Lacey Creep Theory
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Transcript of Lacey Creep Theory
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Laceys Regime TheoryGerald Lacey -- 1930
Lacey followed Lindleys hypothesis:
dimensions and slope of a channel to carry a given discharge and silt load ineasily erodible soil are uniquely determined by nature.
According to Lacey:
Silt is kept in suspension by the vertical component of eddies generated atall points of forces normal to the wetted perimeter.
Regime Channel
A channel is said to in regime, if there is neither silting nor scouring.
According to Lacey there may be three regime conditions:
(i) True regime;
(ii) Initial regime; and
(iii) Final regime.
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(1)True regime
A channel shall be in 'true regime' if the following conditions are satisfied:
(i) Discharge is constant;
(ii) Flow is uniform;
(iii) Silt charge is constant; i.e. the amount of silt is constant;
(iv) Silt grade is constant; i.e., the type and size of silt is always the same; and
(v) Channel is flowing through a material which can be scoured as easily as it
can be deposited (such soil is known as incoherent alluvium), and is of the
same grade as is transported.
But in practice, all these conditions can never be satisfied. And, therefore,artificial channels can never be in 'true regime; they can either be in initial regimeor final regime.
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(ii) Initial regime
cross-section or wetted perimeter remains unaffected
bed slope of a channel varies
(iii) Final regime
all the variables such as perimeter, depth, slope, etc. are equally free to
vary and achieve permanent stability, called Final Regime.
In such a channel,
The coarser the silt, the flatter is the semi-ellipse.
The finer the silt, the more nearly the section attains a semi-circle.
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Laceys Equations:
Fundamental Equations:
Derived Equations:
(Laceys Non-regime flow equation)
R
VffRV
2
2
5or
5
2
52 140VAf
21
32
8.10 SRV
QP 75.4
61
2
140
QfV
21
23
4980R
fS
61
35
3340Q
fS
21
431
SRN
Va
mmin size iclegrain/part average is D
,76.1 where
50
50Df
The equations for determination of Velocity, Slope,
etc are function of the silt factor, whereas silt factor
is function of sediment size.
For upper Indus basin, f = 0.8 to 1.3
For Sindh plain, f = 0.7 to 0.8
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The above scour depth will be applicable if river width follows the
relationship
For other values of active river width,
where
q = discharge intensity, and
L = actual river width at the given site
31
473.0DepthScour Regime Normal sLacey'
f
Q
QP 75.4
L
Qq
f
q
,35.1DepthScour Normal sLacey'
31
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Laceys Channel Design Procedure
Determine D and B using these
relationships for trapezoidal
section with side slope 1/2:1
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Problem:
Design an irrigation channel in alluvial soil from following data using Laceys
theory:
Discharge = 15.0 cumec; Laceys silt factor = 1.0; Side slope = : 1
Solution:
sec/ 689.0)140
115()
140( 6
16
12
mQf
V
2 77.21689.0
15m
V
QA
m 18.4 1575.475.4 QP
m 36.1742.3
)77.21(944.6)4.18(4.18
742.3
944.622
APP
D
m 36.15)36.1(54.185 DPB
m 185.11
)689.0(
2
5
2
5 22
f
VR
52451
)15(3340
)1(
3340 61
35
61
35
Q
fS
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Problem:
The slope of an irrigation channel is 0.2 per thousand. Laceys silt factor = 1.0,
channel side slope = : 1. Find the full supply discharge and dimensions of
the channel.
Data:
S = 0.2/1000 = (0.2 x 5) / (1000 x 5) = 1/5000
Solution:
cumecS
fQ
Q
fS 25.11
500013340
1
33403340
6
35
61
35
mS
fR
R
fS 008.1
500014980
1)
4980(
4980
2
22
3
21
23
mQP 93.1525.1175.475.4
206.16008.193.15 mPRA
m 153.1742.3
)06.16(944.6)93.15(93.15
742.3
944.622
APP
D
m 35.13)153.1(593.155 DPB
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Problem:
Design an earthen channel of 10 cumec capacity. The value of Laceys silt
factor in the neighboring canal system is 0.9. General grade of the country is
1 in 8000.
Data:
Q = 10 cumec; f = 0.9; Sn=1/8000; B = ?; D = ?; Sreq= ?.
Solution:
Which is steeper than the natural grade of the country (i.e. 1 in 8000),
therefore not feasible.
m/sec 622.0
140
9.010
140
61
261
2
QfV
2m 08.16622.0
10
V
QA
m 02.151075.475.4 QP
m 25.1742.3
)08.16(944.6)02.15(02.15
742.3
944.622
APP
D
m 22.12)25.1(502.155 DPB
58441
103340
9.0
3340 61
35
61
35
Q
fSreq
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Now putting S = 1/8000 in the relationship
Hence silt factor will be reduced to 0.7454 by not allowing coarser silt to enter the
canal system by providing silt ejectors and silt excluders.
i.e. silt having mean diameter > 0.179 mm will not be allowed to enter the canal
system.
7454.0108000
1334033403340
53
615
3
61
61
35
SQf
Q
fS
mm 179.076.1
76.12
5050
fDDf
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Lacey's Shock Theory
Lacey considered absolute rugosity coefficient Na as;
Constant and
Independent of channel dimensions.
In practice Na varies because of irregularities or mounds in the sides and bed of the channel (i.e. ripples), pressure on front is more than the pressure on the rear.
The resistance to flow due to this difference of pressure on the two sides of the mound is called form resistance.
Lacey termed this loss as shock loss, which is different from frictional resistance or tangential drag.
Shock loss = f (size, shape and spacing of bed forms)
Total resistance = frictional resistance + form resistance (i.e. shock loss)
(due to bed) (due to irregularities)
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Lacey suggested:Na should remain constantSlope should be splitted
to overcome friction andto meet shock loss
i.e.
where, s = slope required to withstand shock losses.
According to LaceyNa = 0.025 with shock lossNa = 0.0225 without shock loss
Therefore, s = 0.19 S
i.e. for a channel in good condition19 % slope for shock loss
and 81 % slope for friction
21
431
sSRN
Va
214321430225.0
1
025.0
1sSRSR
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Drawbacks in Laceys theory:
The concept of true regime is only theoretical and cannot be
achieved practically.
The various equations are derived by considering the silt
factor only, that is not appropriate for various phases of flow
along different bed and side conditions.
The concentration of silt is not taken into account.
The silt grade and silt charge are not clearly defined.
The equations are empirical and based on the available data
from a particular type of channel.
The characteristics of regime of channel may not be same for
all cases.
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Kennedy theory Laceys theory
1.It states that the silt carried by the flowing
water is kept in suspension by the vertical
component of eddies which are generated from
the bed of the channel.
1.It states that the silt carried by the flowing
water is kept in suspension by the vertical
component of eddies which are generated from
the entire wetted perimeter of the channel.
2. Relation between V & D. 2. Relation between V & R.
3. Critical velocity ratio m is introduced to
make the equation applicable to diff. channels
with diff. silt grades.
3. Silt factor f is introduced to make the
equation applicable to diff. channels with diff.
silt grades.
4. Kutters equation is used for finding the mean
velocity.
4. This theory gives an equation for finding the
mean velocity.
5. This theory gives no equation for bed slope. 5. This theory gives an equation for bed slope.
6.In this theory, the design is based on trial and
error method.
6. This theory does not involve trial and error
method.