Contents preface (VII) introduction 1—37

10.7. TRAPEZOIDAL NOTCH FALL
A trapezoidal notch fall can be designed [i.e., determine α and L, Fig. 10.3 (b)] to maintain the normal depth in the upstream channel for extreme values [say 1 and 2, Fig. 10.3 (c)] of a specified range of discharge, Q, using the following discharge equation for free flow condition:

Q =	2	C	F	3 / 2	+	4	H	5 /2	I	(10.8)
3	2g G LH		5		tan αJ
				H					K

Here, H is the depth of water above the notch cill up to the normal water surface and is measured upstream of the fall where the streamlines are relatively straight. The value of the coefficient of discharge C may be taken as 0.78 for canal notches, and 0.70 for distributary notches (2). For two values of discharge, Q₁ and Q₂, and corresponding values of H₁ and H₂, one can obtain the following two equations for the determination of two unknowns L and α:

Q =

2 C

2 g ^F LH

3 / 2

+ ^4

H ^5 /2 tan α^I

(10.9)

1

3

G

1

5

1

J

H

K

Q =

2

C

F

3 / 2

+

4

5 /

2

tan

I

(10.10)

3

2g G LH2

5

H2

αJ

2

H

K

On solving Eqs. (10.9) and (10.10), one obtains

15

Q H

3 / 2

− Q H 3 /2

tan α =

2

1

1

2

(10.11)

8 C

2 g H 1^3 / 2 H 2^3 /2 ( H 2 − H1)

and

L =

Q1

−

4

H1 tan α

(10.12)

(2 / 3)

C 2 g H1^3 /2

5

Trapezoidal notch falls are designed for the full supply discharge and half of the full supply discharge (1).
Similarly, using the following equation for the submerged flow condition, the unknowns L and α can be determined for two sets of known values of Q, H and h_d (i.e., the submergence head) for the two stages of the channel (2):

Q =	2	C 2g (H − hd )^3 /2 {(L + 2hd tan α ) + 0.8 tan	α (H − hd )}
	3
		+ C	2g	( H − h	) ^1/ 2 ( L + h	tan α) h		(10.13)
				d	d	d

The number of notches is so adjusted that the top width of the flow in the notch lies between 3/4th to full water depth above the cill of the notch. The minimum thickness of notch piers is half the depth and can be more if the piers have to support a heavy superstructure.

362 IRRIGATION AND WATER RESOURCES ENGINEERING
10.8. SARDA FALL
It is a raised-crest fall with a vertical-impact cistern. For discharges of less than 14 m³/s, a rectangular crest with both faces vertical is adopted. If the canal discharge exceeds 14 m³/s, a trapezoidal crest with sloping downstream and upstream faces is selected. The slopes of the downstream and upstream faces are 1 in 8 and 1 in 3, respectively. Both types of crests (Fig. 10.11) have a narrow and flat top with rounded corners. In Sarda fall, the length of the crest L is generally kept the same as the channel width. However, for future and other specific requirements, the crest length may exceed the bed width of the channel by an amount equal to the depth of flow in the channel.

For a rectangular-crest type Sarda fall, the discharge expressed as (2)

Q = 0.415 2g LH	3 /2 F	H I 1/ 6
	G	J
	H	B K

Q under free flow condition is

(10.14)

Here, H is the head over the crest, and B is the width of crest which is related to the height of the crest above the downstream bed d as follows:

B = 0.55 d
Obviously, H + d = h₁ + D
and, therefore, d = h₁ + D – H
U/S TEL

(10.15)
(10.16)

Fig. 10.11 Types of cross-sections of crest for Sarda fall

Here, D is the drop in the bed level, and h₁ is the upstream depth of flow. Equations (10.14) and (10.15) are solved by trial for obtaining the values of B and H for the rectangular-crest type Sarda fall.

CANAL REGULATION STRUCTURES
For the trapezoidal-crest type Sarda fall, the discharge expressed as (2)

Q = 0.45 2g LH	3 /2 F	H I 1/ 6
	G	J
	H	B K

363
Q under free flow condition is

(10.17)

Here,	B = 0.55	H + d
∴	B = 0.55	h1 + D	(10.18)

For known h₁ and D, one can determine B using Eq. (10.18). The head H is obtained from Eq. (10.17).
For submerged flow conditions, one should use the following discharge equation (2):

Q =	C	2gL ^F ^2	H	L	^3 /2 + h H	I	(10.19)
d	G		d	L J
		H 3				K

Here, H_L is the difference between the upstream and the downstream water levels, and h_d is the submergence head as shown in Fig. 10.11 (a). The coefficient of discharge C_d is usually assigned an average value of 0.65. Equation (10.19) ignores the effect of the approach velocity. For given conditions, one can determine h_d from Eq. (10.19) and, hence, the height of the crest above the upstream bed which equals [h₁ – (H_L + h_d)]. Alternatively, one can use the following equation for the submerged flow (3):

Q = C d	L	2	{( H L + ha )	3 / 2	3 /2	} + hd { H L + ha }	1/ 2 O	(10.20)
2g L M	3		− ha	P
		N					Q

Here, h_a is the approach velocity head.
The base width of a fall is decided by the requirement of concrete cover for stability and the slopes of the upstream and downstream faces of the fall.
A depressed cistern having suitable length and depression is provided immediately downstream of the crest and below the downstream bed level. The cistern and the downstream floor are usually lined with bricks laid on edge so that repair work would only involve brick surfacing and, hence, be relatively simple.
The depths of the cutoffs are as follows (3):

F h1	I
Depth of upstream cutoff = G		+ 0.6	m
3	J
	H	K

with a minimum of 0.8 m

F h1	I
Depth of downstream cutoff = G		+ 0.6J	m
2
	H	K

with a minimum of 1.0 m
Here, h₁ is the upstream depth of flow in metres. The thickness of the cutoff is generally kept 40 cm.
The length of impervious floor is decided on the basis of either Bligh’s theory or method proposed by Khosla et al. (Sec. 9.3.3). For all major works, the method of Khosla et al. should always be used. The most critical condition with respect to seepage would occur when water is up to the crest level with no overflow. The minimum floor length l_d, which must be provided downstream of a fall, is given by (2)
l_d = 2h₁ + H_L + 2.4

364 IRRIGATION AND WATER RESOURCES ENGINEERING
A thickness of 0.30 m is usually sufficient for the upstream floor. The thickness of the downstream floor is calculated from considerations of uplift pressure subject to a minimum of 0.45 to 0.60 m for larger falls and 0.3 to 0.45 m for smaller falls.
Brick pitching is provided on the channel bed immediately upstream of the fall structure. It is laid at a slope of 1 : 10 for a distance equal to the upstream depth of flow h₁. Few drain holes of diameter about 15 to 30 cm are provided in the raised-crest wall at the bed level to drain out the upstream bed when the channel is closed for maintenance or other purposes.
Radius of curvature of the upstream wing walls is around 5 to 6 times H. These walls subtend an angle of 60° at the centre and extend into earthen banks such that these are embedded in the channel banks by a minimum of 1 m. The wing walls should continue up to the end of the upstream impervious floor and for this purpose, if necessary, the walls may run along straight banks tangential to the wall segment.
Downstream of the fall structure, the wing walls are lowered down to the levels of the downstream wing walls through a series of steps. The downstream wing walls are kept vertical
for a distance of about 5 to 8 times EH_L from the fall structure. These walls are then flared

so that their slope changes from vertical to the side slope of the downstream channel. The wing walls are designed as the retaining walls to resist the earth pressures when the channel is not running.

Downstream of the warped wing walls, pitching protection is provided on the bed and sides of the channel. Pitching is either brick work or stones laid dry on a surface without the use of mortar. Pitching is, therefore, pervious. It is provided for a length equal to about three times the downstream depth of flow (3). Alternatively, Table 10.1 can be used for deciding the length of bed pitching. Bed pitching is kept horizontal up to the end of wing walls and, thereafter, it slopes at 1 in 10. The pitching on the side slopes of the channel is provided up to the line originating from the end of the bed pitching and inclined at 45° towards the upstream (Fig. 10.12). A toe wall at the junction of the bed and the side pitching is necessary for providing firm support to the side pitching.