Contents preface (VII) introduction 1—37

Enlarged detail at A
diaphragm
				Sediment	X
X			ejector
			escape
			channel
Flow
Y		Hoist
Plan at diaphragm level			Emergency gate
Full supply level		deck	Min. head 1 m
Diaphragm			HFL
			To
Flow			outfall
			channel

Tunnels	Regulating gate
	Section X-X

465

Flow	-Y
Diaphragm–A	Tunnels SectionY

Fig. 13.15 Typical layout of a sediment ejector
The efficiency (E) of the sediment ejector can be defined as (13)

E =	I u − Id	× 100 per cent	(13.13)
	^Iu

Here, I_u and I_d refer, respectively, to the silt concentration in the canal at the upstream and the downstream of the ejector. A similar definition of efficiency can be used for sediment excluder too.
Recently, Vittal and Shivcharan Rao (14) suggested a rational method to decide on the height of the ejector diaphragm. The method is based primarily on the premises that : (i) the suspended load above the diaphragm only passes the ejector and enters the canal downstream of the ejector, and (ii) this suspended load (above the diaphragm) should be equal to the total sediment load transport capacity (i.e. , the sum of the bed load and suspended load) of the canal downstream of the ejector, if it is to be neither silted nor scoured. In addition, the proposed method also assumed uniform size of sediment and validity of Rouse’s equation, Eq. (7.34), for the variation of sediment concentration along a vertical and the logarithmic variation of velocity in sediment-laden flows. Also, river-bed material of coarser size is assumed to have been removed by the sediment excluder. The development of the method is as follows (14).
If X is the ratio of the transport rate of the suspended load above the diaphragm (of height h) to that in the total depth of flow D, one can write (see Art. 7.5.2)



466

in which

IRRIGATION AND WATER RESOURCES ENGINEERING

1.0 F

C I F u I

zh / D G

J G

J

d ( y / D)

q

sh

C

u

X =

=

H

a K H

* K

(13.14)

^qst

1.0 F

C I F

u I

G

J G

J

d ( y / D)

z2d / D H

Ca K H u* K

C	FF	D − yI F	2d	I I	Z
	= GG		J G		J J	(13.15)
Ca
	HH	y K H	D − 2dK K

u	=	2.3	log	y	(13.16)
u	k	y′
*

where
u = the velocity at a height y above the bed, C = the sediment concentration at y,

C_a = the reference concentration at y = a = 2d, d = the size of the sediment,
Z = w u_*/k,
w = fall velocity of the sediment particles, u_* = the shear velocity,
k = von Karman’s constant, and y′ = d/30.
Combining Eqs. (13.14–13.16) and then rearranging the terms,

LF

y I F

I O ^Z

1.0

MG

1 −

J G 2d / D J P

2.3

F F

y I F

DI

I

D

zh / D

M

P

log G G

J G

J

(30)J

d (y / D)

y / D ^J G

2d J

k

G

P

H H

DK H

d K

K

M

J G 1 −

J

G

MH

K H

D K P

X =

N

Q

(13.17)

LF

y I F

I O ^Z

2.3

F F y I F DI

I

MG

1 −

D J G 2d / D J P

1.0

M

P

log G G

J G

J

(30)J d (y / D)

y / D ^J G

2d J

k

z2d / D ^G

P

H H

DK H

d K

K

M

J G

1 −

J

G

MH

K H

D K P

N

Q

Equation (13.17), therefore, suggests that X should depend on h/D, Z and D/d. On substituting the values of h/D (between 0 and 1), Z (between 0.03125 and 4.0) and D/ d (between 500 and 10,000) in the final combined equation, they obtained variation of X with h/D and Z (as the third variable) as shown in Fig. 13.16. The parameter D/d did not seem to affect the relationship of Fig. 13.16.
The value of X can also be obtained indirectly as follows (14): By definition, the total sediment transport rate (Q_st) equals the sum of the bed load transport rate, Q_b and suspended load transport rate, Q_s.

	Qst = Qb + Qs	(13.18)
	^Qst	= Qb	+ Qs	(13.19)
	1	1	1
and	^Qst	= Qb	+ Qs	(13.20)
	2	2	2

CANAL HEADWORKS																			467
1.0
								Curve no.				Z
								1			0.0312
								2			0.0625
0.8								3			0.1250
								4			0.2500
								5				0.5000
								6			1.0000
								7				2.0000
0.6								8			4.0000
X
								2^1
0.4							4	3
				6		5
0.2
	7
		8
	0
0	0.2	0.4		0.6			0.8			1.0

h/D