Contents preface (VII) introduction 1—37

193


5.12.1. Weirs
Weirs have been in use as discharge measuring devices in open channels for almost two centuries. A weir is an obstruction over which flow of a liquid occurs (Fig. 5.11). Head H over the weir is related to the discharge flowing and, hence, the weir forms a useful discharge measuring device. Weirs can be broadly classified as thin-plate (or sharp-crested) and broad-crested weirs.

Drawdown

_H Nappe

W

Section along AA

A		A

b

Plan of suppressed weir

A		A
b1	b		b

Plan of contracted weir

Sideviews

Fig. 5.11 Flow over suppressed and contracted weirs
5.12.1.1. Thin-Plate Weirs
A sharp-crested (or thin-plate) weir is formed in a smooth, plane, and vertical plate and its edges are bevelled on the downstream side to give minimum contact with the liquid. The area of flow is most commonly either triangular or rectangular and, accordingly, the weir is said to be a triangular or rectangular weir. In general, the triangular weir (or simply the V-notch) is used for the measurement of low discharges, and the rectangular weir for the measurement of large discharges.
The pattern of the flow over a thin-plate weir is very complex and cannot be analysed theoretically. This is due to the non-hydrostatic pressure variation (on account of curvature of streamlines), turbulence and frictional effects, and the approach flow conditions. The effects of

194 IRRIGATION AND WATER RESOURCES ENGINEERING
viscosity and surface tension also become important at low heads. Therefore, the analytical relation (between the rate of flow and the head over the weir), obtained after some simplifying assumptions, are suitably modified by experimentally determined coefficients. Following this


approach, Ranga Raju and Asawa (5) obtained the following discharge equations:

For thin-plate triangular weir with notch angle θ
Q =	k	8 C	d	2g (tan θ/2)	H 5 /2
1
		15
For a suppressed thin-plate rectangular weir

	L 2	F	+ 0.075	H I	2 gH	3 /2 O	k1
	Q = M	G 0.611	J b	P
	N ^3	H		W K		Q
where,	Q = discharge flowing over the weir,

H = head over the weir, b = width of the weir,
C_d = coefficient of discharge for triangular weir (Fig. 5.12), A = area of cross-section of the approach flow,

(5.14)

(5.15)

k₁ = correction factor to account for the effects of viscosity and surface tension (Fig. 5.13),
R_e = g^1/2 H^3/2/ν (typical Reynolds number),
ν = kinematic viscosity of the flowing liquid, W₁ = ρgH²/σ (typical Weber number),
σ = surface tension of the flowing liquid, ρ = mass density of the flowing liquid, and g = acceleration due to gravity.
It should be noted that k₁ = 1.0 for R_e^0.2 W₁^0.6 greater than 900. This limit corresponds to a head of 11.0 cm for water at 20°C. The mean line drawn in Fig. 5.13 can be used to find the value of k₁. The scatter of data (not shown in the figure) was generally less than 5 per cent implying maximum error of ± 5 per cent in the prediction of discharge.
Equation (5.15) along with Fig. 5.13, and Eq. (5.14) along with Figs. 5.12 and 5.13 enable computations of discharge over a suppressed thin-plate rectangular weir and a thin-plate 90°-triangular weir, respectively. A weir is termed suppressed when its width equals the channel width and in such cases the ventilation of nappe becomes essential.
5.12.1.2. Broad-Crested Weirs
Broad-crested weirs are generally used as diversion and metering structures in irrigation systems in India. The weir (Fig. 5.14) has a broad horizontal crest raised sufficiently above the bed so that the cross-sectional area of the approaching flow is much larger than the cross-sectional area of flow over the top of the weir. The upstream edge of the weir is well rounded to avoid undue eddy formation and consequent loss of energy. The derivation of the discharge equation for flow over a broad-crested weir is based on the concept of critical flow. Ranga Raju and Asawa (6) proposed the following discharge equation for a broad-crested weir with well-rounded upstream edge and vertical upstream and downstream faces:

CANAL IRRIGATION 195

0.67

0.66

0.65

0.64

0.63
C_d

0.62

0.61

0.60

0.59

0.58

0 0.1 0.2 0.3 0.4 0.5

2

H /A