History behind Kennedy’s Theory:
R.G. Kennedy, invented Kennedy’s theory by carried research on the canal reaches in the upper Bari Doab Canal system in Punjab, India. He chose a straight region of the canal section where there was no silting and scouring in the previous 30 years.
From the observation, he concluded that the silt supporting power in a channel cross-section was mainly dependent upon the generation of eddies, rising to the surface.
The friction of the flowing water with the channel section is the main cause of these eddies. So, the silting is avoided by kipping velocity sufficient such that it can generate sufficient eddies and keep the sediments just in suspension.
Kennedy simply gave the idea that a non-silting, non-scouring velocity channel will be a regime channel.
The canal, which takes off from; a river has to draw a fair hare of silt flowing in the river. This silt is carried in suspension with water or flows along the bed of the canal.
The silt load carried by the canal impress a difficult problem in a channel design should be such that the silt flowing in the channel is not dropped on the bed
Kennedy selected a number of sites for their experience and gave following conclusion:
i)The silt supporting power is proportional to the bed width of the stream and not to its wetted perimeter.
ii) He defined the critical velocity as non-silting-non scouring velocity and gave a relation between critical velocity to the depth of flowing water, V = 0.55 * y^0.64
Based upon this concept, he defined the critical velocity (v.) in at channel as the mean velocity, which will just keep the channel free from silting or scouring, and related it to the depth of flow by the equation.
V= c1 * yᶺc2
Where c1 and c2 are constants depending upon silt charge. C1 and c2 were found to be 0.55 and 0.64 (In M.K.S. or S.I. units), respectively.
v= 0.55 * y^0.64
But this formula will be true only for the Upper Bari Doab Canal System and not for other canal reaches. He introduced a factor named critical velocity ratio (C.V.R.) and denoted by m, and it depends upon the silt grade and type of soil.
Vo= critical velocity in the channel in m/sec.
=0.55 *m y^0.64 (Where y is in meters)
For sands coarser than the standard, the values of m where given from 1.0 to 1.2; and for sands finer than the standard, m was valued between 1.0 to 0.7, as shown in the following table.
Recommended Values of C.V.R. (m)
|S. No.||Types of silt||Values of m|
|1||Silt of River Indus (Pakistan)||0.7|
|2||Light sandy silt in North Indian||1.0|
|3||Light sandy silt, a little coarser||1.1|
|4||Sandy, loamy silt||1.2|
|5||Debris of hard soil||1.3|
What is the critical velocity ratio(CVR)?
The ratio of mean velocity ‘V’ to the critical velocity “Vo’ is known as the critical velocity ratio (CVR). It is denoted by m i.e.
CVR (m) = V/Vo
When m=1, there will be no silting or scouring.
When m> 1, scouring will occur
When m< 1, silting will occur
We can easily predict the canal condition as silting or scouring by finding the value of m.
Kennedy consider the followings assumption to support his theory:
1. The eddy current is developed due to the roughness of the bed.
2. The quality of suspended silt is directly proportional to bed width.
3. It is applicable to those channels which are flowing through the bed consisting of sandy silt or the same grade of silt.
Design of Irrigation Channels by Kennedy’s Theory:
When an irrigation channel is to be designed by the Kennedy theory it is essential to know Full Supply Discharge (FSD) (Q), coefficient of rugosity (n), CVR (m), and longitudinal slope of the channel (S).
Procedure Type 1:
When Q, n, m, and S ratios are given
i. Assume the reasonable full supply depth, y.
ii. Using equation (1) find out value of V using V = 0.55* m* y^0.64
iii. With this value of V, find out A using Q = A.V
iv. Assuming side slopes and from the knowledge of A and y find out bed width B i.e.
v. Calculate R which is the ratio of area and wetted perimeter using
R = A/P,
A =By+zy2 &
vi. Find out the value of actual velocity V using V = C√(RS)
The given below Kutter’s formula is used to find the value of ‘C’
N= manning’s rugosity coefficient which is taken as an unlined earthen channel.
When the assumed value of y is correct, the value of V in step (vi) will be the same as calculated in step (ii), if not assume another suitable value of y and repeat the procedure both values of velocity come out to be the same.
Normally, the trial depth is assumed between 1 m to 2 m.
If the condition is not satisfied within this limit, then it may be assumed accordingly.
In order to increase the critical velocity (Vo), we have to increase the depth. So increase the depth.
Procedure Type 2:
When Q, n, m, and B/y ratios are given
- Express V in terms of y only using V = 0.55* m* y^0.64
- From the given B/y ratio and side slopes calculate area A in terms of depth y only (if side slopes are not given take ½: 1 as side slopes for the alluvial tract).
Use A = By+zy2
iii. Obtain another relation between V and y only.
- Solve these two simultaneous equations and find out the value of y.
- Calculate the value of B from the known B/y ratio.
- Calculate V from Kennedy’s equation V = 0.55* m* y064
- Using Chezy’s equation calculate the value of S, V = C√(RS).
What are the drawbacks of Kennedy’s theory?
1. The theory is limited to average regime channel only.
2. The design of the channel is based on the trial and error method.
3. The value of m was fixed arbitrarily.
4. Perfect definitions of silt grade and silt charge are not given.
5. There is no equation for determining the bed slope and it depends on Kutter’s equation only.
6. The ratio of ‘B’ to ‘y’ has no significance in his theory.
7 In the absence of B/y relation the Kenned’y theory do not provide easy basis for fixing channel dimensions uniquely.
8. Complex phenomenon of silt transportation is not fully accounted and only critical velocity ratio (m) concept is considered sufficient.
9 There is no provision to decide on the longitudinal slope under the scope of the theory.
10. By use of Kutter’sformula inherent limitations therein remain applicable in Kennedy’s channel design procedure.
Uses of Kennedy’s Theory
Uses of Garrets and other diagrams
Garret’s diagram gives the graphical method of designing the channel dimensions based on Kennedy’s theory. The diagram has the discharge plotted on the abscissa. The ordinates on left indicate the slope and on right the water depth in the channel, and critical velocity, V. The discharge lines are curved and bed width lines are dotted.
Procedure for design.
In designing the channel following steps are followed:
i) Find out the discharge for which the channel is to be designed.
ii) Find out the slope of the channel from its longitudinal section.
iii) Follow the discharge line and find out its intersection with the horizontal lines from the slope. Let intersection point be interpolation is also done if required.
iv) Draw a vertical line through the point of intersection. This will intersect several bed-width curves. Each point of intersection of the vertical line and bed width curve gives a depth on the right-hand side curve.
v) Choose a pair of bed width, depth, and v, corresponding to the point of intersection obtained in step iv.
vi) Calculate the area of channel section A corresponding to bed width-depth obtained in step v.
vii) Calculate the velocity, v in the channel corresponding to this area A.
viii) Calculate. This should be equal to 1 or m
ix) Repeat the procedure with other values of bed width and V depth till the value obtained is the same as the value of m given for channel design.
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