Contents preface (VII) introduction 1—37

Fig. 5.12 Variation of C_d with H ²/A for 90°-triangular weir (5)



196 IRRIGATION AND WATER RESOURCES ENGINEERING

					Broad - crested weir
1.30	1.25	1.20	1.15	1	1.10	1.05	1.00
k	4	10

Rangeofvariation	3	10
	.6	1
weirs	.2	W
R
				e
Thin-plate
Broad-crestedweirs	2	10

														0.9030
1.25	1.20	1.15	1.10	k	1.05	1.00	0.95
								1
						Thin - plate weir

for influence of viscosity and surface tension (5, 6)

1

Fig. 5.13 Correction factor k

CANAL IRRIGATION

197

H

h_C

W

Fig. 5.14 Flow over a broad-crested weir

Q = k	1	k Cb g H^3/2	(5.16)
		2

Here, k₂ is the correction for the effect of curvature of flow over the weir crest (Fig. 5.15), and L is the length of the weir along the flow direction. C is obtained from Fig. 5.16 which is based on the following equation:

H	=	3 [C^2 / 3 − (2/3)]^1/ 2	(5.17)
H + W	(b/b ) C
		1

For suppressed broad-crested weirs b = b₁. Here, b₁ is the width of the channel. Thus, one uses the curve for b/b₁ = 1.0 in Fig. 5.16 to find C. k₁ is obtained from Fig. 5.13. For broad-crested weirs with sloping upstream and downstream faces one can use Eq. (5.16) with different functional relations for k₁ and k₂ shown in Figs. 5.17 and 5.18, respectively.
1.2

1.1
1.0

^k2 0.9
0.8
0.7

0.02	0.1	1.0	2.0
		H/L

Fig. 5.15 Variation of k₂ with H/L for vertical-faced weir with rounded corner
For a submerged broad-crested weir, the discharge equation is written as (7, 8)

Q = Cb g H ^3 /2 k1 k2 k4

(5.18)

Assuming that C, k₁, and k₂ remain unaffected due to submergence, relationship for k₄ is as shown in Fig. 5.19. It should be noted that the discharge on broad- crested weirs remains unaffected up to submergence (H₂/H₁) as high as 75 per cent. Figure 5.20 compares the discharge characteristics of submerged broad-crested weirs with those of sharp-crested weirs.

198 IRRIGATION AND WATER RESOURCES ENGINEERING
Weirs of widths smaller than that of the approach channel are termed contracted weirs. The above-mentioned relationships, Eq. (5.15) for sharp-crested rectangular weirs and Eq. (5.16) for broad-crested weirs, require some modifications for contracted weirs. Ranga Raju and Asawa (6) suggested the following equation for the actual discharge over a contracted sharp-crested rectangular weir:

Q = k k		2	[0.611 + C (H/W)] b 2gH^3 /2	(5.19)
1	3	3	1

in which k₃ is the correction factor for lateral contraction and C₁ is a function of b/b₁ as shown in Fig. 5.21. k ₃ should logically be a function of H/b. On analysing the experimental data, the average value of k₃ was found to be 0.95 for H/b ranging from 0.1 to 1.0 (6).
Similarly, the actual discharge over a contracted broad-crested weir may be written as
(6)

Q = k	k k Cb g H ^3 /2	(5.20)
1	2	3

in which k₃ is a correction factor for contraction effects and the value of C for various values of b/b₁, as obtained by solving Eq. (5.17), can be read from Fig. 5.16. Logically, k₃ should be a function of H/b. Based on the analysis of experimental data, the value of k₃ can be taken as unity for H/b ranging from 0.1 to 1.0 (6).

0.68

0.66

0.64
Suppressed weir
0.62
C
0.60

0.58

0.56

0.54

0.52

0	0.1	0.2	0.3	0.4	0.5	0.6	0.7
					H/(H + W)

			0
		.
	=	1
b/b	1

0	.	9

	8
.
0

0.7

.6 0
.5 0
0.4 0.2
0.8 0.9 1.0

Fig. 5.16 Variation of C with H/(H + W) and b/b₁ for broad-crested weirs (6)

CANAL IRRIGATION 199

1.4	Symbol	L	W		Su	Sd
		cm	cm
		25	15	1.0		3							L
		10	15	0.5		3			W	Su			SD
1.3		10	15	1.0		3				1			1
		10	15	1.0		3
		25	10	0.5		3
1.2		25	10	1.0		3
k1
1.1
1.0
0.9	2	4	6	8			2	2	4	6	8		3	2	4
	10	10
										.2	.6
										Re	W1

Fig. 5.17 Variation of k₁ for broad-crested weirs with sloping faces (7)

1.3

1.2

1.1

1.0
k₂
0.9

0.8

Broad-crested weir with sloping face

Vertical-faced broad-crested weir with rounded corner

Vertical-faced broad-crested weir with sharp corner

0.7
0.1			H/L	1.0	2.0