11. Silt Theories [Lacey's Theory].pdf

Silt Theories (Lacey's Theory)

1. CE-402 Irrigation Engineering

11. Alluvial Channel Design-Silt Theories
[Lacey’s Theory]

B.Sc. Civil Engineering 8! Semester

Muhammad Ajmal (PhD)
Lecturer
Agri. Engg. Deptt.

2. Lacey’s Regime Theory
Gerald Lacey -- 1930
O Lacey followed Lindley’s hypothesis
“dimensions and slope of a channel to carry a given discharge and silt load in easily erodable soil
are uniquely determined by nature”.

Q According to Lacey
“Silt is kept in suspension by the vertical component of eddies generated at all points of forces
normal to the wetted perimeter”.

Q Regime Channel
“A channel is said to be in regime, if there is neither silting nor scouring”.

Q According to Lacey there may be three regime conditions:
(i) True regime;

i) Initial regime; and

(iii) Final regime.

3. (1) True regime

Q 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.

Q 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 regime or final regime.

4. (2) Initial regime
% bed slope of a channel varies
“cross-section or wetted perimeter remains unaffected

(3) Final regime
«1 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.

Channel shape
carrying coarse
silt

Channel shape
carrying medium

sized silt Channel shape

carrying fine silt

5. Q Lacey’s Equations
Q Fundamental Equations
where f =1.764/D50.

Doo is average grain/particle size in mm

Q Derived Equations

P=4.75/0

O The equations for determination of Velocity, Slope, etc are
function of the silt factor, whereas silt factor is function of

sediment size.

Q For upper Indus basin, f= 0.8 to 1.3
Q For Sindh plain, f=0.7 00.8

(Lacey’s Non-regime flow equation)

6. 13
Lacey's Normal Regime Scour Depth=0.473 (2)

Q The above scour depth will be applicable if river width follows the relationship

Q For other values of active river width, p = 4.750
Lacey's Normal Scour Depth = raf) q -2

where f

q = discharge intensity, and

L=actual river width at the given site

7. Q Lacey’s Channel Design Procedure

(1) Calculate the velocity from equation

ne
v= [QE] msec.

where Q is in cumecs :
Vis in m/s ; and
fis the silt factor, given by
F= 1.76 - Vdm
where dm = Average particle size in mm

(2) Work out the hydraulic mean depth (R) from the equation

s(y PVP -69444
Rr=2 E 2
2 F 3.742
where Vis in m/sec ; 7
Ris in m. B= PSD

(3) Compute area of channel section A =2

(4) Compute wetted perimeter, P = 4.75 YO :

(5) Knowing these values, the channel section is known ; and finally the bed slope
Sis determined by the equation |

gl
3340 9%

8. Problem 1
Design an irrigation channel in alluvial soil from following data using Lacey’s theory:

Discharge = 15.0 cumec; Lacey’s silt factor = 1.0; Side slope=Y2: 1

Solution: Note

Problem 2

The slope of an irrigation channel is 0.2 per thousand. Lacey’s silt factor = 1.0, channel side slope
=: 1. Find the full supply discharge and dimensions of the channel.

Solution: Note

Problem 3

Design an earthen channel of 10 cumec capacity. The value of Lacey’s silt factor in the
neighboring canal system is 0.9. General grade of the country is 1 in 8000.

Solution: Note

9. Drawbacks in Lacey’s theory

Q The concept of true regime is only theoretical and cannot be achieved practically.

Q The various equations are derived by considering the silt factor of which is not at all

constant.
Q The concentration of silt is not taken into account.
Q The silt grade and silt charge are not clearly defined.

Q The equations are empirical and based on the available data from a particular type of

channel.

Q The characteristics of regime of channel may not be same for all cases.

10. Kennedy theory

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.

Lacey’s theory

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.

Relation between ‘V’ & ‘D’.

Relation between ‘V’ & *R”.

Critical velocity ratio ‘m’ is introduced to take
the equation applicable to diff. channels with
diff. silt grades.

Silt factor ‘f is introduced to make the
equation applicable to diff. channels with diff.
silt grades.

Kutter’s equation is used for finding the mean
velocity.

This theory gives an equation for finding the
mean velocity.

This theory gives no equation for bed slope.

This theory gives an equation for bed slope.

In this theory, the design is based on trial and
error method.

This theory does not involve trial and error
method.