrated that
of sediments in
than previously
believed.
use of closed-circuit
equipment has shown that
se'lterage systems contain
large
significant
lengths
deposits.
of
A
a CIRIA (1987) research project
survey carried
out for
suggested that
up to 25,000km of sewers and drains
the IJK may be affected.
deposits
or flooding,
maximr:m flow
coping with
enough to cause regular
they will
stil-I
reduce the
of a system and prevent
capacity
the flood
in
Even though many such
may not be large
surcharging
in
event
for
it
was
which it
designed.
The second developnent
placed
is
on enviro:rmental
Storrmrater
the greater
aspects
sewerage systems,
combined, are responsible
of the pollution
watercourses,
enters
particularly
such as water
either
separate
estuaries,
for
or
rivers
in urban areas.
the biological
quality.
proportion
a significant
many of the pollutants
has shown that
responsible
that
for
emphasis now
and
Research
such as those
and chernical o:glgen
dernand become closely
associated
particles
Thus, sediments discharged
directly
in sewers.
from separate
storm sewer overflovs
pollution
with
storm water
in the receiving
therefore
transported
irnportant
through
sewers or from
in combined systems will
waters.
able to study methods of improving
is
the sediment
In order
water
to understand
cause
to be
quality,
how sediment
a sewerage system.
it
is
The build-up
of deposits
near storm sewer overflows
them to operate more frequently
thereby produce additional
Experimental
research
has been carried
than necessary and
pollution.
on sediment movement in sewers
Research (HR) since
out at Hydraulics
1975, under two studies
funded by the Department of
(DoE). fhe first
the Environnent
study between 1975
and 1982 was concerned principally
improved criterion
for
Experiments
diameter
smooth plastic
velocity
needed to prevent
concentration,
Results
were made using
developing
an
pipes,
77mm and 158rrn
and showed how the flow
the formation
of deposits
such as the sediment
particle
of this
with
the design of self-cleansing
sewers.
depended on factors
can also cause
size and pipe diameter.
study were described
in reports
by May
(1975 , L9B2).
The second study,
forms part
which is the subject
of the River
programme.
This is
research into
covers field
of sewers on rivers,
laboratory
are being carried
by the Regional
Directorate
model-s.
Indj.viclual
funding
(and their
l,Iater Authorities
the Science and Engineering
and the Construction
Industry
of DoE.
A major component of the prograrme
computational
water
quality
being developed at HR (with
the UK water
variations
and the
and HR, with
successor organisations),
Research Council
studies
and
out by the Water Research
Centre (WRe), universities
provided
prograrrne of
a co-ordinated
development of computational
projects
report,
Basin Management (RBM)
the effects
work,
of this
industry.
to determine
rates
The oqlerimental
model for
sewers, which is
DoE funding)
In order
in water quality
is MOSQITO, a
for
use by
to be able to predict
in sewers, it
of sediment deposition
is necessary
and erosion.
study on sedi:nent movement described
in this
report
extends
the scope of the
therefore
self-cleansing
information
has two functions
: it
1975-L982 work on
sewers and secondly provides
necessary for
the development of MOSQITO.
SCOPEOF STUDY
The principal
of the present
objective
study is
the development of improved guidelines
of self-cleansing
sewers carrying
practice
Current
for
sediment.
either
the flow velocity
the shear stress
produced by the flov
certain
value.
gpical
linked
shear stress.
with
minimum values
given depth of flow
with
Such limits
a requirement
a given
that
(eg with
minimun gradient
below which gravity
is
they are intended
contained
at a
fu1l)
or
(eg once a day on average for
freguency
of various
are usually
the pipe half
These conditions
survey
are in
and I N/nz to
they be achieved
combined sewer).
be lai.d if
or
exceeds a
the range 0.75m/s to l.Om/s for velocity
4 N/m2 for
the design
the design of self-cleansing
sewers is to ensure that
liniting
for
to aid
guidelines
lead to values
of
sewers should not
to be self-cleansing,
for
self-cleansi-ng
A
sewers
in Appendix G of CIRIA (1987)
Recent laboratory
studies,
i-ncluding
the work carried
out at HR under the first
DoE contract,
self-cleansing
cannot be defined
conditions
terms of a fixed
value of veloci.ty
showed that
sinply
in
or shear stress
but
need to take account of the rate
of sediment entering
the system,
of the sediment,
the diameter
include
the size
they were mostly
diameter.
usually
and density
of the pipe.
these extra
non-cohesive
a
factors
Various
formulae
sediments
in smooth pipes
Sediments in separate
remain non-cohesive,
they inay become coated with
which
have been developed,
based on experiments
and
carried
but
out with
of small
storm water
se\ilers
but in combined systems
biological
sljmes
and
(1988) classified
greases.
Crabtree
into
broad categories.
five
corresponds
deposits
sedirnent which forms bed
to the coarser
of granular
consists
organic
content
carried
out by Williams
material
of about 10%. Rtreological
(f989)
et al
was cohesive,
with
non-cohesive
applied
with
caution
will
it
conditions
diameter.
tested.
systems.
the
However,
sediments
is
to take
part
report
the resulti-ng
conditions
in order
size
Although
described
to
in
designed to investigate
pipes of 300run
in concrete
which are more typical
The results
of those
are
from previous
data and eguations
to identify
formulae
than those originally
used in many sewerage systems.
compared with
of
when extrapolated
of the new study
was, therefore,
and 450nm diarneter,
smooth pipes
out with
predictisns
larger
Itre first
self-cleansing
more accurately
studies
the effects
of
and texture.
earlier
have disagreed
studies
needed to prevent
conditions
most predict
with
A
on self-cleansing
Unfortunately,
pipes significantly
flow
that
be difficult
have been carried
give widely-differing
pipe
tests
account of cohesive effects.
As rnentioned, most studies
this
an
from laboratory
of non-cohesive
understood properly,
with
sediments may need to be
to conbined
the behaviour
it
on four $pe
indicated
so results
studies
small
showed that
sand and gravel
samples from sewers in Cardiff
correct
A material
$pe
in combined sewers; analysis
typically
until
sewer sediments
that
the required
pipe size.
increasing
the minim:m gradients
sedjment
flow velocity
The implication
of large
> 0.5m) should be steeper
specified
at present.
significantly
increases
is
that
than those
A change in design guidelines
research could,
increase
deposition,
se'rrers (eg having
diameters
based on recent
on the precise
the costs
therefore,
of new sewerage
schemes by requiring
is a possibility
adopted for
formation
that
the criterion
depths of sediment deposit
minimum flow velocity;
be argued that
ilhether
questions.
until
First1y,
to form, will
blocked?'
guestions
criteria
3
for
or will
are allowed
they grow in
the pipe surcharges or becomes
the additional
be large
capacity
was carried
enough to
of the study described
out to answer these
guidance
sewers carrying
hydraulic
of the sewer
The second part
and provide
form a
in the self-cleansing
due to the deposits
report
usually
sediment deposits
Secondly, will
significantly?
always remain
the next storm occurs.
they remain small
reduce the hydrauli.c
can also
depends on the answers to tvo
if
ultimately
resistance
It
the
of no sediment deposition
a storm and will
is justified
size until
to reduce the values of
pipe gradients.
or not a relaxation
criterion
under design
because some sediment will
deposit
small
in turn would allow
the eriterion
in a sewer after
stationary
If
are permitted
this
use of somewhat flatter
is a fiction
necessary.
may be possible
it
usually
- nannely, no
sediment deposits - may be
of stationary
conditions,
However,
conditions
"self-cleansingt'
more severe than is actually
in this
at greater
more punping would also be needed.
depths;
there
pipes to be laid
on suitable
design
sedi.ment.
PREVIOUS
STUDIES
3 . 1 Definitions
Sewers are usually
exactly
different
(a)
what this
required
means is
definitions
Ttrreshold
suffieient
to be rrself-cleansingrr
seldom made clear.
but
Three
can be envisaged:
of movement.
Flow conditions
to cause particles
to start
are just
moving
(either
along the pipe
along the srnooth invert
of
the pipe or over other deposited particles).
(b)
Transport
without
are sufficient
pipe
deposition.
to transport
at the rate
stationary
Flow conditions
sediment along the
without
(termed rrflume
at which it
deposits
enters
forming
traction").
(c)
Transport
with
sufficient
to transport
at the rate
Flow conditions
deposition.
at which it
sediment along the pipe
enters,
with
stationary
deposits
proportion
of the pipe dianeter.
Although the threshold
of movement is of interest,
appropriate
self-cleansing
conditions
is
deposits
rate
to increase
as a definition
zero;
viI1
continuously
recent
criterion,
require
in Section
steep gradients
of deposition
is
for
design
2 it
nay
larger
exceeded,
pipes.
separate
dunes tend to occur at the flow velocities
and sediment concentrations
sewers.
of most of the
an appropriate
but as described
relatively
isolated
termed the limit
research on self-cleansing
provides
It
lfhen the li$it
time.
and has been the subject
experimental
conditions.
is
the
cause the
with
The boundary between (b) and (c)
of deposition,
of sediment
sediment entering
therefore
it
of
because the rate
effectively
system at a finite
the depth of
to a certain
limited
is not in fact
transporL
are
The dunes travel
slowly
means of a caterpillar-track
Particles
transported
found in gravity
typically
along the pipe by
t54pe of motion.
at the upstream end of a dune are
forward
by the flow
where they are retained
to the downstream end
by a separation
the steep leading
edge of the dune.
belov
remain stationary
the surface
zone formed by
The parti-cles
until
they become
exposed at the upstream end, so the dunes can be
considered
as being effectively
beyond the limit
of depositi-on,
continuous
bed; particles
transported
by the flow
particles
Well
the sediment
forms a
at the surface
over a layer
are
of other
r.rhich remain stationary.
Previous research
to the present
relevant
surunari"sed in the following
sections
alternative
definitions
A fuIl
of the symbols used is
list
beginning
3.2
stationary.
study is
under the three
of self-cleansing
conditions.
given at the
of thi-s report.
Threshold o f
movement
(1975) measured conditions
Novak & Nalluri
threshold
sizes
of movement for
at the
(with
particles
individual
in the range d = 0.15rrn to 2.0mn) in smooth
circular
and rectangular
relation
for
channels.
the threshold
The best-fit
velocity
Vr" or a smooth
bed was
-oc27
rA
V.
E,S
= 0 . 6 1 te (s- r ) dl' " ( d/R)
( l)
where s is the specific
gravity
is
of the flow.
the hydraulib
the well-known
radius
Shields
diagram for
movement, the data points
particles
resting
Novak & Nalluri
rectangular
of
particles,
as
frictional
by a smooth surface.
(1984) extended their
channels with
velocity - t rV-_ for
the threshold
on
lay below the curve for
due to the lower
offered
and R
When plotted
on a bed of similar
would be oqrected
resistance
of the particle
rough beds.
an j-ndividual
was found to be higher
particle
was
work to
The threshold
on a rough bed
than the corresponding
Vr" ot a smooth one; the relationshi-p
between the two values
earlier
velocity
established
-Oo4
(Vtrlvrs)=1+1.43G/k)
where d is
size
and k the size
of the bed
(d varied
between 0.6rrn and 50rrn and was
than k in all the tests).
br.periments 'were
roughness
larger
the sediment
(2)
also carried
out on small groups of particles.
case of particles
the channel,
it
In the
touchJ.ng in rows across the width
was found that
the threshold
velocity
both rough and srnooth channels
Va was the same for
of
and
given by
Va = 0.50 tg (s-l)
3.3
-or4o
U
(3)
dl'" (d/R)
Transport without
deposition
Several
studi-es have been carried
e>qlerimental
determine
between flow
the relationship
sediment transport
rate
at the limit
The sediment concentration,
in terms of volumetric
C.r, will
transport
out to
conditions
of deposition.
here be defined
rates
so that
Qs
v
and
(4)
Q*Q"
where Q is the water discharge and Q" the voh:metric
sediment discharge.
Since typical values of C., in
sewers are in the range 10 to 100 parts per rnillion
(ppm) by volurne, there is no significant
difference
in
using the more usual but less precise definition
."=+
(5)
Laursen (1956) surrnarised the results
investigations
diameter
carried
smooth pipes
out with
using
of four
Slnrn and 152nm
sands with
sizes
between
0.25mn and 1.6rmn. Results for the limit
\rere presented
but l{ay (1975) showed that
graphically,
these could be approximated
vr,
by
L/3
--------
-
,.v
v--
[2 g (s-r) y]h
where V, is
(6)
v
the limiting
and y is
veloci.ty
significantly
152nm diameter
the depth of flow.
concentrations
(1972) carried
smooth pipes
out tests
flowing
in
fuII
102nrn and
with
Ttre sediment
provide
on the transportation
with
0o105
was
0o055
(7)
where d__ is the sediment size in mn and O is
mn
(positive
angle of the pipe to the horizontal
smooth pipes
were carried
Research using
and sediment sizes
May (1982) fitted
semi-theoretical
cu=
of deposition
at Hydraulics
and 7.9mn.
the
for
an
pipe) .
Tests on the limit
dianeter
The
0.928 C
d
vmn
(1 - tan o)
pr G-tG'z
upwards-sloping
other
of sedj.ments at very
.equation to the results
vi,
a link
(up to C., = 3 x 10s ppm).
concentrations
previously
sediment
were in the range 103 ppm to
7 x 104 ppm, so the results
best-fit
Note that
was found not to depend
of 0.45nm and 0.B8rsn.
studies
at the limit
on the sediment size.
Robinson & Graf
high
in the pipe
the mean velocity
of deposition,
sizes
of deposition
equation
the results
out
77rrn and 158nun
between 0.6rrn
to a
and obtained
2.05x10-2 (A/Dz)-1 (d/R)0.5 [1 - (Vts/VL)]4.
?
vt
f' g
"1
(s-l) D
!.2
(8)
Va= is the threshold
particle
of an isolated
velocity
given by Novak &
on a smooth bed, and has the value
Equation (1); A is the cross-sectional
Nalluri's
area
of the flow.
Macke (1982) measured the limit
smooth pipes
with
diameters
of deposition
of
in
192nrn, 290rmnand 445rm
and used sands with sizes of 0.l6rrn and 0.37nm.
These results,
together
were analysed
transported
with
data from other
on the assurnption that
in suspension,
sources,
the sedirnent was
and were found to fit
the
eguat,ion
Q" ee (s-l) w
-4
1r5
= 1.64 x 10
where w is the fal1
for
t
1.07 N,/m2
o
(e)
velocity
of the particles
is the average shear stress
around the pipe.
equation
is
In order
to compare it
Iimiting
velocity,
dimensional
and SI units
with
other
and ro
The
should be used.
fornulae
for
the
(9) can be expressed in
Equation
the form
VL = 1.98 I
where ), is
-0r6
rr
( 10)
t(s-l) A Cvl
the Darcy-Weisbach
friction
factor
of the
flow.
(1988) carried
Mayerle
the limit
diameter
widths
of deposition
of
using
a smooth pipe with
L52rrn and two rectangular
with
sediment were used ranging
0.50rm to B.7nm (w'ith s = 2.49 to 2.6L).
different
data correlations
of the best
channels
both smooth and rough inverts.
of uniform
fits
pipe was given by
10
Six
from
I'lany
were investigated,
to the data for
a
channels with
of 311nunand 462rrn; the rectangular
were tested
sizes
out ercperiments to determine
and one
the smooth circular
vr,
-0o40
= 0.89
r, ("-1);;u
D
Oo19
C
gr
v
-1r05
-Oo20
(d/R)
I
(1r)
where D__ is a non-dimensional grain parzrmeter defined
gr
as
D-- = [g (s-l)/u
2
7.. t
{L2)
]
Er
Information
on the effect
rectangular
channels was also used to develop an
alternative
equation
for
hoped would be suitable
pipes.
The resulting
& Nalluri
of bed roughness in the
pipes.which
circular
for
was
it
both rough and smooth
reconrnended by Mayerle
equation
(1989) was
vt
-0o14
ts ("-1) dP
= 14.43 D
0r18
(d/R)
C_ -
gtv
-0r55
r
Oo18
(13)
The value
of the friction
from the Colebrook-!{hite
-0o5
I
R
is
factor
equation
-0o5
=-)
logro[(2.51
I can be calculated
I
,/R-) + (kss R
the Reynolds number of the flow
conposite
is the
ss
roughness of the pipe when carrying sediment
at the limit
determined
/r4.8)l
( 14)
of deposition.
Ttre value
from the following
best-fit
and k
of k""can
relation
be
given
by Mayerle & Nalluri
(' -k' s s - -k- s)"/ R
- - = 0- . 0 1 3 0 o 0 0 z a a 0 0 4 0
gr
v
An alternative
deposition
approach to predicting
( 15)
the linit
of
was developed by Ackers (1978, 1984), who
li
the HR data for
earlier)
using the well-established
sediment transport
(see
77nrn and 158mmpipes
analysed
Ackers-White
Certain
equation.
necessary
in order
changes were made to the latter
equation
permit
(eg replacement of
its
to pipes
appli-catio1
flow depth by hydraulic
radius),
(determined
coefficients
from alluvial
were assumed to be unchanged.
analysis
showed that
with
effect,ive
of sedinent
A ful1
the Ackers-White
rates
equation
if
the
of the pipe
in the invert
equal to 10 particle
of the application
description
equation
the
of deposition
the Ackers*White
was taken to be approximately
diameters.
basis,
On this
at the limit
lrere consistent
the
channel data)
the sediment transport
observed in the HR tests
width
but otherwise
to
to pipe
of
given
in
studies, it
is
flow
is
crRrA (1987).
Whencomparing results
of different
relevant to know whether, just prior
the sediment particles
to deposition,
were being transported as
Ttre dividing
bed-load or as suspended-load.
between the two modes of transport
line
is seldom clear
cut, but may be estimated by the following criteria
due respectively to Newitt et al (f955) and Spells
(1e55):
V,
=17w
( 16)
DS
11215
Vb"
= 0.0251 g (s-1) d.,
Here VO" is
transition
the pipe-full
Oo??5
(17)
flow velocity
at the
from bed movement to movement in suspension
and u_ is the kinematic
m
water*sediment mixture;
are finer
(D/u*)
viscosity
85% by weight
than the d65 size.
these formrlae
for
of the
of the particles
Values of VO" given by
a range of particle
sizes are
conpared below (assr:ming D = 0.15m, u* = 1.14 x 10-6
nzls and s = 2.6).
L2
(mm)
(m/s)
o.23
1.5
3.6
9.7
L2.4
the two equations
do not agree very well,
0. 15
0.6
1.5
6.0
Although
they do indicate
Ifunit
Vb" (Eqn 17)
(m/s)
Vb" (Eqn 16)
d
that,
of deposition
0.61
1.9
4.0
for
flow
in gravity
conditions
near the
sewers, particles
coarser than about 0.4mn are like1y
to be moving as
bed load.
3.4
Transport with
deposition
to Laursen (1956),
According
capacity
of a pipe flowing
part-fu1l
deposition
begins.
If
discharges
are kept
constant,
deposits
flows
wiLl
ful1
until
it
entering
deposited
beds only
graphical
relationship
proportional
depth,
the pipe
of the flow
increase
at whieh sediment
Laursen and his
investigated
until
Only then can the
capacity
matches the rate
therefore,
the depth of the
to increase
and surcharges.
the pipe.
decreases once
the sedj.ment and water
continue
sediment-transporting
the sediment-transporting
equilibrium
is
co-researchers,
conditions
for
the case of pipe-fuL1
for
was established
yr/D
flow.
A
between the
of the sediment deposit
and a
parameter
(18)
It is convenient to e:q>ress the relationship
of a formrla, and a reasonable fit
-1
y"/D=2(L+1)
13
by means
is given by
( le)
ft
is
stressed
parti.cular
that
but purely
basis,
theoretical
curve is
scatter
considerably
the
by
(19) from the mean
of Equation
The deviation
describes
curve presented
shape of the mean elq)erimental
Laursen.
does not have any
equation
this
than the erlperimental
snaller
about the mean curve.
Data for
channels and pipes with
the alluvial
deposited
(1968)
beds were anal.ysed by Graf & Acaroglu
and fitted
to an equation
which can be expressed
in
the form
V
-----[8 g (s-l)
R is
is
= 0.732 tr
0o248
c -v
R]z
the hydraulic
the overall
attempt
-0o624
of the free-flow
radius
factor
friction
for
was made to apporti-on
the deposited
Ackers-White
the pipe;
ef,fective
width
equation
water
half-full.
was initially
assumed that
the pipe vas flowing
if
Other choices,
more accurate
equation
width
the predictions
can be expected
which the equation
However, a detailed
than
width
be
in a pipe,
the
of the Ackers-Whj.te
to be, because conditions
those in alluvial
vas originally
evaluation
channels
developed.
of the equation
for
the
beds in pipes has not yet been made
case of deposited
due to the lack
less
of the
of the deposited
the depth of deposit
then approach more closely
for
was equal either
the effective
taken as equal to the aetual
The greater
the
however, can be made, and
CIRIA (19e7) suggested that
bed.
between
to describe
of the pipe or to the width
surface,
no
For the case of a
of sediment transport
to the diameter
and tr
of the pipe.
the movement of sediment in pipes.
bed, it
(20)
Ackers (1978) adapted the
3.3,
sediment transport
deposited
Oo25?
area,
the resistanee
bed and the walls
As mentioned in Section
(d/R)
of suitable
L4
e:<perimental
data.
(1987, 1988) carried
Perrusquia
various
out e>q>eriments with
in a 225m diameter
depths of sediment deposit
concrete pipe using sand sizes of 0.5rrn and !.fum.
the first
stage of the study,
plane stationary
apportioning
bed in order to verify
the overall
the pipe walls
were made with
tests
frictional
resistance
between
and the sediment bed : the method due
In the second stage,
development of bed forms and their
It
ripples./dunes
resulLs.
out at low
were carried
tests
of sediment movement in order
resistance.
to study
effect
the
on flow
the dimensions
was found that
predicted
were reasonably
method due to Engelund & Hansen (1972).
work was considered
relationships
by a
However,
to develop
necessary
i-n pipes.
to sediment deposits
specific
of the
by a method
due to Fredsoe (1982) and the flow resistance
further
a
methods for
to Vanoni & Brooks (f957) gave satisfactory
rates
In
TEST
ARM}TGE}TENT
4.1
General layout
The experiments
wide tilting
supplied
were carried
diameter
pipe by up to three
system passed into
thin
Flow into
plate
part
weir;
into
tilting
allowed the flow rate
entering
for
accurate
sediment was recirculated
proportion
of the liquid
whose discharge
from
the bypass channel by
This system
the sewer pipe to be
simulation
separately
discharge,
was measured using
15
the head of the
of the flow
weir.
means of an adjustable
rapidly
half
the sewer pipe over a 1.22m wide
the punps could be diverted
varied
a 300mn
the pipe was
the other
of the fh:me,
as a bypass channel.
rectangular
Pipes up to
pipe was studied.
mounted in one half
pumps having
but initially
can be installed,
concrete
2.44m
1) in which flow was
of around 0.25m3/s.
capacity
450nrn diameter
acting
(see Figure
flume
to the test
a total
out in a converted
of floods.
with
The
a small
by a slurry
pump
an electro-magnetic
current
meter.
The sediment
concentration
pipe lras measured using
recirculation
in the
an infra-red
sensor (see 4.2).
pipe was made up of 2.52m long ROCLA
The test
pipes with
spun-concrete
of 300mn and a total
length
to have a mean internal
would normally
the pipe
be assembled with
with
was considered
deposition
joints,
was necessary to
pointing
downstream.
a sma1l (approx
because otherwise
mi.ght have occurred
such that
at the
lengths
varied
20m depending on the fit
The pipe was laid
the invert
when the flume was level.
checked along the pipe,
which
sediment
prematurely
gaps between the pipe
joints.
at individual
pointing
in the downstream direction,
from zero to approxirnately
The
which
the spigots
to present
beneficial
Internal
2).
a
at the upstream end, so
sockets
Tfiis caused the joints
2-3mn) o4pansion
was measured
298.83rmn, with
reasons it
to the bulkhead
the pipe was laid
blocks
It
di.ameter of
For practical
downstream.
steps.
of 2lm.
pipes had spigot-and-socket
individual
diameter
internal
of o" = 2.89rrn (see Figure
standard deviation
fix
a nominal
on wooden
as possible
was as level
The invert
and it
levels
vere
was found that
at the
gauge positions
the deviatj.ons A from the mean l.evel
were in the range -A.2s L <2.1rrn; for the pipe as a
whole the range was -4.9< A <2.4nm. Ttre fh:me could
to give a maxim:m pipe
be tilted
slope of around
1/ 100.
Eaeh pipe
length
had tvo 900 x 9&rn slots
top to a1low observation
length
of the pipe.
were built
flow,
whj.lst
still
flle depth of flow
using
an adjustable
16
of bed conditions
Flush-fitting,
to re-seal
cut in the
the pipe
allowing
for
along the
transparent
tests
observation
at pipe-fuIl
of the bed.
in the pipe rras controlled
sluice
lids
initially
gate at the downstream end.
The gate was later
replaced
allowed more precise
These were
depth control.
panels which were introduced
vertical
of the pipe outlet.
freely
from both sides
Flow from the pipe discharged
a hopper where the sediment was allowed
into
settle.
with
The sediment was extracted,
proportion
the hopper into
prevented
the outer
the build-up
punp.
The hydraulic
five
sediment
were used to
in the
along the pipe was measured
gradient
electronic
depth gauges mounted
digital
along part
gauges were fitted
The point
from
of the screens.
above the pipe at 2,52m intervals
length.
a
in suspension
Water jets
tank.
of
Mesh screens
of sediment deposits
hopper and the clogging
using
thus maintaining
tank,
head over the slurry
escaping into
over the siII
flow discharged
an outer
around the si1l
prevent
a sma1l
pump to the head of the
by the slurry
The remaining
constant
to
of the f1ow, from the bottom of the hopper,
and recirculated
sewer.
which
by restrictors
with
of its
a
which
electronic
detector circuit,
an audible rtsgueakfl when the tip of the.gauge
battery-powered
emitted
was in contact
assistance
with
This was of particular
the water.
in the tests
part-full
with
flow when the
and fluctuations
was measured directly,
caused the gauge to ildip" into and out of the water.
water
surface
For pipe-full
wells
flow
was measured in stilling
the level
perspex
mounted on the transparent
rrere connected with
stilling
wells
diameter
holes,
periodic
fluctuations
point
the pipe via 0.5rrn
which were smal1 enough to reduce
The sand bed profile
electronic
Ihese
lids.
in water
to around tkun.
vas measured with
gauge with
was zeroed on the pipe
digital
invert.
measurements was approximately
L7
leve1
a portable
read out,
The accuracy
+Q.25mn.
which
of the
4.2 Sedinent
concentration
measurement
fn the earlier
with
HR tests
diameter pipes,
the 77run and 158rrn
dry sand was added at the upstream end
of the pipes using a vibrating
injector,
and removed at the downstream end by
collecting
it
large
AIso,
quanti-ties
upon to maintain
was necessary to keep drying
it
a constant
to achieve
expected
in the larger
for
concentration
concentrations.
the test
is
rig,
affecting
in type to the
used for measuring silt
showed that
register
Ttris lras essential
because it
sedinent
similar
would satisfactorily
the wet re-circulated
without
set of
of an infra-red
Development tests
sand particles.
every test,
which measures sediment
by the interrupti-on
The instrument
rates
without
the present
Partech device which is widely
instrument
pipes,
This used a re-circulating
system and a new instrument
beam.
transport
of dry sand for
a new method was devised
it
of supply.
rate
di-aneter
before
could not be relied
the nuch higher
demanding huge quantities
light
every test
and the injector
In order
extrleriments.
size as the testing
its
of sand after
could be re-used,
tended to
The screw-injector
the sand, reducing
continued.
This was found to have a
in a hopper.
number of drawbacks.
grind
screw sediment
the
much coarser
to the concept of
enabled the concentration
of
sand to be measured continuously
equilibrium
conditions
in the sewer
Pipe.
The sand from the hopper at the downstream end of the
sewer pipe was pumped at a pre-set
head of the system via
flow velocity
measured using
in this
a 75 rrn diameter
sediment
return
an electro-magnetic
which was not affected
concentrations.
l8
velocity
by snall
to the
pipe.
The
pipe was
current-meter
sediment
(EC!l)
fhe sediment
section,
with
against
3).
of signal
at the sensor.
arriving
settings.
of
which converted
clear
converter
reaching
water.
to a counter.
The counter
for
that
passing the sensor the sand and water
After
were fed back into
the head of the sewer pipe
(downstream of the thin-plate
system.
could
from 1 second
up to 9999 seconds to give a mean reading
a constant
recorder
a voltage-
be set to count over a given time period
period.
the
From the
was fed both to a chart
to produce a hard copy, and through
frequency
mean sediment
Figure
weir),
transport
thus maintaining
rate
through
the layout
4 shows schemati.cally
the
of
the measurement and recording
system.
The response of the infra-red
device rras found to be
dependent on both sediment size
the sediment pipe.
was advantageous,
rates
a wide range of transport
the pipe velocity
concentration
therefore
for
a given
reduces sediment
transport
rate,
and
reduces the response of the infra-red
The flow
velocity
in the sediment pipe
values
in
could be covered by only a few pipe velocities:
inereasing
sensor.
and flow velocity
ltre dependence on flow velocity
in that
without
in the selrer pipe.
l9
and sediment concentration
could be altered
affecting
it
these !'rere . set to
.988 V for no signal
the signal
The sensor
using gain and balance
down to around 0.1.V for
amplifier,
also
in the range 0-1
For the sediment tests
give an output
sensor,
unit
which was nominally
but could be varied
it,
the beam, and reduced the
was fed to an amplifier
to a voltage,
volts
beam across
Sand passing
of the pipe.
interrupted
(see
of the pipe
of the pipe to a sensor opposite
the pipe
signal
source mounted
on the outside
mounted on the outside
strength
light
The source shone a "pencil"
the diameter
along
a lm long perspex
contained
an infra-red
the invert
Figure
pipe
return
to suitable
the corresponding
conditions
was necessary to
Before the system could be used, it
calibrate
sensor over a range of
the infra-red
and sediment pipe
sedirnent concentrations
velocities.
rates
Based on expected transport
to be studied,
range of sewer velocities
calibration
tested
flow
were initially
velocities
over the ful1
for
the
two
chosen, and
response range of the sensor
using 0.72wn sand.
Before and after
a sensor reading was
each calibration
taken with no sediment present.
This, the
ttclear-rvaterrr reading, was found to vary by a few
percent
to another.
from one test
the scale,
a reading
\ras taken with
confirming
not affecting
that
the infra-red
levels
ambient light
were
the readlngs.
ltre sedirnent sensor calibrations
plasti-c
using a 2 litre
sizes drilled
injection
end of
This reading was found to be
source switched off.
constant,
At the other
were carried
beaker, with
out
holes of various
in the base to al1ow a range of
Ttre holes were taped over,
rates.
wj-th sand and weighed.
beaker filled
It
and the
was then
mounted above the hopper at the downstream end of the
serrer pipe,
with
a funnel
the sand frorn the beaker and carry
pump intake.
the slurry
the required
calibration
from one or more hoIes,
pipe
and vertical
it
down to
directly
I,Iith the return
velocity,
to catch
pipe
set at
tape was removed
and a stop watctr was started.
Sand was then added to the beaker from a pre-veighed
supply,
to keep it
When all
the pre-weighed
\rere resealed
initial
level.
sand had been used, the holes
and the stopwatch
was then reweighed,
calculated
topped up to a constant
stopped.
and the mean injection
The beaker
rate
as
beaker sand + pre-weighqd
duration
2A
sand - finaL
of test
beaker sand
sand was chosen to give a
five minutes - at the very
The amount of pre*weighed
test
duration
highest
of at least
injection
made a longer
calibration
of the ealibration
recorder,
steady
It
and rras useful
output,
was found that
remained during
rate
the lowest
transport
how
the test.
(below
rates
could not be achieved using this
in the beaker if
steady rate
than about 4rrn, and a
was smaller
it
of supply could not be relied
wire,
a simple vibrating
and hole diameter
calibrations
driven
rras added to permit
motor,
equivalent
in determini"ng
as the sand tended to arch above the hole
arrangement
electric
served only as a check on
record
the sand supply
Therefore
from the chart
which was set at a l00s counting
The chart
approx 2g/s)
was retained
sensor readings were obtained
but actual
the counter
A hard copy
impracticable.
output
from the counter,
period.
the amount of sand required
rates
to be used.
by a small
beaker
a smaller
Tlris allowed
down to 0.L6 g/s,
to be carried
to the lowest
upon.
sedirnent transport
which was
rate
expected in the sewer pipe.
It
was necessary
to normalise
some way to account
reading.
for
the sensor output
variations
in the clear-water
could be ascribed
These variations
in
to two
main causes:
1.
Changes in the sensitivity
temperature
2.
of the sensor,
and power fluctuations.
Changes in the transmissivity
presence of fines
Other possible
interference
due to
from other
included
electrical
equipment and physical
movement of the heads, but
2L
due to
and air.
factors
be significant.
of the water
these were not thought
to
If
one introduces
ie.
the reading
air
or fines
will
'fpure waterrt reading
a theoretical
which is obtainable
from water with
present
then the normalised reading
be equal to the change in signal
presence of sediment,
divided
no
due to the
by the full
range of the
instrument
actual reading - clear water reading
source off reading - pure water reading
1 .'-'
e
If
the sensitivity
of the sensor changes, then all
readings below "source off" should change
proportionately,
including the rrpure water"
Therefore,
if
it
were assumed that
clear
water
only,
then the quantity
reading
fluctuations
were due to changes in sensitivity
should be constant,
and it
is appropriate
to normalise
as
actual reading - clear water reading
source off reading - elear water reading
If
aII
fluctuations
transmissivity
reading
were due only
of the water,
would be constant
would be proportional
actual
Early
reading
calibrations
relationship
with
to changes in the
then the rrpure waterrr
and the normalised
- clear
tests
water
yielded
reading
a very non-linear
the sensor showing a tendency
well
response lras unacceptable
short-term
variations
the calculated
22
and concentration,
to rrsaturaterr at
below those required.
non-linear
time,
readings
to
between sensor output
concentrations
in
read.ing - clear_water reading
reading - pure water reading
source off
source off
the output
all
reading.
ltris
because,
were meaned with
mean concentration
respect
if
to
would have
been distorted
strength
true value.
from its
was possible
of the source it
approximately
(i.e
concentration
giving
smaller
70% of the signal
signal.
lhis
their
reaching
the sensor.
problen
linear
the velocity
calibrations
normalizing
Iittle
transport
results
techniques
covering
using
fu1I
deviation
range,
that
changes in the sensitivity
was decided
- clear
vater
Once some initial
there
were due to
were those calculated
reading
a
that
than to
of the measuring
1.39m/s in the sediment return
weighing
as approximately
of the water
5 shows the calibration
infra-red
The
both the
fluctuations
changes in the transmissivity
Figure
pipe.
sediment
and both having
It
of 8.4%.
\ras more evidence
actual
by suitably
tras found between them, both giving
over 70% of
the calibrations
the
above, and very
described
a response which could be regarded
standard
a
over a range of velocities
were determined
difference
linear
rates
from 0.16 up to around 50g/s.
rates
others,
strength
in the sediment return
were obtained
which gave consi-stent
transport
blanket
however, present
This did not,
range at the higher
Calibrations
was expected,
was possibLe to stay within
because it
increasing
will
on the signal
net effect
range,
exceeds a certain
some of the sand particles
reducing
"source
produced progressively
in concentration
changes in output
for
beyond the linear
because once the concentration
value,
to achieve an
water up to a
from clear
For concentrations
increases
the
response over about 70% of the
linear
sensor range.
off").
By reducing
system,
so
using
reading
obtained
=
at velocity
pipe.
problems were overcome, the
sensor worked well
of sand samples.
23
and saved much drying
By allowing
and
the system to
for
settle
around 30 rninutes before
measurements, variations
reduced to below 5%.
taking
Errors
for
reading were
in clear-water
were further
readings before
clear-water
using it
reduced by
and after
each
test.
EXPERIMENTAL
PROCEDURE
5.1 Clear-water
roughness
with
Before any oq)eriments
series
of clear-water
to obtain
equivalent
systern for
Clear-water
irnnediately
prior
particular
to each limit
adjust
the flow
pipe
gauges.
was set
water
stilling
of deposition
depth to the required
gradient
value
this
state
reason.
as a datum for
gradient.
such that
The reading
24
the
the
to minimise
was obtained
by
(or
The
to the next unless
A'sti11-water"
calculation
gate
rlas reached.
was taken at each fh:me slope setting,
acting
the digital
were within
slope was not changed from one test
this
and take
the slope of the
the downstream sluice
until
then
Ttre pipe was surcharged
leakage around the lids.
necessary for
was to set a
using
and as low as possible
flow restrictors)
test
va1ue,
tests,
at some convenient
adjusting
at
sediment present,
For pipe-full
wells,
gradually
conditions
at the gauging points
levels
a workable
these tests
without
a measurement of hydraulic
point
(Nikuradse
and depth of flow.
adopted in all
discharge
in order
roughness was also measured
the same discharge
the procedure
flow
a
the 299run diameter
to develop
uniform
part-fuIl.
with
for
and in order
setting
out,
of the val-ue of k"
sand roughness)
pipe,
concrete
was carried
tests
an estimate
took place,
sediment
this
reading
reading
of hydraulic
by stoppering
the
sewer at the downstream end and filling
until
it
slowly
water l-evel could be measured in each of
a still
the gauged stilling
These sti1l-water
wells.
were checked periodically
readings
the gauges
to ensure that
had not moved.
For part-full
as close as possible
conditions
to uniform
was not always easy, particularly
near to critical
Disturbances
pipe
depth for
caused the water
the required
elsewhere
and exit
15nrmfor
waves with
standing
flows,
subcritical
adjustment
The criteria
necessarily
flexible.
Generally
adjustments
were made until
gauges gave the required
Ihe five
all
five
values.
deposition
readings
calculated
for
Prior
each test
were
three
depth to within
and the average
in most eases,
using,
to studying
the limit
condition,
two sets
were taken to determine
for
at least
gauges were then read,
gradient
of up
and as rm:ch as 20rrn
therefore
of the five
and
arnplitudes
and gate setting
of flume slope
A1so,
at the joints
when the flow was supercritical.
hydraulic
from the
to fluctuate
surface
in pipe section
created
This
velocity.
by 2-3mn at the gauge positions.
irregularities
tlrrn.
flow.
normal depth was
if
at entry
of the flow
periodically
to
to achieve
the slope was adjusted
tests,
of
of depth
the clear-watet
roughness.
5.2
Threshold o f
movement
Tests were carried
for the velocity
would start
out to obtain an approximate val-ue
at which isolated
sand particles
to move in the ser{er pipe.
was to set a flow depth and velocity,
sand particles
then add a fe!.r
by hand and see whether they continued
to move having fallen
failed
The procedure
to the bed.
to move the velocity
25
If the particles
was marginally
increased
and the slope
uniform
until
re-set
flow
in order
to obtain
Ttris process
conditions.
movement was observed.
specifically
designed for
was not practicable
the invert,
and. Yz fulI
was continued
was not
The rig
such measurements, and it
to position
nor to carry
I\ro readings
approximately
particl-es
out tests
were obtained,
carefully
pipe-fu1l
for
at approxirnately
on
flow.
% fult
conditions.
5.3 Lini.t of
deposition
Once the gradient
and sediment sensor readings
been recorded
clear
gradually
all
for
water
conditions,
added to the system.
had
sediment was
Ttre sediment used in
the tests
described
in this
narrow-graded
sand with
d5o = 0.72w{t and a specific
gravity
of 2.62;
to prevent
order
found that
into
the grading
the jet
is shown in Figure
fusnediate formation
the best
of dunes, it
into
fe1l
the water
by the slurry
This allowed
escaping
was
large
over the sill
the
in the hopper before
pump, rather
quantities
being
than travelling
along the sediment pipe as one "slug".
was found that
In
the hopper from the
downstream end of the sewer pipe.
extracted
6.
method was to add sand by hand
as it
sand to mix with
was a
report
At first
it
of sediment were
of the hopper,
so the nesh
screens were added, and the back of the tank was
raised
to accornnodate the additional
head difference
across
the mesh.
was that
the sand deposited
than falling
(45")
sides
hopper.
tests,
Another
difficul.ty
on the sides
to the bottom,
this
and considerable
of the hopper rather
despite
turbulence
This became most apparent
In order
was less
to minimise
added in the corners
off, the sides
be collected
this
within
with
turbulence
deposition,
the
the part-full
in the hopper.
lrater
jets
were
of the hopper to wash the sand
and back into
by the punp.
26
the steep
from the sewer pipe was
when the discharge
reduced and there
some of
suspension
where it
could
Sand was added until
observed.
of deposition
the limit
(below around lm/s),
At low flow velocities
was taken to be the point
this
was
at which particles
would bunch together
and cease to move for
a few
seeonds before
dispersed
away by the
being
and carried
This condition could be satisfactorily
tests,
from above - in the case of pipe-fulI
observed
flow.
easily
through
the pipe.
velocities,
from flume traction
to flow
bed.
fn this
night
be in continuous
impacts with
directly
by the layer
transmitted
the shear force
this
became less
to judge the limit
from above,
until
would thicken
on the
resistance
instance
In this
of
above.
than the frictional
it
of deposition
as the particles
and
was not
solely
by
on the
For
by a continuous moving bed.
reason windows 'were installed
along the invert of
were obscured
the pipe to a1low observation
It
on the invert
on the particles
exerted
they ceased to move.
invert
in
in the flow vas
when the concentration
observations
being rnoved
A snal1 increase
high enough, ttre moving deposit
possible
when
packed and move onLy as a result
to become closely
invert
just
were still
would cause the particles
concentration
Eventually,
The limit
above.
was taken to be the condition
by the flow.
shear forces
on the invert
but rrere moved by
in the layer
on the invert
moving
they were not
by the flow,
particles
of deposition
particles
particles
motion,
as
transition
over a continuous
case, although
directly
was found that
it
was a gradual
more sand was added there
transported
windows in the top of
the transparent
At higher
very
was necessary
certain
determining
the U$Iit
as loca1 disburbances
sections
of the pipe
to decide which section
should be used for
deposition,
from below.
to deposit
before
of
in the flow caused
others.
A
was chosen, wtrich
section around nid-length
seemed to be rrt5picalrr in terms of how soon it would
particular
form a deposit
relative
27
to other parts
of the Pipe.
Judgement was primarily
point,
this
based on the conditions
of the pipe was always
length
but the full
checked to ensure that
dunes had not
local
at
formed
elsewhere.
Once it
was decided that
deposition,
for
the flow was at the limit
a minimum of about
the system to reach equilibrium.
consecutive
mean concentration
gradient
the slope was adjusted,
flow
readings
level
detect
the small
water
and the linit
concentration
recorded.
ten to fifteen
conditions.
of deposition
is
so that
it
was not easy to
and achieve
more sediment
there
will
steady
the
accumrlates
is
starved
not be at the
the
The system of recirculating
sediment to the head of the pipe
certain
degree of unsteadiness
supply,
and it
several
minutes
only
that
starvation
causes a
inevitably
in the rate
of sediment
the mean concentration
renains
of deposition
28
the
sediment
the downstream portion
of deposition.
due to this
whilst
consequence of reaching
that
of sediment and the flow
the limit
conditions
as above from the mean of
of deposition
An inevitable
is
to
were being
the limiting
Sometimes however,
in the pipe,
difficult
minutes
readings
was calculated
the limit
in water
Ii-lnit of deposition
In these cases,
identify
the
of deposition.
for
readings.
1evel
in roughness betrreen clear
and head loss
concentration
limit
The fluctuations
increases
In most of the tests,
were maintained
as with
tended to make it
described
tests
to restore
of water
each test,
measurement.
already
limit
Trvo sets
for
part-full
necessary,
conditions.
were taken
clear-water
if
the
The hydraulic
and for
was measured again,
uniform
representing
a 100s period.
for
of 5-10
from the
each reading
sensor,
was allowed
A series
readi-ngs rrere recorded
concentration
all
15 minutes
of
constant.
fn some cases
would be observed,
effect,
over
but then
the concentration
would
subsequently
only
fal1
to a lower value.
observed to be at the limit
in the calculation.
readings
rcere only used with
reading
act as a weir
pipe.
until
sensor.
for
gate was lowered to
in the sewer
the sediment
of deposition
flowed past
water
the infra-red
sensor reading was recorded
at the
Ttre sand concentration
using
was then calculated
calibration
at the
reading
the equivalent
of the test.
appropriate
5.4
clear
comparison with
limit
had been taken at the
the sluice
The clear-water
beginning
the same period.
pipe was then al-lowed to continue
The slurry
running
the corresponding
taken for
and retain
'water level
Sirnilarly,
Once the necessary readings
of deposition,
were
of deposition
included
limit
occurred,
taken when the flow was actually
the readings
concentration
this
If
(Section
curve
the
4.2).
Deposited bed
At the start
through
the ocperimental
concentration
introduced
clear
of each test,
sensor.
and readings
rig
The sediment was then
the sewer pipe and distributed
system by tilting
discharge
sensor readings
in the sewer pipe.
were taken over
ten sets of readings
I.Iater depth and temperature
determined
reading
uniform
T\rro sediment
1000 seconds and a
1.00 seconds.
measurements were recorded
If
dunes were
speed along the pipe was
and the time interval
extended to take into
movement of the sand bed.
29
and the
until
taken over
the 1000 second interval.
then their
to have
Ttre
and fh:me slope were then set,
adjusted
a high
sensor reading
1000 seconds was constant.
flow was achieved
present,
was considered
when the sediment
downstream flow restrictors
during
around the
and using
the flume steeply
reached equilibrir:m
further
uniformly
The distribution
averaged over
taken on the
the hopper at the downstream end of
into
discharge.
water was conveyed
for
the sensor
accor:nt the irregular
Three different
with
this
depths of sedirnent bed were tested
technique:
deposited
bed tests
continuation
0.044m, 0.010m and 0.O022n.
were later
for
tests,
from zero to 0.009m.
thus varied
procedure
out as a
of deposition
of the linit
thicknesses
carried
these tests
5.3),
and then gradually
until
a deposited
and bed
The
was to reach the limit
of the sedirnent (as described
deposition
of
in Section
additional
inject
Some
sediment
bed had formed.
Once the relevant
measurements had been
hydraulic
made, the flow was slowed to a non-transporting
velocity
and the deposited
the downstream flow
discharge
bed preserved
restrictors
simultaneously.
continuous,
five
If
and reducing
twenty
width
section.
the
the sediment bed was
measurements of the deposit
were taken along each pipe section.
not continuous
by closing
If
width
the bed was
dunes were formed,
and intermittent
each pipe
measurements were made along
The average depth of sediment was calculated
from bed wi-dth and pipe
geometry.
EXPERIMENTAL
RESULTS
Details
of the e:<periments carried
diameter
3.
concrete
Table
the 299rrn
in TabLes J." 2 and
1 shows the measurements taken
water analysis
the Ii-nit
pipe are listed
out with
for
clear
of the pipe roughness, Tab1e 2 Lists
data and Table 3 the deposited
of deposition
bed data.
6.1
Pipe friction
For pipe-full
tests,
to be the mean water
still-water
reading.
from water levels
squares regression.
disagreement
with
regression.
30
the hydraulic
surface
gradient
slope with
This was calculated
in the stilling
If
one point
the others
it
wells,
was taken
respect
to the
directly
using least
gauge was clearly
was excluded
in
from the
The method used to determine
for part-fu1l
velocity
tests
vras as follows.
was calculated
on the recorded
Speeific
determined
at each gauge position,
E at each point
based
discharge.
could then be
from:-
(2I)
E=y+Yz/2g
where y is
the flow depth at the centreline.
mean velocity
at the section,
calculated
divided
by flow area at the section,
gravity
constant.
(positive
i
Mean flow
flow depth and total
energy,
gradient
the hydraulic
for
and g is
the
m
in the downstream
direction)
was determined using least-squares
regression
on all
A11 points
were normally
catrculation
the
as discharge
energy gradient,
The best-fit
E increasing
V is
the points.
used so as not to bias
of mean velocity
and because it
the
was found
that
points gave less consistent
omitting
roughness
'The
values.
gradient i was then found
hydraulic
from: -
i=S
o
-m
where So is
(22)
the slope
In both pipe-full
of the pipe
and part-full
Darcy-Weisbach friction
factor
invert.
cases, the
was calculated
from:-
tr = SgRi/Vz
(23)
where R is the hydraulic
radius
corresponding
to the
mean depth along the profile.
A rrmeasuredrr value
the Colebrook-I{hite
31
of k" could then be determined
formula
for
conmercial
pipes
from
-2.sl/Refl)
k" = 14.8R 0or/2{\
(24)
the Reynolds number (=4VR/v)
where R- is
e'
For comparison, values of Manningts n were also
calculated
from
n = R2,e j-t,z/Y
A large
(25)
number of measurements was made to determine
the clear-water
ks,
roughness value,
of the concrete
pipe to be used in the Colebrook-White
forrmrla.
remain approxinately
These measurements
and just
% fuLI,
to /o tutt,
depths approximating
pipe full,
range of
in the range 0.18 to 2.09m/s,
covered flow velocities
full,
of k" would
over the full
constant
to be studied.
flow conditions
at flow
the value
was err.pected that
It
resistance
%
(y/D =
below pipe full
0.95).
TLre measurenents at y/D = 0.95 were made in an
attempt
to assess any influence
measured imrnediately before
each lirnj.t
be studied.
Ttre previ-ous HR tests
158nrn pipes)
had shown that
necessary if
the increase
measured at the same flow
AII
the 77rrn and
in head loss due to sediment
was not sufficient
it
conditions
but at a
time.
clear-water
calculated
in Figure
(with
in Table 1, and
of k" are shown plotted
values
7.
are included
results
The results
are reasonably
against
are several
outliers,
occurring
The overall
m€asurements is k
s
32
R"
consistent
over a wide range of Reynolds nr:mbers' although
velocities.
to
value of tr, or even on values
on a predicted
different
of deposition
measurement was
this
was to be observed accurately;
to rely
was also
and depth as that
the same flow velocity
with
have
night
gradient
ltre hydraulic
had on the roughness.
test,
the lids
particularly
there
at low
mean value of k" from all
= 0.192rm4with
a standard
of o- = 0.235rnm. Ttris suggests that it
s
improbable that any roughness measurement
deviation
highly
greater
it
than 0.663run (being ks + 2os) is correct,
justifiable
is therefore
values
and
to exclude such outlying
from the analysis.
The mean of all
the analysis
water measurements included
clear
in
= 0.147nunwith o" = 0.113nrn; the
is ["
estirnated standard error
of the mean is o
By treating
the results
separately,
the mean value
vary
is
for
different
= 0.012nrn.
n
of y/D
values
of k" can be observed
to
from 0.296rrn at y/D = 0.75 to 0.093mn at y/D =
0.375, see Tabl.e 4.
These variations
some cases determined
from relatively
statistically
significant
The predicted
values
Darcy-Weisbach
in k",
whilst
few values,
at 50% confidence
in
are
levels.
of Manningrs n and the
friction
factor
tr, calculated
assr:ming
k- = 0.147rmn for pipe full conditions,
are compared in
s
Figures 8 and 9 with the measured values.
The scatter
of the measured points
from the standard
for
various
values
flow
deviations
depths.
of the pipe
0.0099 with
about a mean can be appreciated
for
listed
in Tables
The overall
clear-water
5 and 6
mean roughness
conditions
o- = 0.00058, and tr = 0.0185 with
s's
were n =
o_ -
o.oo202.
An additional
how closely
analysis was carried
out to determine
the measured n and )t data for pipe-full
conditions fitted the predicted curve for
k = 0.l47rmr. Ttre mean value of the ratio
s
n-observed,/n-predicted was 0.99 with o" = 0.O42, 3..e
all
the observed pipe-full
107%of the predicted
data lay between 91X and
curve in Figure 8.
Si:nilarly
the mean value of the ratio tr-observed/tr-predicted was
1.00 with o_ = 0.085, so that measured friction
s
factors for pipe-full
conditions lay between 83% and
117%of the predicted curve in Figure 9.
33
Some of the variation
of k" with
in the value
radius
depth may be because the hydraulic
the Colebrook-White
equation
the characteristics
of part-full
is
sufficient
only if
distributions
factorrt
and shear stress
part-ful1,
so an additional
its
is needed when estimating
for pipe-full
a formula
Several
a circular
shape factors
suitable
"shape
resistance
from
flow.
out in the past to
studj-es have been carried
determine
Ttris parameter
f1ow.
This is not the case for
of the channel.
describe
around the wetted perimeter
are uniform
pipe flowing
R used in
does not fully
the velocity
flow
for
open-channel
flows.
Engelund (1964) proposed the use of a
,resistance
radius" in place of hydraulic radius,
developed
the distributions
rather
calculations,
lengthy
Engelund made a nr:mber of simplifying
applicable
would not hold
ltrese assumptions
considered
carried
out numerous experimental
other
open channels
resistance
to derive
studies
an essentially
A further
on from this,
data,
along with
(1979)
on channels
empirical
factor
study by Kazenipour
on semi-circular
Nalluri
forrnula which was applicable
channels.
& Adepoju (1985) used
ovn, to develop a
to flow
depths greater
than 0.5D.
Ihe drawback to both these studies
channels
that
smooth pipe
values
they were empirically
data.
of )t to fit
34
&
data from May (1982) and
measurements of their
is
for
pipe
from standard
to be determined
formulae.
Following
further
the part-circular
and also used data fron
(1980) concentrated
Apelt
rough region.
which would aLlow the friction
correction,
this
here.
cross-sections,
researchers
and
Kazemipour & Apelt
section
of various
for
The
assumptions
in the fully
to wide channels
about
and shear stress.
of velocity
method involves
assumptions
based on certain
a theory
and
derived
fhe Kazemipour forrmrla shifts
the Karman-Prandtl
equation
on pipe
from
= 2log1s Refl -0.8
L/{t
and Nalluri
Blasius
(26)
data with
& Adepoju compared their
the
equation
(27)
l, = 0.316/ R 0.25
e
Nalluri
& Adepoju suggested an equation
form as the Blasius
shape factor
y/P,
forrnula
pipes,
is
a correction
comparing their
a nodified
and using
intended
but incorporating
equation,
= Yy/v.
number,- eR^__
y
Although Nalluri
for
direet
factor
formula
study with
well
He found that
the present
the values
region,
but that
than for
by
for
variations
equation.
data obtained
predicted
flow
in
by the
and Nalluri
method fitted
neither
results
in smooth
the Blasius
methods due to Kazemipour & Apelt
Adepoju.
& Adepojurs
can be calculated
with
a
Reynolds
use only
Hare (1988) compared the resistance
the present
of the same
&
very
in the transition
were generally
smaller
smooth pipes.
Comparing the k- values for each flow depth, shown in
s
Table 4, it can be seen that the effective
roughness
increases
with
proportional
depth up to a maximurn at
y/D = 0.75 and then reduces towards pipe
full.
In
terms of n and )t, the naxirnum roughness occurs at y/D
= 0.95.
The overall mean value of k" = 0.147rnm is
consistent
with
the design value
recornrnendedby IIR (1983) for
of k" = 0. l5mn
spun-concrete
pipes
in
normal condition.
6.2
Ttrreshold o f
movement
lko
tests
velocity
were carried
out to measure the threshold
of the sand particles
35
but were intended
as
indication
conditions
The results
tested.
with
together
threshold
are shown in Table 7
predicted
velocities
by
(2) and (3) due to Novak &. Nalluri
(1),
Equations
the particular
for
only an approximate
(see
Section 3.2).
It
can be seen that
(1) but lower than
than those given by Equation
higher
those given by (Z) and (3).
because the first
eguation
This is not unoq>ected
was developed
channels
and the other
surfaces
than occur in concrete pipes.
o<ploratory
further
were
the observed velocities
work to determine
cornrnercial pipes with
for
two equations
smooth
rougher
Ttrese
suggest the need for
therefore,
results,
for
velocities
threshold
in
types of surface
intermediate
texture.
6.3
Linit
of
deposition
Measurements of the sediment concentration
gradient
hydraulic
obtained
for
at the linit
and are presented
of deposition
and pipe-full
both part-full
in Table 2.
were either
below the limit
5.3,
and these results
As previously
of deposition
had been reached,
hydraulic
gradient
the head-loss
out,
a number of readings
concentrations
hope that
concentration
that
this
small relative
two readings
were also
taken at
carried
of deposition,
with
in the
increasing
The results
showed
because the variations
to the overall
35
to determine
test
of head-loss
feasible
of
In the first
could be observed.
was not
once the limit
mentioned,
below the limit
the variation
in section
)LD or (tD as
were taken in order
gradient.
was
that
as defined
are Labelled
appropriate.
conditi.ons,
beyond or slightly
slightly
of deposition,
were
In some cases it
decided at the time of the observations
conditions
and
scatter,
so in
were
subsequent tests
readings
were taken only at the limit
Figure
of deposition.
10 shows the change in head loss
sediment when the flow is at the limit
The proportionate
relative
plotted
caused by the
of deposition.
change in the friction
to the equivalent
clear
factor
tr
water value tro is
against the limiti-ng flow velocity
Vr; the
(I - Io)/tro is also equal to the proportionate
ratio
change in head loss.
definite
trend
resistance
It
f1ow.
greater
part-full
for
level
and standing
average proportionate
only
the change in
that
waves in tbe pipe.
increase
A.73%; this
measurements caused
in head loss
is
equi.valent
in the mean value of k" from 0.147nrn for
to 0.155nrn at the linit
During
each test
The
for
length
all
to a change
clear
water
of deposition.
a mean sedi-ment concentration
(ppm) was determined
appropriate
flow than
and are probably
to be unlikely,
in the water
by fluctuations
the data is
except
any
Negative values of the head-1oss
are considered
due to errors
is hard to detect
in the data,
is usually
for pipe-full
ratio
gradient
of the hydraulic
from the infra-red
of time.
Cr.
sensor over an
A corresponding
mean flow
depth, nominally y/D = 1, 0.75, O.5, 0.38 was
calculated
accurately
frorn this
a mean value
(m/s) deternined.
relationship
pipe
between C' and V, for
and part-fu11
L2 to 15, the erqrerimental
alternative
velocity
V,
1l shows the resultant
depth are shovn separately,
several
depth gauges, and
of the lfuniting
Figure
for both full
Figures
from the five
equations
the 299nn concrete
conditions.
data for
fn
each flow
and are compared rith
for
predicting
the limit
of deposition.
Figure
12 shows all
compared with
the measured pipe
three versions
37
fuLl
data
of Mayrs equation.
Version number I is
3.3 which was derived
a., = ffi
HR tests
from earlier
smooth pipes,
and 158mindiameter
in Section
described
the equation
on 77rmn
and has the form
(t-vtd/v;}4
o z / A ) ( d / R ) o o 6t v { / e ( s - t ) D l r . s
(28)
where Va" = threshold
Equation (l).
Nalluri's
the limiting
in all
This equation overpredicts
Agreement is
between 0.6mls and 1.0m/s,
range of velocities
values are in all
measured, particularly
At half-full
circumstances
with
a much wider
pipe-fuIl
a given velocity
than for
flow velocity
of standing
to judge the limit
Version
number 2 in Figures
instead
12 to
of the threshold
a nodifi.ed
to be suitable
change is
The najor
velocity
from Novak &
ones, and has the advantage of
of isolated
for
to small groups of particles
both rough and smooth pipes.
HR data for
the 77mn and 158rrn dianeter
(but not the new 299mn data)
re-analysed
best-fit
15 is
(8) which was intended
(3) applies
being valid
earlier
precisely.
Equation (3) in place of Equation (1).
Nallurirs
Equation
of V" = 1.07mls when
of deposition
both rough and smooth pipes.
the calculation
the
\raves along the pipe made it
difficult
form of Equation
over
occurred
Some of these variations
near the critical
for
are less
results
scattered
results.
than
depths.
measured concentrations
range for
the existence
higher
at the two shallowest
f1ow, the experimental
consistent
conditions
trend is apparent (Figures L3 to 15);
tested a similar
predicted
by a
overpredicts
For the three part-full
of 2.
good over the
reasonably
but at the extremes the equation
factor
in the 299rrn pipe
sediment concentrations
cases.
central
given by Novak &
velocity
using Equation
equation
38
was
were therefore
(3).
Ttre resulting
The
pipes
1.03
uqo
c.r=:O-O--(Dz/A) (d/R)
tYr/e (s-l)Dl3'2
q
(t-
(2s)
which is
similar
to Equation
(B) except for
the
numerical
constant
(d/R).
can be seen in Figures 12 to 15 that
It
and the power of the parameter
(28) gives
Equation
steeper curves of C' versus V,
than does the original
flow,
version
(B).
Equation
2 underpredicts
For pipe-fuIl
at velocities
below
about O.7m/s but overpredicts
increasingly
velociti.es
above this
For part-fu11
csnditions,
Equation
va1ue.
(2B) overpredicts
at
in nearly
cases, and at high values the discrepancies
all
become
substantial.
Version
nr:rnber 3 is based on the original
but uses the observed threshold
(8)
Equation
of V, =
velocity
O.256m/s which was measured in the 299nn diameter
concrete
.pipe when flowing
(see Section 6.2).
and shows a better
versions
that
it
still
This result
velocities
somewhat higher
in Figure 14,
to the experimental
fit
velocities.
threshold
half-full
Version 3 is plotted
1 and 2, although
the higher
approximately
overpredicts
confirms
are
given by Equation
than the values
with
at
the view
pipes
in corsnercial
(which was based on tests
data than
only
smooth pipes
(1)
and
channels).
The extrlerimental
pipe
data
for
the 299rrn diarneter
are cornpared in Fi-gures 16-19 with
formrlae
for
the lirnit
of deposition;
several
Laursen (1956), Equation (6)
{2')
Robinson &, Graf
(3)
Macke (1982), Equation (10)
(4)
Mayerle (1988), Equation (11)
(5)
Mayerle &, NaIIuri
(L972), Equation
other
those selected
from Section 3.3 are:
(1)
concrete
(7)
(1989), Equation (13)
The values
of tr used in the last
average values
three
measured in the 299run diameter
pipe at each flow depth.
sand particles
The falI
water were calculated
concrete
w of the
velocity
viscosity
and the kinematic
were
equations
u of the
given
from the equations
in
Appendix A.
fhe following
can be drawn from the
conclusions
comparisons.
(1)
This equation overpredicts the limiting
taursen
sediment concentrations
the discrepancies
2.5 and 4.0;
the flos
depth decreases.
equation
is
become larger
as
Thre slope of the
parallel
approximately
the highest velocities,
(2)
between about
by factors
ie.
to the data at
C' o VL..
Robinson & Graf
The equation
and Figure
is valid
only
L6 shows that
its
for
pipe-fu}1
flow,
passes through
line
data at a flow velocity
the o<perimental
of
However, the gradi-ent of the line
1.0n/s.
much too steep,
liniting
causing
i-t to overpredict
substantially
concentrations
is
the
at higher
velocities.
(3)
Macke
Ttris equation
to version
gives
similar
Equation (8)).
therefore
overpredicts
concentrations
for
the pipe
the
Mackers equation
sediment
the limiting
in nearly
results
(ie
number I of May's forrotrla
original
better
very
all
flowing
agreenent
cases;
full
becomes worse as the proportional
and 314-fu11
is
and
depth of fl.ow
decreaseg.
(4)
Maverle and (5) Maverle
two equatlons
were derived
same set of data,
40
& Nalluri
they give
Although
from basically
suprisingly
these
the
different
predictions
when applied
Mayerle's
equation
and shows bigger
equation
the data quite
By contrast,
flow,
well
However, in the
Mayerle's
formula fits
for velocities
Mayerle & Nalluri's
underpredicts
below 0.9n,/s.
equation
by a faetor
"a better fit
the other equations.
the limit
than Mackers
flow.
but gives
In Figures
in most cases,
discrepancies
case of half-fu11
generally
overpredicts
pipe-full
for
to the 299rsn pipe.
to the 3/8-fu11
of deposition
in 77mn, 15&mn and 299mn
pipes
formulae
due to May (Equation
are combined and compared with
(8),
of the friction
was used when calculating
(9) and (13).
Equations
been arranged
so that
linearly
proportional
concentration;
this
direct
Figures has
axis
conrparisons to be
of the three
equations.
is presented
the lirniting
flowing
pipes.
(8) in Figure
to the results
the 77nrn
In the case of the 299mn
sediment
at half-depth
(9) in Figure
significantly
concentration
when
or less.
21 gives a satisfactory
sand in the 77nrn and 15&nn
According
4T
for
20
was the data set, from rrhich
seen, the equation
to the data for
diameter
this
was derived.
Macke's Equation
fit
fit
since
as already
the pipe is
for
to the sediment
enables
a reasonable
overpredicts
positions
on the vertical
May's Equation
and l5&run pipes
pipe,
Ttre
l, in each test
Each of the three
the value
to
in Table 8.
Not suprisingly,
the equation
equivalent
perf,ormance of each equation
statistically
provides
factor
the plotting
made between the predictions
The overall
nrunber I
(Equation (13)).
and Uayerle & Nalluri
measured value
the
i-e version
in Figures 12-15), Macke (Equation (9),
is
data than
20 to 22 the complete sets of HR data for
diameter
(10)),
of about 2-3
to Macke, the equation
is
not valid
but the plot
i.ndicates
can readily
reasonable
the equation
be seen that
for much coarser particles
limiting
since it
Macke's equation
particularly
underestimates
the
by a factor
of
the concentrations,
overpredicts
at the lower values of shear stress:
performance is
to that
similar
underestimates
sand but overestimates
with
are quite
buL the differences
the predicted
measured values
varying
concentrations
by factors
method of plotting
for
the two
substantial,
from the
of about 2 to 5.
Ttre
22 does, however,
in Figure
the data for
in nearly
at the higher
Agreement is better
velocities,
of Mayrs equation.
the sediment concentrations
the tests
its
Equation (13) in Figure 22
Mayerle & Nalluri's
correlate
It
In the case of the 299mmdiameter pipe,
about 40.
with
these
is unsuitable
of the gravels
concentrations
gravels.
agreement for
down to a value of to = 0.5 N,/mz.
two pipe sizes
all
to ( 1.07 N/m2,
for values of shear stress
the three
sizes
of pipe
reasonably well.
6.4
Unsteady flow
conditi-ons
After
for
studying
conditi-ons
at the lfunit
of deposition
tests
were carried
steady fl-ows, two additional
out to determine
fn the first
of tfune-varying
the effect
the pipe was arranged to flow fulI
test,
at a steady mean velocity
of 1.26m/s, and sediment was
then added to the recirculation
conditions
Next,
were just
the tilting
the discharge
so that
half-fu1l
of deposition.
the bypass charmel (see Figure
of 1.0m/s.
reduced the sedirnent transporting-capacity
dune features.
and resulted
Tttis
of the fLow
in a deposited
Ttre unsteady-flow
42
1),
pipe was now flowing
a mean velocity
in the 299nrn pipe
some of
was lowered to divert
the 299mn diameter
with
system until
at the lfunit
weir
into
fIorys.
test
bed with
was then
started
by gradually
discharge
raising
the side weir
and depth of flow
the original
pipe-full
was carried
in the pipe
conditions.
out over a period
si-rnulate a typical
the discharge
to
procedure
Ihis
event in a sewer.
the bed deposits
increased,
returned
the
of 22 minutes so as to
storm flow
was observed that
so that
It
became smaller
and when pipe-fuIl
as
conditions
rrere reached the sediment was found to be moving again
in flume traction
The second test
way, but with
was flowing
at the limit
was carried
out in a generally
a flow velocity
ful1
when flowing
of deposition.
of 0.8m/s when the pipe
at the limit
half-full.
of deposition
At the half-fu1l
large
very
As the flow
increased,
along the pipe.
dune which moved
the dune became shorter;
when the pipe was again
disappeared
and the
flowing
sedirnent
and 0.6mls
condition,
the sedi.ment formed a single
slowly
similar
rate
after
ful1,
was
65 minutes,
the dune had
was moving at the 1funit
of deposition.
These tests
occurred
showed that
at the same flow
approached from below
(deposited
effect.
with
bed) i there
A1so, varying
tine
the tinit
did not alter
conditions
(flume
whether
traction)
it
was
or from above
vas therefore
no hysteresis
the flow rate
fairly
the conditions
Inertial
effects
velocity
were to vary
unlikely
to occur under typieal
night
of deposLtion
affect
very
the lfuait
rapidly,
for
if
slowly
deposition.
the flor
but this
is
storm conditions
in
serrers.
6.5
Deposited bed
Measurementsof the rate of sediment transport
hydraulic
linit
gradient
of deposition
for flow conditions
pipe.
After
43
beyond the
in the 299mn concrete pipe are
presented in Table 3.
formed isolated
and the
In most tests the sedirnent
dunes separated by sections of clear
eaeh test,
the bulk volume of sedirnent in
the pipe was determined.
y",
sediment depth,
given
r'rhich would have resulted
of pipe.
section
in the recirculation
constant,
it
by changes in water discharge
a series
for
of bed deposit.
pipe flowing
either
full
takes account
Figures
obtained
the
Each velocity
or half-fu11.
bed and is
of the deposited
depths
out with
were carried
in Table 3 and the related
to be
constant
of approxinately
The tests
and
between
rate
and sediment transport
flow velocity
discharge
of ys was not
the value
This enabled the relationship
flow depth.
given
system was kept
was found that
affected
studied
along the measured
When the amount of sediment
contained
greatly
material
the deposited
uniforrnly
had been distributed
the rnean depth
in Tab1e 3 is
if
of
value
The corresponding
the
by di.viding
area of the
by the net cross-sectional
f1ow.
(expressed
(see 7.1).
dunes.
curves through these
only
eontained
I?rerefore,
mean sediment depth,
I",
of the same order as the particle
scatter.
However, it
pipe-fu11
\ras often
from its
small
flow with
44
a deposited
and
the
23 show some
generally
as
value at the
AIso shown in the plot
to two equations
the
size.
can be seen that
C., increases
of deposition.
corresponding
of the pipe,
and the data in Figure
full,
y"/D increases,
limit
one or two small
few measurements were taken with
OnIy relatively
flowing
of
If,hen the volume of the
dunes rras averaged along the length
resulting
of deposition
Just beyond the limit
the pipe
fu1l
the
the U.nit
with best-fit
together
deposition,
and the depth
velocity
also contain
measurements for
coresponding
isolated
flow
bed when the pipe was flowi-ng
Both plots
and half-full.
(see 6.3),
with
varied
of the deposited
points
sediment
in terms of the volunetric
concentration)
pipe
rate
23 and 24 show how the sedirnent transport
Figures
are lines
which apply to
bed : Equation
(19)
developed from Laursenrs resuLts and Graf & Acaroglurs
Equation (20), see Section 3.4.
The two equations are
in reasonable agreement, but overestimate
sediment transport.
the values
Laursenrs
of deposition
of between 3 and 10, but underestimates
is probably
deposit
not suitable
of sediment
area.
for
the hydraulic
significantly
The only
radius
to the depth
R of the free
flow
the value of R does
so the equation predicts
the relative
depth of
becomes large.
A larger
flowing
here.
(20) which relates
change in C., until
deposit
suggests that
depths of sediment
At small values of yr/D,
not alter
lj-ttle
is
the increases
equation
as sma1l as those studied
parameter in Equation
by factors
in the depth of deposit.
The form of Graf & Acaroglurs
it
of
formula overpredicts
of C' at the lfunit
in Croproduced by increases
the rate
number of tests
half-fuIl,
more clearly
and the results
the effect
deposition;
it
appears that
to those at the lfunit
some points
the pipe
depth on the rate
Just beyond the lirnit
(V"/D < 0.001),
of C,,, remain close
out vith
in Figure 23 show
of deposit
of sediment transport.
deposition
was carried
of
the values
of
correspond to a slight
reduction
in C-_ but the changes are not 1arger than
v
the overall
scatter
in the data.
!,lhen the sedirnent
depth reaches y"/D = 0.006, a clear trend becomes
established
of increasing
C' with
increasing
ys/D.
Anomalies in the data are apparent
at flow velocities
around l.m,/s, and these may be due to the effect of
standing waves rrhich formed when the Froude number of
the flow was close
anomalies,
curves
to unity.
Ignoring
drawn through
the data for
0.006, 0.03 and 0.13 show a similar
velocities,
but displaced
these
pattern.
the curves are approxirnately
from the mean line
limit-of-deposition
curves become flatter
lirait-of-deposition
45
data;
through
at higher
y"/D
At lower
paralle1
to
the
velocities,
the
and tend towards the
line.
this
is
=
to be orpected
because as the flow velocity
movement will
a greater
occur through
bed; when the particles
deposited
to move, conditions
sediment
is increased,
depth of
at the invert
start
correspond to those at the limit
of deposition.
The experimental
compared in Figure
predicted
3.4).
deposited beds are
for
results
25 with
the sediment concentrations
by the Ackers-White
Values of C., were calculated
gradient
hydraulic
using the measured
bed width
and an effective
corresponding
to the mean sediment depth y".
25 shows that
the Ackers-White
overestimates
the rate
than for
the half-full
predicted
data;
channels
for
originally
the mean ratios
corresponding
tests,
the
be the most appropriate
transport
rates.
resistance
of bed deposits
shown in Figures
26 and 27.
are expressed
in the friction
corresponding
the quantity
proportionate
are 3.13 and
is fairly
in alluvia1
equation
was
sediment bed was not
the bed width
vhen calculating
on the hydraulic
of the 299mn diaraeter
resistance
between
to the mean sediment depth nay not
therefore
The effects
data
should also be remembered
It
along the pipe;
continuous
increase
the pipe-full
for
which the Ackers-White
in the present
Figure
can be
and it
of sediment transport
developed.
We
consistently
This margin of error
conmon in studies
usually
of transport,
and observed concentrations
1.93 respectively.
that
equation
agreement is poorer
seen that
(see
equation
transport
concrete
In Figure
pipe are
26, changes in
in terms of the proportionate
factor
tr relative
to the
mean clear-water value tro (see table
(I - Io)/tro is also equal to the
increase
in the hydraulic
6);
gradient,
(i - i^)/i^.
In Figure 27, Etre changes in resistance
oo
are shown in terms of the conposite k"" value of the
pipe;
as described in Section 6.1,
clear-water
the mean
roughness was found to be k" = 0.15rrn.
46
It
can be seen from these plots
significant
effect
that
deposition
on flow resistance
has no
the mean
until
sediment depth exceeds a value of about yr/D = O.O74.
When the bed depth reaches yr/D - 0.034,
value
is about 0.54rrn compared with
value of 0.15run.
the clear-water
As an example, this
would reduce the flow
the mean k"
change in k"
capaci-ty of a 300mmpipe
laid
a slope of 1/500 by about 11%; alternatively,
maintain
the same capacity,
at
to
the slope of the pipe
would need to be increased
to about L/4O0.
DISCUSSION
7.L
Limit
of
deposition
Analysis
of the oqperi.mental
the effect
data drew attention
which the proportional
pipe has on conditions
deposition.
depth of flow in a
at the lirnit
of sediment
developed by May (L982) from
The equation
the earlier
HR study on l58rrrn and 77mn pipe was
C . , ,= 2 . 0 5 x 1 0 - z ( A / D z ) - 1 ( d / R ) 0 . 5 [ 1 -
(Vts/Vi14
vr'
3/?
ttT=il-d
For a given
the liniting
half-fu11
Equation
similar
flow velocity,
sedinent
liniting
flowing
pipe
lfutrit
formula
concentration
(8)
predicts
in a pipe
that
flowing
in a pipe flowing
that
full.
(10) due to Macke (1982) also predicts
By contrast,
developed respectively
(1989) relate
therefore
this
should be twice
change.
Nalluri
to
predict
C.,,to R (instead of A), and
that,
for
the effect
of deposition
these two predictions.
47
the same velocity,
the
should be equal in pipes
and half-fuIl.
showed that
(11) and (13)
by Mayerle (1988) and Mayerle &
concentrations
full
Equations
a
The results
of part-full
was in fact
for
flow
intermediate
the 299nrn
on the
between
Ttris pronpted
data for
first
of the earli-er
a re-analysis
158rmnand 77nn pipes.
the
E q u a t i o n ( 8 ) , it
can be seen that
to
Referring
the quantity
v,2
X = C.,(A/Dz)tr - (vrlvl)l-4 tr]fu
Figure
28 shows the data plotted
versus
(d/R),
corresponding
listed
with
in Table 9.
in the form of X
the values are also
Each point
a given test
size,
and proportional
cases there
makes it
data.
into
was found that
it
diameter pipe flowing
depth).
the main trends
to identify
TakJ-ng the proportional
account,
(ie pipe
condition
In most
about
method of presentation
but this
easier
the
amount of scatter
was a signi-ficant
each mean point,
28 is
in Figute
mean value of X for
sediment size
line
the best-fit
(8);
to Equation
(d./R).
sediment size
should depend on the relative
together
(30)
part
ful1
depth of flow
the data for
were well
in the
(y/D)
the
15&rn
correlated
by the quantity
-0136
Y = X $/D)
(3 1 )
Values of Y are listed
(d/R)
in Figure
158mn pipe
is
29.
in Table 9 and plotted
in the data for
ttre seatter
considerably
against
reduced compared with
in Fi.gure 28, and the resulting
best-fit
the
that
equation
for
the 77rrn end l58run pipes becomes
Cu = 2.11x10-z (y,/D)0.r0 (A/Dr)-1 (d/R)0.6
V, '
t.2
t t - ( v t l v l ) 1 4t * G f f i
The value
of the numerical
as to minimise
predicted
constant
the proportionate
values
of Crr.
48
Equation
was determined
errors
in the
(32) represents
G2)
so
only a minor revision
of the origi.nal
but provides
description
part-fulI
a better
flow on the limit
Equation
(8),
of the effects
of
of deposition.
As demonstrated in Section 6.3, Equati.on (B)
signi-ficantly
overpredicts
eoncentrations
possible
that
it
can be envisaged.
Firstly,
so
does not take proper account of the effect
Secondly, the discrepancies
to the rougher
relative
considered
surface
texture
previously.
less likely
to correlate
no obvious
could be due
of the 299rrn concrete
The first
reason is
because Equation
data satisfactorily
for
(B) was found
a two-fold
(from 77mn to l58rrn);
in pipe size
variation
of
of the smooth 77nrn and 158nrn
to that
pipes tested
(from
fwo
form of the equation may be incorrect
pipe size.
pipe
this
sediment
pipe.
in the 299run diameter
reasons for
the general
the limiting
reason why a further
follow
is
increase
two-fold
15&rrn to 299mn) should not
there
a simi.lar
pattern.
According
to the theoretical
model which led to
Equation (B), see May (19B2), an increase in the
surface
roughness of a pipe
can be erqrected to affect
the transport
of sediment along the invert
'ways. Firstly,
it increases the hydraulic
and causes the 1ocaI velocity
decrease relative
this
particles
by the flow.
so that
a larger
in motion.
driving
Referring
constant
Both factors
that
force
of
increases
is needed to keep then
(8),
the first
to reduce the value
and the second factor
e><pected to increase
on the
and the pipe
to Equation
can be expected
nurnerical
exerted
to
of the flow;
Seeondly, the coefficient
between the partieles
friction
factor
force
resistance,
around the particles
to the mean velocity
reduces the driving
in two
the effective
of the
can be
threshold
velocity.
serve to reduce the amount of sediment
can be transported
49
by a rough pipe
relative
to an
equivalent
smooth one.
(10) and Mayerle's
increase
By contrast,
Equation (11) indicate
in the pipe friction
the limiting
factor
As explained
in Section
yet available
for
6.2,
the effective
tests
the results
flow,
the threshold
(32).
C,, = constant
Regression
(33)
of the data in Table 2 (excluding
analysis
at y/D = 0.5)
suprisingly
consistent
data,
but are higher
flow;
the actual
than the value
pipe were internediate
of the quantity
50
analysis
gave an overall
mean
was
This figure
Y; these are listed
(d/R)
data for
close to the best-fit
pipe-full
(30) and (31) to calculate
then used in Equations
can be seen that
of the
measured in the
of the regression
of V, = 0.30m/s.
against
are
between these two lirnits.
the results
velocity
for
velocities
accordi-ng to the nurnber of tests
It
part*fulI
given the variability
threshold
the corresponding
thus enabled best-fit
as shown in Table 7.
the pipe flowing
for
and plotted
depth of
Yr,
The results
threshold
by
that
values of Va to be determined,
Weighting
by analysing
(vL - vt) 4
.
of
V, in the present
velocity
suggests
one anomalous test
values
Estimates
For a given proportional
the equation
velocity
to the framework provided
according
is
in a cormnercial pipe
the 299rrn pi-pe can be obtained
with
Equation
threshold
study.
equation
(eg concrete).
a non-smooth finish
predi.ction
this
no suitable
determining
an
of the present
sedjment particle
of an isolated
that
tr should increase
sediment concentration;
is not supported by the results
with
Macke's Equation
the
in Figure
the
in Table 9
29, together
with
l58mrn and 77nrn pipes.
299wn results
line
mean
now fall
given by Equation
quite
(32).
AII
the HR data are shown plotted
GD
in Fi.gure 30, and statistical
degree of fit
limit
indicate
pipes,
on the
of conditions
provided
approximately
at the
the effective
threshold
For smooth
from Equation (1).
Vt" should be calculated
pipes,
(32)
Equation
can be determined correctly.
For concrete
V, is
information
that
a reasonable estimate
of deposition,
velocity
Equation
is sunmnarised in Table B.
Overa11, the results
provides
against
the present
study indicates
equal to 4Va"/3,
known over what range of conditions
but it
this
that
is not
relationship
holds.
Equation
(32) has been briefly
data for
sand sizes
significantly.
the rneasured sediment transport
This is believed
the sands were fine
By contrast,
specifically
therefore
for
recomrnended that
(32) relates
Equation
finer
it
in
used in the
to bed=load transport,
sand particles
to be because
enough to be transported
suspensi.on at the flow velocitj.es
experiments.
Macke's
of 0.16rnm and 0.37rmn, and was
found to underestimate
rates
compared with
and it
is
should not be applied
than about 0.4nun to 0.5run
(see also the discussj-on of the conditions
for
suspended-Ioad transport
Equation
in Section
(32) and Macke's Equation
sfunilarly
for
also
gives
determine
Mackers equation
the rate
a better
concrete pipe,
(10) appear to behave fairly
rnedium sands in smooth pipes,
coarser particles
underestimates
3.3).
fit
the effective
Equation
to the new data for
tests
for
significantly
of transport.
but further
but
the
(32)
299wn
are needed to
threshold
velocity
of sediment
in such pipes.
7.2
Deposited bed
The results
transition
in Figures 23 and 24 show that the
from flume traction
to movementwith a
deposited bed does not significantly
51
decrease the
sediment-transporting
the limit
the transport
of deposition,
y" is the uniform
result
if
uniformly
with
I?ris finding
the start
(assuming constant
of the change in hydraulic
resistance
its
velocity;
the gain
in Figure
this
for
of deposited
the 299run pipe
in hydraulic
such as those for
in
deeper and reduce
flow
some or all
tend to offset
will
the pipe
caused by
An increase
24.
However, Figure
bed.
there
25
lras no signi-ficant
the rnean
until
resistance
of
due to the
capacity
in sediment-transporting
shows that
until
and sediment
results
make the water
increased width
increase
water
resistance
when considering
will
in a
is necessary to take account
However, it
flow
important
of deposition
continues
in which deposition
discharges).
is
need not produce an unstable
part-full
surcharges
half-full
which would
depth of deposit
distance.
means that
pipe flowing
deposition
as explained
the sediment in the pipe were distributed
because it
situation
increases
rate
as the mean sediment depth y" increases;
in 6.4,
Beyond
of the flow.
capacity
sediment depth reached about y" = 0.03 D.
suggest
The results
of the present study therefore
that the trno-deposit" criterion
for self-cleansing
sewers could be usefully
effeets.
Figure
lirnit
the lirniting
sediment
would be about 7 times
the value
24 indicates
of deposition
that
when the flow velocity
and about 2 times when the velocity
effect
is
at the
is 0.6m./s
The
1.2-m/s.
and gradients
on minirmrm velocities
sewers
for
by an example of a 300mn concrete
can be illustrated
pipe required
to eater
concentration
of 25ppm when flowing
for
Assuming, conservatively,
sediment-transporting
limit
adverse
sediment depth of y=/D = 1%,
For a deposited
concentration
without
relaxed
of deposition,
a volumetric
half-fulI.
a two-fold
capacity
relative
the required
sediment
increase
in
to that
at the
minimun vel.ocity
would be reduced from about 0.85m/s to 0.75m/s; this
52
would allow
the minimum gradient
of the pipe
to be
decreased by about 20%, which would be worthwhile
economically.
Based on the present
suitable
criterion
selrers.
This
for
is suggested that
depth would not increase
of a pipe significantly
of at least
criterion.
two relative
velocity
a
the hydraulic
but would increase
capacity
A conservative
minimum flow
a
the design of self-cleansing
the sediment-transporting
factor
it
depth of y"/D = l% could provide
mean deposited
resistance
findings,
of the flow by a
to the rrno-deposit"
method of estimating
Vro consistent
with
the
a sediment
depth of y^/D = 1% could therefore be obtained by
s
applying a factor of about two to Equation (32) to
give
cr, = 4.0 x 10-z (A/D?)-1 (y/D)o.so (d/R)0.5
v?
3.?
t1 - (vtlvm)14fg#d
Tttis suggestion is obviously based on a limited
(34)
nr:mber
of tests and should be reviewed as more exllerimental
data become available.
transport
Future studies on sediment
in pipes with deposited beds may also
provide alternative
relationship
coneentration
formulae for predicting
between mini:mrm flow velocity,
the
sediment
and depth of sediment deposit.
coNctusroNs
(1)
Previous HR test data on the lirnit
deposition
of sediment
in l58rrn and 77nrndiameter smooth
pipes lrere re-analysed to detennine more
precisely the effect of proportional flow depths.
The resulting
best-fit
equation for predicting
the flow veloci-ty required at the Limit of
deposition is given by Equation (32).
53
Q)
New tests
limit
out to study the
have been carried
in a 299mmdiameter
of deposition
pipe using 0.7kwn sand, flow velocities
0.5nls
and l.5mls,
between
sediment
between 0.3 ppm and 440 ppm, and
concentrations
proportional
volumetric
concrete
depths of flow between 3/8-fu11
and
pipe-ful1.
(3)
Analysis
of the new data showed that,
velocity
and depth of f1ov,
the limiting
sediment
in the eoncrete pipe was typically
concentration
tralf
a given
for
oqpected in a smooth pipe of the same
that
diameter.
(4)
pipe is
consi-dered to be due to greater
between the sediment
frictional
resistance
particles
and the pipe
and maintain
The data ana}ysis
threshold
of sinilar
33% greater
satisfactorily.
fitted
it
(6)
the equation
both rough and smooth pipes
velocity
the threshold
the sediment
is
of the sediment
Equation
transported
should not therefore
finer
the results
(32)
Equation
suggests that
this
is assessed correctly.
that
adjusted
was found that
it
the 299:nn pipe
for
pipe was
than in a smooth pipe
Using this
velocity,
suitable
the effective
in the concrete
diameter.
threshold
provided
sediment
individual
that
indicated
velocity
approximately
is
velocity
in motion along the pi-pe.
particles
for
Ihese factors
in the threshold
cause an increase
needed to start
and to ehanges in
invert
in the pipe.
profile
the velocity
(s)
of the concrete
capacity
The lower transporting
be applied
(32) assumes
and
as bed-load,
for
sand sizes
than about 0.4rnm to 0.5mm.
Linited
unsteady
tests
flows
54
were made to study the effect
on the l-imit
of deposition.
of
The
transition
between flume traction
was not altered
the limit
by gradually
remained
and deposition
varying
f1ows,
and
the same when approached
frorn
above or below.
(7)
Tests were also carried
out in the 299mn concrete
pipe to measure hydraulic
sediment
transport
bed deposit.
Slightly
deposition,
uniforrnly
capacity
slowly
along the
sediment was
and converted
distributed
by the onset of deposition;
the transporting
flowing
velocity
of
the lfunit
capacity
depth increased.
half-ful1
and a deposit
concentration
beyond
increased
With the
depth of
at a flow
1.2m/s was about two times that
of deposition;
the ratio
at a flow velocity
increased
of the sedirnent deposits
resistance
did not become significant
reached about 3U; at this
of
point,
on hydraulic
until
y=/D
the average k"
of the pipe was 0.55nnr compared with
clear-water
at
to about seven times.
The effect
a nean
value of 0.15rn.
Based on these findings, it is suggested that a
deposit depth of y"/D = 1% could provide a
satisfactory
criterion
for the design of
rrself-cleansing" sewers. It would allow a
worthwhile reduction
in rninirm:mvelocities
gradients, particularly
55
to
the sediment transporting
Y"/D = 1%, the sediment
value
of
of the flow was not reduced
lirait,
0.6mls,
y",
mean depth,
as the mean sediment
(9)
formed a series
condition
showed that
significantly
pipe
of
along the pipe.
The results
this
each test
of
depths of
beyond the limit
The volume of deposited
an eErivalent
and rates
small
dunes whieh travelled
measured for
(8)
various
the sediment
isolated
pipe.
for
resistance
for larger pipes,
and
cortrpared with
"no-depositrl
and would not result
criterion,
significant
Equation
the previous
reduction
in hydraulic
capacity.
a possible
rnethod of
(34) provides
determining
in any
minimr:m velocitj.es
a deposit
for
depth of y",/D = L%, and should give
conservative
results.
(10) These suggestions
oq>erimental
transport
should be reviewed as more
data become avaiLable
in pipes with
deposited
on sedirnent
beds.
ACKNOWTEDGEMENTS
The ercperimental
measurements were carried
Mr G R Hare and Mr K D Jones.
The data were analysed
by Mrs P l{ Brown and Mr R Payne.
supervised
River
The project
by ilr R W P May, and carried
Engineering
56
out by
was
out in the
Department headed by Dr W R l{hi-te.
10
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TABLES
TABTE 1
Experirrental
IEST l{,o ym
T1CLR O.50
TzCLR O.50
T3CIR 0.52
T4CLR 0.50
T5CLR 0.50
T6CIR 0.5{)
T?CIR 0.50
TBCLR O.5O
TgCLR 0.50
T1OCLRO.50
T11CT,R0.50
T12CLR 0.50
T14CLR O.50
T15CIR 0.50
T16CT,R0.75
T17CLR 0.75
TIBC{R 0.?5
T2OCIR 0_38
Tz1CLR 0.38
Tez$;R 0.50
Tz3CT,R0.75
T24CI,R 0.75
?25CtE 0.?5
T26CT,R0.38
Tz?CT,R0.39
Tz8CLR 0.38
TzgCT,R0.50
T30CT,R0.50
T31CT,RO.?5
T3zCT,R1.00
1
0.93
2
0.94
3
0.95
6
0.50
7
0.51
I
0.51
I
0.50
10
0.51
11
0.51
t2
a.25
13
0.25
74
0.25
15
0.25
16
A.25
L7
0.75
18
0.75
19
0.?5
2A
0.76
2L
0.73
22
0.?5
23
1.00
results
ks
for
299rm pipe - clear
Re
0.2388 177980
0.1505 200352
0.2772
226702
0.04tr8
252521
0.0095 278084
0.0218 302745
0.2555 324034
0.02?0 250044
0.0103 279492
0.1702 349600
0.0770 3s6241
0.0833 303828
0.1458 152868
0.4771 128?38
0.4981
155535
0.1912
249287
0.0316
343427
0.1156 166201
4.1292 230515
0.3790
13447A
0.628s 161412
0.2327
355838
0.8294
249691
0.0632
133827
0.0533
127593
0.1056 298251
0.1121
41L624
0.2821
129909
0.3769
194377
4.0222 35913?
0.2657
3?7378
0.1135
274899
0.3940
162807
0.2149 131479
0.2716 134298
0.0816 196338
0.1194 27t942
0.2089
377974
0.2941
541483
0.1789
259036
0.0661 206888
0.1545
tr5224
0.1323 116415
0.050?
?5359
0.6995
139934
1.2911
142707
0.1867
228639
0.0997 310610
0.0750
443755
0.0?41
657992
0.3667
126960
n
0.01045
CI.01005
0. 01053
t).00929
i). 00896
0.0090t
0. 01034
0. 0i)915
0.0089?
0.00945
0. 00935
0.00950
0.0101?
0.01125
0.01139
0.01032
0.00926
0.00977
0.00969
0.01100
0.01166
0. CI1036
0.01946
0. 00962
0.00960
0.00945
0.0095?
0.01074
0.01102
0.00891
0.01045
0.00987
0.01108
0.01051
0.01069
0. 00972
0. 00976
0. 01011
0.01039
0.00966
0.00901
0.00981
0.009?1
0.00956
0.01183
a.oL272
0.01033
0.00978
0.00945
0.00930
0 .0 1 098
raater resistance
V
m/s
0.705
0.804
0.862
0.990
1.09S
1.200
1-290
1.002
1.096
1.394
1 .5L1
1.191
CI.600
0.503
0.500
0.804
1.102
0.802
1 . 102
0.498
0.501
1.104
0.803
0,595
0.595
1.409
1.499
0,499
0.59s
1.401
1.286
0.925
0.545
0.520
0.5e0
0.730
1.020
1.382
1.950
1. ?35
1.370
o .757
o .757
0.493
0.458
0.461
0.731
0.981
1.396
2.094
0.494
lambda
0.02040
0.01884
0.02054
0.01612
0.01498
0.01516
0.01989
0.01563
0.01500
0.01841
0.01628
0.01680
a.0t927
0.02364
a.02270
0.01863
0.01502
0.01903
0.01874
0.02253
0.023?8
0.01881
a.02497
0.01844
0.01836
0.01?84
0.01?04
0.0e146
0.021?4
0.01480
0.01934
0.01731
0.02185
0.02057
0.02125
0.01758
0.0177?
0.01899
0.02007
0.02085
0.01810
0.02148
0.02095
A.A2A32
0.A2449
0.02834
0.01869
0.01675
0.01568
0.01514
0.A2249
T
"C
13.?
13.8
14.6
14.0
13.7
14.0
13.6
14.:i
14.8
14.5
L4.6
14.4
L4.7
14.3
14.4
14.8
14.4
14.1
L4.7
15.8
15.8
15.8
74.4
17.0
15.1
16.8
16.8
16.8
16.8
15.8
13.6
14.4
14.8
13.5
r4.2
15.?
15.s
16.4
16.s
14.2
14.5
14.8
14.8
L4.7
13.?
L4.Z
L4.e,
15.0
15.5
14.9
14.3
TABLE 1 (contd)
TffiT No ym
238
1.00
248
1.00
258
1.00
268
1.00
27A
1 . t)0
z7B
1.00
zBA
1.00
3BB
1.00
Rz?A 1.00
R?78 f . ilO
RzBA 1.00
nzBB 1.00
R?64 1.00
R26B 1.00
n25A 1.00
R25B 1.00
N3
1.CI0
N4
0.49
N5
0.25
A1CLR 1.00
A1CIR11.00
A1CLRz1.00
A1CIR31.00
A 1 C I R 41 . 0 0
A1CIR51.00
AzCLR 1.00
A2CLR11.OO
A3CLR 1.OO
A3CLR11.OO
A4CIR 1.00
A4CL,R1
1.00
ASCI;R 1.00
A5CIR1 1.00
A6CIR 1.00
A6CI,R11.00
A10C1,R
1.00
A10CT,R
1.00
A11CT,R
1. OO
A11CT,R
1. OO
A1zCT,R
O.5O
A14CLR0.25
A15CT,R
0.74
A16CIR 0.49
AI?CLR 0.50
A18CT,R
0.49
A20CtR0.49
Az1Cl,R0.50
AzzCLR0.50
ks
0.8009
fi.0538
0. 1092
0. 1276
0.0465
-0.0?35
0.0647
0.0398
0. i1792
0. 1296
0 _0494
0.0595
0. 1948
0. 110?
0. 104?
0.0982
1.5381
0. 1560
0.08?9
0.201?
0.1109
0.1384
0.0973
0. 10?2
0.1332
0. 1209
0. 1371
0. 1327
0.1243
0. 0880
4.1922
0.14?0
0.1123
o.L4L2
0.1676
0. 1210
0.1180
0.1479
0.1682
o.L524
0.0652
0.3264
0.0896
0.0?20
0. 1304
o.2L52
0.0255
0.1493
Re
129324
398968
256663
L64927
L23441
1.)l
l.al-l
1?li
| !,
43443?
44?115
11665ti
116650
400425
4001?6
162194
161185
257544
256412
42746
1839CI4
69514
205651
205651
207915
207915
212663
212663
230248
z3a?,48
183942
183942
15931?
159317
113243
113243
L37239
13?239
25274b
252745
L2,4231
124231
230473
136599
?81559
231817
L64434
185467
2625t5
280543
30L24?
v
n
tl.01191
0.00914
0. 009?3
0.01005
0. 00983
il.0{t915
0.0(t920
0. 0CI896
0.01006
0. 01026
0.00910
0.00919
0. 01033
0. 00998
0. 00970
0.0096?
0.01324
0.01010
0.00982
0 " 01026
0.00985
0.00998
0.0097?
0.00981
0.00994
0.00984
0.00992
0.01001
0.00997
0.00988
0.01033
0.01033
0.01022
0.01021
0.01031
0.00980
0.00978
0.01030
0.0103?
0 - 01000
0.00923
0.01075
0.00966
0.00948
0. 00998
a.0Lo22
0.00911
0. 00989
m./s
i).494
1.524
I
t\4Q
0.630
o.474
0.469
1.638
1.643
0.4?u
iJ.4?0
1.609
1.608
0.643
0.639
L.0zt
t.a2?
0.180
0.7?9
0.494
0.901
0.901
O.B9B
0.898
0.898
O.BSB
1.003
1.003
0.799
0.799
0.698
0.698
0.499
0.499
0.603
0.603
1.101
1.101
0.549
0.549
0.997
0.994
1.019
1.019
0 .? 0 4
0.814
1.131
1.195
t.274
lambda
T
orr
v
t).02646
0.01559
0.01?65
0. 01881
0.01802
0.01560
0.0L577
0.01496
0. 01885
0.01964
0.01545
0.01_575
0.01990
0.01857
0.01755
0.01742
0.03268
0.0191L
0.02138
0.01962
0.0180?
0.01856
0.017?9
0.01794
0.01842
0.01806
0.01836
0.01868
0.01853
0.01819
0.01990
0.01990
0.01946
0.01943
0.01983
0.01?91
0.01?85
0.01976
0.02005
0.01863
0.01896
0.02027
0.01744
0.01677
0.01865
0.01954
0.01545
0.01817
15. tr
1 5 .f J
13.4
1 5 .f J
15.t}
t4.5
15.5
16.5
1 3 .i j
1 3 .t l
13.1
13.1
13.6
13.6
13.€
13.4
11.4
11.?
11.4
10.0
10.0
10.5
10.5
11.3
11.3
10.?
10.2
10.3
10.3
10.0
10.0
9.8
9.8
9.9
9.S
10.2
ta.2
g.?
9.7
10.4
10.8
10.3
L0.2
10.9
10.3
11.0
10.9
11.0
TABTE 2
Ereerinental
D
(m)
ri.29883
0.29883
ri-t9883
0. ?9883
0.29883
{J.29883
{i.29883
rJ.:gB8:3
i].I9BB3
{1.u9883
0.29883
0.2988;3
0.ug883
0.29883
0.29883
0.29883
A2OSmr 0.29883
A215ED 0.29883
CI.29883
A22Sm
0.29883
T15ED
0.29883
T2SED
0.29883
TSSED
0.29883
T4Sm
T5smt 0.29883
T6SED 0.29883
0-29883
TTSm
TSSm
0.29883
T9SED 0-29863
TlOSm 0.29883
T11Sm 0.29883
TTzgED 0 . 2 9 8 8 3
T135ED 0-29883
T14SED 0.29883
T17SED 0.29883
Tl8Sm 0.29883
T20Sm 0.29883
0.29883
T2lsm
T22gm 0.29883
T23Sm 0.29883
T24SED 0.29883
T25gm 0.29883
T26SED 0.29883
Tz7SED 0.29883
Tz8SED {).29883
T29SEf,l 0.29883
T3OSED 0-29883
T3lgED 0.29883
T3zSED 0 . 2 9 8 8 3
TEST
l{c
AlSEDIO
A2SED
A3SED
A45S
ASSEI}
A6SED
A9ggD
Al0SElt
A11gED
A12Smi
Al3SET}
41s$El'
AI6SED
A1?SED
AIBgED
4195m
results
d50
(m)
0. i)00?2
0. t){1072
0.00072
0. f10072
0.00072
0.0{l{i7?
{i . r}00?:
ll
frfll1717
0.00{i?2
0. rl00?2
0.0 0 0 7 2
0.0 0 0 7 2
0 - 00072
0.00072
0.000?2
0.00072
0 .0 0 0 7 2
0.00072
0.00072
0.00072
0.00072
0- 00072
0.000?2
0.00072
0.0 0 0 7 2
0.00072
0.00072
0.00072
0.00072
0.000?2
0.000?2
0.000?2
0 .0 0 0 ? 2
0.000?2
0.00072
0.00072
0.00072
0.000?2
0.00072
0 .0 0 0 ? 2
0.00072
0 .0 0 0 7 2
0.0007e
0 .0 0 0 ? 2
fJ.00072
0.0fJ072
0.00072
0.000?2
for 299mn plpe - limlt
tAI'IBDA
v/n
u.0185rl
CI.01817
{"}.01934
0. 019?1
0.01979
0.01890
t].0175t
0.01784
r].02084
0 - tJ1896
0. {i1886
0. rl1?84
0. ti1769
0.01803
0.01815
f.il
1.rl
1.0
a.aza27
tl. 111638
0.01583
0.01932
0.01885
0.01639
0.01981
0.01668
0.0159?
0.01739
0.u2026
s.01?90
0.01648
0.01950
0.016?ll
0.016?8
0.0138U
0.01595
0.01842
0.01?46
0.01889
0.01902
0.02336
0.02231
0.01646
a.o224L
0.01829
0.01880
0.01884
0.01721
0.4ufi4
0.02015
0.01509
1n
lfi
1.t.,
r:f depositlorr
V,.
{mls)
r).893
I,UUb
0. BOIJ
0.698
i/r
trna\
0.603
1 {l
1.196
1fi
1.099
0.549
1.0
0 . 5 1 1 *.97',J
i1.504 0.896
0.?34 1 . 0 1 6
CI.490 L . A z L
0.499 0.7{J2
0.494 0.812
0.513 0.8?0
0.498 1.108
0-502 1.191
.Ja
0 . 5 1 9 1L - &C2'7
0.49
0.7L4
a.B2Z
CI.49
0.864
0.52
0.983
0.51
1-066
0.51
1.119
0.52
1.290
0.50
0.948
0.52
1.035
0.53
1.386
0.50
1.498
0.50
1.191
0.50
L.294
0.50
0.599
0.50
0.805
0.?5
1. 129
0.73
0.801
0.38
1.100
0.38
0.499
0.50
0.502
0.75
1. 10?
0.75
0.809
$.74
0.598
0.37
0.597
0.38
1.396
0.38
1.497
0.50
0.495
0.50
0.603
0.75
1.386
1.00
1.0
Cv
(prm)
2 9_ 8 6
45.5i1
14.50
?.56
i1.67
4.47
69.75
55.29
.? 1?
?0. li]
22.L8
42.54
32.67
6.68
On
Eat
30.47
51.52
55.?3
135.54
9.57
2A.76
29 -42
24.07
35.17
87 -47
22A,73
35.40
q7 -24
230.45
25L.22
110.00
1?4.51
4.44
8-27
41.56
19.50
98,04
1.00
0.31
66.15
20.69
7.99
2.47
443.OCI
z8{:}.00
4.50
1.55
98.66
T
"c
13.5
10.4
10.3
10.0
9.8
D(f
AP
1 0 .t
9.5
1 1 .{ }
10.2
10.5
1 0 .g
10.3
10.0
11.0
10.9
11.4
L3.7
13.8
14.6
14.0
1 3 .?
14.8
13.6
14.3
14.6
14.5
14.8
L4.4
L3.4
t4.7
!4.&
L4.4
14.1
L4.7
15.8
1 5 .S
15.8
L4.4
1?.0
1 5 .1
16.8
1 6 .B
16.8
16.8
15"8
TABTE 3
E:<perimental results
Test
V
(m,/s)
No
DE1 0.609
DF,z 0.7CI0
DB3 0.834
DB4 4.972
DB 5 1 . 1 4 0
DE6 L.522
DB? 1.417
DB 8 1 . 3 1 7
DBg L.215
DE10 1.123
DB11 1.014
DB12 0.921
DB13 0.823
DB14 0.735
DB15 0.602
DB16 0.516
DB1? 1.495
DB18 1.399
DB19 1.296
0ts20 1.192
DB21 1.092
DB22 1.003
DB23 1,003
DF,2,40.893
DB25 0.?s9
DB26 0.694
DB27 0.596
DB28 0.500
DB29 1.008
DB30 0.993
DB31 0.902
DF32 0.801
DB33 0.?95
DB34 0.699
DB35 0.602
DB36 1.000
DB37 0.902
DBSB 1.001
Dts39 1.105
DBro 1.104
DBtl 1.209
DBd'? 1.e97
DBIS \.4L2
DB14 1.009
YM
0.501
0.502
0.503
0.505
0.500
0.501
c}.502
0.503
0.502
0.501
0.500
0.501
0.501
0.499
0.503
0.499
0.504
0.502
0.502
0.50e
0.502
0.502
0.499
0.503
0.504
0.501
0.502
0.502
0.500
vslD
0. 1479
0.1332
0. 1386
0.1497
0.1623
o.0322
0. 0293
0. 0265
0.0342
0. 0360
0. 0332
0.0338
0. 0428
0.0505
0.0286
0.0340
0.0120
0.0087
0.0062
0.00?3
0.007?
0.0069
0.0064
0.0067
0.0089
0.0072
0.00?8
0.0003
0.0018
o.502 0 . 0 0 1 6
0 .5 0 3 0 . 0 0 1 0
0 .5 0 0 0 . 0 0 0 1
0.503 0,0009
0 .5 0 3 0 . 0
0 .5 0 2 0 . 0
1.0
0.0152
1.0
0.0013
1.0
0.0008
1.0
0.0
1.0
0.0281
1.0
0. 0314
1.0
0.0030
1.0
0.0290
1.0
0.0369
for 299un pipe - deposited
Re
145466
168377
198024
226258
257025
396410
362634
342540
313268
288097
267181
234787
199448
182498
150697
129883
381994
355134
332834
306117
281150
267854
258693
230900
20618?
178677
\5427A
130864
23831?
232736
2L1579
186825
185378
16218?
139372
230535
?45477
231113
255L64
252768
275638
297750
322L57
232194
ks
(rm)
2.8222
2.1885
1.5254
1.2197
0.320:J
4.L922
0.4050
0.53?6
0.?419
0.1881
0.3099
0.5033
0.?003
0.7103
1.1646
1.5882
0.2681
0.2486
A.4326
0.3515
4.2A47
0.L7A4
0.1182
0.2053
A.t272
-0.08e1
0.1195
0.08?2
0.0692
0.185?
0.1862
0.1161
0.1017
-0.0345
0.0760
0.1109
0,0311
4.1243
0.0296
0.119?
0.0715
0.1159
A 3527
0.5208
So*1gg
0.2904
0 .34t2
4.4364
o.5647
0-5778
0.7508
0.7568
0.6s75
tJ- 5052
o.4157
0.3808
4.3422
o.2994
0.2430
0.1810
0-1466
0.7594
0.657?
0 .6361
0.5152
0.3916
0.3215
0.3069
0 .?647
0.1061
0.1100
4.114?,
0,0?96
0.2935
0.3223
4.2677
0.2011
0.1945
0.12?8
0.1129
0.3062
0.2277
0.2533
0.3292
0.3?48
0.0314
0.5043
0.7294
0.4115
bed
T
Cv
(ppm) "C
280.36 77.?.
3 3 0 .1 9 l _ 6 . 5
422.91 16.3
54:Z.09 16.0
1186.68 16.0
1165.08 15.3
11L2.45 14.5
800.98 15.il
543.68 14 .9
356.49 14.fJ
355.23 L5.2
327.30 14.5
3 2 5 . 0 6 1 2 .g
236.14 14.1
107.21 13.6
52.38 14.0
410.4? 14.0
437.42 13.8
310.76 L4.2
282.41 14.?
1?6.46 14.3
151.58 15.?
109.26 L4.5
1 1 3 . 5 1 1 4. 5
76.18 14.3
30.66 14.3
24.54 14.5
27.17 14.8
53.20 !1.2
56.06 10.8
29.5L 10.8
11.63 10.7
23.31 10.6
5.68 10.4
71.O2 10.4
61.86 10.4
64.66 9.Er
34.99 10.4
21_.73 10.4
162.12 10.3
t43.42 10.e
203.84 10.3
319.80 10.2
142.2L 10.6
TABLE 4 : Values of k
for clear water in 299mnpipe
"
["
vlD
1.0
37
0.95
(mn)
o
s
o
n
0. 116
0.0676
0.0111
0.258
0.1404
0.0810
0.75
T2
o.296
0.248L
0 . 0 71 6
0.50
30
0.150
0.1089
0.0I99
0.375
0.093
0.0333
0.0149
0.25
0. 105
0.0500
0 . 0t B 9
0. i47
0.1135
0 .0 1 1 7
94
A11 data
Mean k
for
99 points
k
ss
o=
s
+2o
=
0. l92rrn
0.236mn
=
0.664rrn
A11 values > 0.664rsnwere eliminated
detailed
above
from analysis
leaving
the 94 values
TABIE 5 : Values of n for clear water in 299runpipe
v/D
N
1.0
37
0.95
n
o
s
n
0.00987
0. 00046
0.000075
0.01047
0.00060
0.00035
o.75
L2
0.01033
0.00082
0.00024
0.50
30
0.00988
0.00059
0.00011.
o.375
0.00963
0.00012
0.00005
o.25
0.00955
0 . 0 0 0 31
0 . 0 0 01 2
0.0099
0.00058
0. 000060
94
TABLE 6 : ValueE of )t for clear water in 299nrnpipe
v/D
1.0
I
37
0.95
o
s
o
n
0.0182
0.0016
0.00027
0.0195
0.0023
0 . 0 01 3
0.75
L2
0.0188
0. 0029
0.0009
0.50
30
0.0183
0.0021
0.00039
0.375
0 . 01 8 5
0.00045
0 . 0 0 01 9
o.25
o.0202
0.0012
0.00048
0.0185
o.oo202
0.00021
94
TABLE7 : Measuredand predicted threshold velocities
Threshold velocities
Measured
ila
in 299nmpipe
(m/s)
Predicted
Predicted
Predicted
Eqn (1)
Eqn (2)
Eqn (3)
0.268
0,224
0.201
0.353
o.282
0.489
0.256
0.228
0.401
0.339
yld
Effective
threshold
velocity*
1.0
o.206
0 . 74 4
0.330
0.506
0.322
0.374
0.344
weighted mean
0.301
* calculated
frorn limit
Number of tests
(rnls)
of deposition
10
25
47
data
(see 7.1)
TABTE I
lteasured and predicted
all tlR data
D
{rms)
concerrtrations
d50
(rms}
ym
i1.57
0.64
0. {i4
il-64
0.64
a
l-
at limit
of deposition
-
o
o(%)
0.3s1
fi.110
0.t9?
0 -1 8 0
0,170
0.578
a-t27
0.181
0.155
0-311
0.237
0.215
11.1
18.?
2$.7
t1.1
78.5
12.4
91.5
2L-g
52.3
4?.3
59.5
0.791
a- z z L
32.0
0.959
1.024
0.933
1.001
1.011
0.998
0.818
L.274
1.015
1.075
0.?89
s.114
0.195
a.221
0.236
fi.787
0.138
0.196
a.4?.3
0.373
1.00e
0.288
11.9
19.0
:'3.7
23- 6
77.8
13.8
23.9
33.3
36.?
93.t
36.S
1.029
0.450
42.9
0.730
1.079
0.981
1.020
0.856
(30.38)x
(35.62)x
a.742
0.?59
0.595
0.90?
0.130
0.243
0.150
4.2L2
0,699
{3-61)r
{5.11)x
fr.199
0.266
a,242
0.14?
t7.8
22.5
15.3
?'6.7
81.6
{11.9)*
{ 14.3):tr
26.8
35.0
40.7
16.2
0.795+
0.256+
34.83+
CV(rcas ) /CV(pred)
Mav (Eqn B)
76
1trO
L.J1)
158
158
r58
158
158
?o11
-1Aq
?rfq
399
.\
n ??E
ER
I
7q
1
0.?2
0.72
0.?2
0.?2
?tr
{-rF
I
r-\ ?t
11
q
n
1?tr
rl.9B7
1.054
D .8 6 8
{1.804
0.?36
1 .027
0.849
0.?07
0.595
0.501
l{ay (Eqn gZ)
76
158
158
158
158
158
158
299
299
9{fq
9f)()
0.57
0.64
0.64
0.64
0.64
5.8
7.9
0.72
4.72
4.72
4.72
t
l-
1
0"75
0.5
0.375
1
1
I
0.75
0.5
lJ.,7(J
t.tacJne(Eqn 9)
76
158
158
158
158
158
158
299
299
299
t99
0.57
0.64
0.64
0.64
0.64
5.8
7.9
a.7z
4.72
a-72
0.?2
+ Excluding
points
1
1
0.75
0.5
0.3?5
1
!
I
1
0.?5
0.5
0.375
rnarl<ed with .*
TABL,EI {eontd)
D
{rms)
d50
(rrus)
ym
CV(neas),z0v(pred)
€
c(%l
Mayqrle (F,rm 11)
76
1F1}
1EA
1FA
158
158
1_58
?(f,q
e99
?qq
?qq
l{ayerle & Nalluri
A -249
0.416
0.319
0.874
L.882
LT-{'
33.9
14.11
30.4
tr2.2
ft
lfiQ
\J.LLJ
14
e
IA.d
0.113
0.134
0.373
0.523
0.089
19.0
26.5
85.?
69.6
t0.6
1 .1 1 3
a.473
43.6
0.75
0.5
2.035
3.259
4-329
5.506
4.693
0 -?'97
0 .1 7 1
z.ZLA
3- 298
z,-546
n
1
1.265
1.296
1.914
1,002
5.335
0.052
0.053
a.947
2_0a2
r.Bg3
0.306
62.t,
39.8
44.2
18.t
113.6
L 7. F r
31.G
42.8
60.?
74.3
20.t
1.389
52.5
nE7
1
0.64
{1.s4
il_s4
r1.64
1
L-424
t.227
r,
l-)E
r)_375
FO
I
7-9
4.72
0.?2
$.72
1
t
t] 7q
a-72
n
(Eqn 13)
?s
0.57
158
0.64
158
0.64
158
0.64
l5B
0.64
5.8
158
158
7-9
9qo
n '7t
399
399
t99
A-72
CI.72
CI.72
NA
a?R
1
I
n7€
0.5
0.375
1
1
l-
a?R
1 C- E:.
2.878
2.041
fi.859
0.595
{1.505
0.435
0.751
0.431
tle
2.842
TABLE9 : Analysis of data for limit
D
(rrn)
d
v/d
of deposition
t
d/R
Y
Y (R/d) 0.3 6
(rnn)
76.7
0.57
1.0
2 . 9 7 3 x L 0 -z
158.3
0.64
1.0
1 . 6 1 7 x 1 0 -2
38
1 5 8 .3
0.64
0.7s0
1 . 3 4 0 x 1 0 -z
8
158.3
0.64
0.501
5
158.3
0.64
o.379
1.615x10-2
I . 9 6 6 x 1 0- z
158.3
5.8
1.0
1 . 4 6 6 x 1 0 -1
2 . 4 5 0 x 1 0 -3
2.450x10-3
2.019x10-2
1.805x10-:
1 . 4 2 3 x 1 0r-
1 . 8 0 5 x 1 0 -3
1 . 5 7 8 x 1 0 -3
2. L44xLO-2
2 . 0 9 8 x 1 0 -2
L . 7 7 7 x I 0 -3
2. 1l3xl0 - z
7
1 . 3 8 6 x 1 031 . 4 2 0 x 1 03-
2 . 0 1 4 x 1 0 -3
2. L27xL0- 2
5
7.O97xLO-3
7.097x10-t
2.246xL0-2
5
7 . 0 8 5 x 1 0 -3
7.085x10*3
1.863x10-z
1 . 6 0 6 x 1 0r1 . 0 2 1 x 1 03-
2.602xI0-z
1 5 8 .3
7.9
1.0
1 . 9 9 6 x 1 0 -r
298.8
0 . 72
1.0
10
298.8
0.72
0.745
9.639x10-:
7 . 9 9 7 x 1 0- I
298.8
0 . 72
0.505
9 . 5 7 3 x 1 0 -3
25
1 . 6 0 6 x 1 0 s9 . 1 8 7 x 1 0aB . 7 9 3 x 1 0- a
2 9 8 .B
0 . 72
0.375
1 . 1 8 1 x 1 0 -z
5
9.624xLO-a
7
l . 1 2 4 x 1 031 . 3 7 0 x 1 03-
1.851x10-z
1. B29xl.0-2
1 . 9 6 6 x 1 02-
weighted
mean
D = 76.7, 158.3nm
weighted
mean
D = 298.8rnm
2.111.x10-z
2 . 0 1 1 x 1 0z-
weighted
mean
all
2.073xLO-2
data
FIGT'RSS
I
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k s v e r s u s R e y n o l d s n u m b e rf o r c l e a r w a t e r l n
2 9 9 m mp l p e
e,
o
a
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Flg I
L a m b d av e r s u s R e y n o l d s n u m b e r f o r c l e o r - w a t e r
l n 2 9 9 m mp t p e
(.o
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HERDLOSSRT L I M I T 0 F D E P O S I T I 0 N E x P e r l m e n t q l
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FI g 11
SEDIMENT
CONCENTRRTION
RT LIMIT OF DEPOSITION
E x p e r l m e n t a l d o . t o ,f o r 2 g g m m p t p e
(\I
F
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Ft g 12
LIMIT OF I]EPOSITIONC o m p o Ir s o n o f e x p e r I m e n to l
data for
2 9 3 m mp l p e w I t h M o y ' s e q u o t I o n s t p t p e f u l I )
I
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Frg 13
Fl
O
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^3
LIMIT OF DEPOSITIONC o m p a Ir s o n o f e x p e r I m e n ta i
plpe w [ t h M a y ' s e q u a t I o n t 3 / 4 f u I 1 ]
data for 299mm
I
II
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Fig 14
LIMIT OF DEPOSITIONC o m p o , r l s o no f e x p e r I m e n t o l
data for
2 9 9 m mp l p e w tt h M a y ' s e q u a tI o n s t t / z
f uI I l
Frg 15
LIMIT OF DEPOSITIONC o m p aIrs o n o i e x p e rI m e n at 1
plpe w [ t h M a y ' s e q u o tI o n s t ' s / B f u l I ]
data for 299mm
ilil 1
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LIMIT OFDEPOSITION
C o m p oIr s o n o J e x p e r I m e n ts l
d a t a f o r 2 9 9 m mp l p e w t t h o i h e r e q n s ( p l p e - f u l l )
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Frg 17
tf,
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LIMIT OF DEPOSITIONC o m p o I, rs o n o f e x p e r I m e n to l
data ior
2 9 9 m mp l p e w l t h o f h e r e q n s ( 3 / 4 f u l i l
e
J
<f
tq
o
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Frg 1B
LIMIT OF DEPOSITiON:C o m p o I, rs o n o f e x p e r I m e n to l
d a t a f o r 2 9 9 m mp f p e w t .t h o f h e r e q n s tl/2 fulll
Frg 19
L]MIT OF DEPOSITIONC o m p a Lr s o n o f e x p e r I m e n tq l
plpe w l t h o f h e r e q n s t3/B f ulll
data for 299mm
Il
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(32)
EquatI on
APPENDIX
APPENDIXA
Formulae for fa1l vlseosity
1.
Kinematic viscosity,
u=
1.79 x 10
and settling
velocity
v
-6
I + 0 . 0 3 3 6 8 T+ 0 . 0 0 0 2 2 1 T 2
where T is the temperature in degrees centigrade.
2.
1/=
FalL velocity
of the particle,
{9 uz + 10-e d2 s (s-l)
w in m/s:
( 0 . 0 3 8 6 9+ 0 . 0 2 4 8 d ) } % - : u
[0.11607 + 0.074405d] x 10-3
Here u = kinematic
and
viscosity
d = sediment
size
s = specific
gravity
of fluid
in mm
of sediment
in m2ls