Contents preface (VII) introduction 1—37

5.12.2.1. Long-Throated Flumes
The constriction of these flumes (Fig. 5.22) is sufficiently long (the length of the throat should be at least twice the maximum head of water that will occur upstream of the flume) so that it produces small curvature in the water surface and the flow in the throat is virtually parallel to the invert of the flume.

Headgauging	Section

R³2 (B – b)	When recovery of head is not
		important, the exit transition may
		be truncated after half its length
B
		b

2hmax 3 To 4hmax	L	³3 (B - b)	Front elevation
			(Level invert)
In a flume without a hump (p = 0),
the invert over this length shall be truly level
	Plan view
p
Connection to stilling well	This radius is chosen so that bottom	Front elevation
(With hump)
		contraction starts at the same section as
	side contractions. For flume with bottom
	contraction only, radius = 4p

Fig. 5.22 Geometry of rectangular long-throated flume

CANAL IRRIGATION

203

This condition results in nearly hydrostatic pressure distribution at the control section (where critical depth occurs) which, in turn, allows analytical derivation of the stage-discharge relation. This gives the designer the freedom to vary the dimensions of the flume in order to meet specific requirements. Such flumes are usually of rectangular, trapezoidal, triangular or U-shaped cross-section. For a rectangular flume, the discharge of an ideal fluid is expressed as

F	2I	3 /2	3 /2	(5.21)
Q = G	J	g bH
H	3K

Here, H represents the upstream energy and b is the typical width dimension for the particular cross-sectional shape of the flume. By introducing suitable coefficients this equation can be generalised in the following form so that it applies to any cross-sectional shape (9):

F	2I 3 /2	g C C C bh^3 /2	(5.22)
Q = G	J	v s d
H	3K

where, C_v = coefficient to take into account the velocity head in the approach channel,

C_s = coefficient to take account of the cross-sectional shape of the flume,
C_d = coefficient for energy loss,
and h = depth of water, upstream of the flume, measured relative to the invert level of
the throat (i.e., gauged head).
5.12.2.2. Short-Throated Flumes
In these flumes, the curvature of the water surface is large and the flow in the throat is not parallel to the invert of the flume. The principle of operation of these flumes is the same as that of long-throated flumes, viz. the creation of critical conditions at the throat. However, non-hydrostatic pressure distribution (due to large curvature of flow) does not permit analytical derivation of the discharge equation. Further, energy loss also cannot be assessed. Therefore, it becomes necessary to rely on direct calibration either in the field or in the laboratory for the determination of the discharge equation. The designer does not have complete freedom in choosing the dimensions of the flume but has to select the closest standard design to meet his requirements. Such flumes, however, require lesser length and, hence, are more economical than long-throated flumes. One of the most commonly used short-throated flumes is the Parshall flume which has been described here.
Parshall (10, 11 and 12) designed a short-throated flume with a depressed bottom (Fig. 5.23) which is now known as the Parshall flume. This was first developed in the 1920’s in the USA and has given satisfactory service at water treatment plants and irrigation projects. It consists of short parallel throat preceded by a uniformly converging section and followed by a uniformly expanding section. The floor is horizontal in the converging section, slopes downwards in the throat, and is inclined upwards in the expanding section. The control section at which the depth is critical, occurs near the downstream end of the contraction.

204					IRRIGATION AND WATER RESOURCES ENGINEERING
	M		B		L	G
			h1		Throat	h2
					section
				a
A	D		Crest		A
P		b	c
					A
							hb
	R	Alternate 45°		Converging	Diverging
		wing wall
					section	section
							Plan
			B		L	G
						Water surface
						(Submerged)
						Water surface
						(Modular flow)
	Flow	E	h1	Crest
			Level floor	N
						K
					y

X