In this article we will discuss about the design of irrigation canals on non-alluvial and alluvial soils with suitable examples.
Design of Canals on Non-Alluvial Soils:
Here non-alluvial soils are supposed to be stable for the purpose of design of an irrigation canal. The dimensions of a canal can be worked out on the basis of the well-known hydraulic formulae. The bed slope of the canal may be kept anything.
Only consideration is that the velocity of flow should be quite close to the critical velocity for the available soil. Generally the side slope of value 1½: 1 (Horizontal: Vertical) in filling and 1: 1 in cutting is given. Knowing the ratio of bed width B and depth D the dimensions of the canal can be determined uniquely.
The hydraulic formulae commonly used are the following:
(1) Q = A.V.
where Q is design discharge in m3/sec
A is cross-sectional area of the canal in m2
and V is mean velocity of flow in m/sec
(2) Chezy’s Formula:
where R is hydraulic mean depth in m
S is bed slope of the canal and
C is Chezy’s constant.
The value of Chezy’s ‘C” can be calculated from the two formulae given below:
(a) Kutter’s formula:
where N is coefficient of rugosity.
(b) Bazin’s Formula:
where K is roughness constant.
The value of K depends on the character of the canal bed and side material (Refer Table 7.4).
(3) Manning’s Formula:
Once V is fixed using Chezy’s or Manning’s formula, sectional area can be determined from the fundamental equation Q = A.V.
Example:
Design an unlined canal in loamy soil to carry a discharge of 50 cubic metres per second, with permissible velocity of one metre per second. Assume side slopes 2: 1 and B/D ratio as 6. Using Manning’s formula calculate bed slope of the canal. Take N = 0.0225.
Solution:
Using fundamental equation Q = A. V.
Design of Canals on Alluvial Soils:
The principle of design of a canal on alluvial soil is totally different from that of a canal on non-alluvial soil. Canals on alluvial soil carry appreciable silt and sand load. Silt concentration in the canal water affects the velocity of flow considerably. Hence the Manning’s formula cannot be used here to determine the velocity of flow. When the canal water has excess silt load silting occurs in the canal.
On the contrary when the water is silt free it picks up the silt from the canal bed and sides. It results in erosion of the canal section. Manning’s equation or Chezy’s equation do not consider this aspect. Taking the problem of silt transportation into account it was necessary to evolve some basis for the design of a stable section with critical velocity. There are two important and most commonly used theories.
i. Kennedy’s Theory:
Kennedy’s silt theory or transportation theory is as mentioned below:
Sediment in flowing canal is kept in suspension solely by the vertical components of the constant eddies which can always be observed over the full width of any stream, boiling up gently to the surface. (The reason for the production of eddies is rough less of the bed).
In order to obtain an expression for the silt supporting power of a stream, it may be safely assumed that the quantity of silt supported is proportional to the width of the bed, all other conditions remaining the same.
It also varies with the velocity of a stream, V0. It may be taken proportional to V0n-1. It is clear that greater the velocity greater will be the force of eddies. The force becomes zero when velocity is zero.
According to Kennedy, though depth is third variable, it could not affect either the number or the force of eddies.
Hence the amount of silt supported in a stream may be expressed by A.B. V0n-1.
where A is some constant;
B is bed width of canal; and
V0 is the velocity in stable state
Then amount of silt transported will be given by:
A.B.V0n-1 × V0 = A.B.V0n
It is essential to recognise here that all the silt sediment is taken to be in suspension. Of course there is no doubt about the fact, that small quantity of heavier silt is carried as a bed load which rolls along the bed. This amount would vary directly as BV0 instead of BV0n. To include rolling silt also the value of n should be taken less, than it would be if the suspended silt were alone considered.
Kennedy plotted various graphs between V0 and depth of flow and finally gave a formula to calculate V0.
The formula is:
V0 = CDn
where V0 is critical velocity in m/sec
D is full supply depth in m
C is a constant.
It depends on the character of silt. Coarser the material greater is the value of ‘C’.
n is some index. It also depends on the type of silt.
For Punjab he gave the formula:
V0 = 0.546 D0.64 … (1)
After recognizing the fact that silt grade also plays an important part, he modified the formula (1).
The new form is:
V = 0.546 m.D0.64
where m is C. V.R. or V/V0 …(2)
For coarse sand value of m may be taken as 1.1 to 1.2.
For finer material it may be kept between 0.8 and 0.9.
Table 7.7 shows values of C and n for various regions:
ii. Design of Irrigation Canal Making use of Kennedy’s Theory:
When an irrigation canal is to be designed by the Kennedy theory it is essential to know, F.S.D.(Q), coefficient of rugosity (N), C.V.R. (m), and longitudinal slope of channel (5) before-hand.
By making use of the following three equations a canal section can be designed by trials:
(1) V = 0.546 m.D0.64
(2) Q = A.V and
(3) V = C√RS
The procedure of design may be outlined in the following steps:
(a) Assume a reasonable full supply depth D.
(b) Using equation (1) find out value of V.
(c) With this value of V, using equation (2) find out A.
(d) Assuming side slopes and from the knowledge of A and D find out bed width B.
(e) Calculate R, which is ratio of area and wetted perimeter.
(f) Using equation (3) find out the value of actual velocity V.
When the assumed value of D is correct, the value of V in step (f) will be same as V calculated in step (b), if not assume another suitable value of D and repeat the procedure till both values of velocity come out to be the same.
It may be recognised here that for same values of Q, N and m but with different values of S various channel sections may be designed. It is needless to mention that all of them would not be equally satisfactory. To give some guidance for fixing particular slope (S), Woods has given a table (Table 7.8) on the basis of experience in which he gives suitable BID ratios for various values of Q, S, N, m.
Another advantage of taking a suitable BID ratio is that it reduces the labour of making trails.
Thus when Q, N, m and BID ratio is known using equation (1) and (2) two unknowns V and D can be accurately and uniquely determined. Then using equation (3) required value of S can be calculated.
Example:
Design an irrigation canal with the following data:
Use Kennedy’s equation.
Solution:
Treating equations (A) and (B) as simultaneous, value of D can be uniquely determined. Equation (B) may be written as:
Table 7.8: Woods design table:
Now equating this equation to (A)
Value of required slope may be calculated from Chezy’s formula. Of course it is true that Chezy’s constant will have to be determined from Bazin’s formula.
iii. Lacey’s Theory:
The definition that a channel is in regime when:
(i) It flows in “incoherent unlimited alluvium” of same character as that transported;
(ii) Silt grade and silt charge is constant; and
(iii) Discharge is constant.
These conditions are very rarely achieved and are very difficult to maintain in practice. Hence according to Lacey’s conception regime conditions may be subdivided as initial and final.
Lacey also states that, the silt is kept in suspension solely by the force of eddies. But Lacey adds that eddies are not only generated on the bed but at all points on wetted perimeter. The force of eddies may be taken normal to the sides, Fig. 7.2.
Obviously the vertical components of the forces due to eddies are responsible for keeping the silt in suspension.
Unlike Kennedy, Lacey takes hydraulic mean radius (R) as a variable rather than depth (D). For wide channel there is hardly any difference between R and D. When the channel section is semi-circular there is no base width and sides actually and hence assumption of R as a variable seems to be more logical. From this point of view velocity is no more dependent on D but it depends on R. Consequently amount of silt transported is not dependent on the base width of the channel only.
On the basis of the above mentioned arguments Lacey plotted a graph between mean velocity (V) and hydraulic mean radius (R) and gave a relationship:
V = K.R1/2 …. (i)
where K is constant.
It can be seen here that power of R is a fixed number and needs no alteration to suit different conditions.
Lacey recognised the importance of silt grade in the problem and introduced a function ‘f’ known as silt factor.
He adjusted the value of ‘f’ such that it also comes under square root sign. Thus it gives scalar conception.
Equation (i) is thus modified as:
Lacey’s standard silt has a silt factor unity. He further states that standard silt is sandy silt in a regime channel with hydraulic mean radius equal to one metre. Lacey gave various equations for designing an irrigation canal.
iv. Design of Irrigation Canal Making Use of the Lacey Theory:
Full supply discharge for any canal is always fixed beforehand. The value of ‘f’ for a particular site may be calculated using equation (9) or if C.V.R. is given then f = m2.
Thus when Q and f are known design can be done in the following steps:
(a) Find out V using equation (10), V = 0.4382 (Qf2)1/6
(b) Calculate value of R using equation (5), R = 2.46 V2/f
(c) Calculate wetted perimeter Pw using Lacey’s regime perimeter equation, Pw = 4.825 Q1/2.
(d) Calculate cross-sectional area A, from equation Q = AV.
(e) Assuming side slopes, calculate the full supply depth from A, Pw and R.
(f) Calculate longitudinal slope of the canal using equation (8),
= f5/3 / 3316 Q1/6
v. Comparison of Kennedy’s and Lacey’s Theories:
(1) The basic concept regarding silt transportation is the same in both the theories. In both the theories it is stated that the silt remains in suspension due to vertical force of eddies.
(2) Kennedy assumes that eddies are generated on the bed only and hence he derives a formula for finding critical velocity in terms of depth.
Lacey proposes that regime section is ultimately semi-circular and eddies are generated along whole wetted perimeter. He derives formula for mean velocity in terms of hydraulic mean radius.
(3) Lacey states that as the shape of an irrigation canal are fixed to particular geometrical figure (generally trapezoidal) it cannot achieve final regime conditions and hence may be said to achieve initial regime.
Kennedy assumes that when there is neither silting nor scouring the channel is in its regime.
(4) Kennedy selects Kutter’s formula for designing irrigation canal. But in Kutter’s formula value of N is arbitrarily fixed.
Lacey has not fixed any value arbitrarily.
(5) Kennedy has made use of term C.V.R. (m) but he did not give any basis for calculating m. He simply states that it depends on the silt charge and silt grade.
Lacey has introduced silt factor ‘f’. He related/to mean diameter of the bed material and given basis to calculate f. The formula is f = 1.76 √mr.
(6) Kennedy gives no clue for calculating longitudinal regime slope.
Lacey produced a regime slope formula.
(7) Design based on Kennedy’s theory can only be done after making trials. Of course Woods has simplified the procedure by giving normal design table which provides BID ratio,
Lacey gave important wetted regime perimeter equation:
Pw = 4.825 Q1/2
He of course admitted that the value of a constant in the above equation is in no way constant and varies from 4 to 5.8 for regime channels.
vi. Defects in Kennedy’s and Lacey’s Theories:
Both the theories lack in the following respects:
(1) In both the theories perfect definitions of silt grade and silt charge are not given.
(2) It is clear that water loss occurs in the channel (say 12 to 15 percent of total discharge). In both the theories effect of this loss on the silt distribution is not considered.
(3) Even though regime condition is reached silt grade is never constant due to attrition. No account is made for this reduction in silt grade.
(4) Irrigation water is distributed to various subsidiary canals from the main canal. None of the two theories mention the effect of this water withdrawal on the regime condition of the canal.