Contents preface (VII) introduction 1—37

Fig. 13.16 Variation of X with h/D and Z for the design of sediment ejector
Here, suffix 1 and 2 represent canal sections upstream and downstream of the ejector. For non-silting and non-scouring conditions in the canal downstream of the ejector, one can write

B q	= Qst	(13.21)
1 sh	2

On dividing Eq. (13.19) with Qst₂ ,

^Qst1 ₌ ^Qb1 ₊ ^Qs1

^Qst₂ ^Qst₂ ^Qst₂

^B1^qst_{1 =} ^B1 ^qb_{1 +} ^B1 ^qs₁

^B2^qst₂ ^B2^qst₂ ^B1 ^qsh

^qst		qb		1		B
	1	=		1	+			2	(13.22)
q	st	q	st	X B
							1
	2				2

Due to the disturbance at the diaphragm entrance, more sediment enters the ejector
and, therefore, qst₂ is reduced to K qst₂ with K being less than 1. There is no information about the variation of K. Equation (13.22) can now be rewritten as follows:

468							IRRIGATION AND WATER RESOURCES ENGINEERING
	^qst			qb			1 B
1		=	1		+			2	(13.23)
	Kq
			Kq		X B
		st	2		st	2		1

Additional water discharge (i.e., escape discharge Q_e) is required in the canal between the canal head regulator and the ejector so as to carry the sediment through ejector ducts into the escape channel without affecting the full supply discharge of the canal downstream of the ejector. The ratio of the escape discharge Q_e (= Q₂ – Q₁) to the discharge Q₁ in the canal upstream of the ejector can be expressed as

		h / D F	u I
		z0		G			J	d ( y / D)
Q			u
e	=			H	*	K			(13.24)
^Q1	1	F		u I
		z0	G				J			d ( y / D)
		H u* K

On substituting the value of u/u_* (Eq. 13.16) in Eq. (13.24), one can obtain the variation of Q_e/ Q₁ with h/D and D/d. Here, again, it was observed by Vittal and Shivcharan Rao that Q_e/Q₁ is not dependent on D/d and

Qe	~ ^h
	−		(13.25)
Q1	D

Using Fig. 13.16 and Eqs. (13.23 and 13.25), one can determine the diaphragm height h and the escape discharge Q_e and the canal discharge Q₁ for given data (d, Q₂, B₂, D₂, slope S₂ and the sediment load upstream of the ejector). The steps for their computation are as follows:

1. 
   Assume canal discharge upstream of the ejector, Q₁ to be higher than Q₂ by, say 20%.
   

Q₁ = 1.2 Q₂

2. 
   Design the upstream canal for known Q₁ to carry the known amount of sediment load of known size (see Art. 8.5.2). Thus, determine D₁, B₁ and S₁.
   

w

3. Compute u_* = ^{g D}1 ^S1 and Z = _u*k

4. Calculate the bed loads q_b1 and q_b2 using Meyer-Peter equation and also the sus-pended loads ^qs₁ and ^qs₂ using Rouse’s equation and, hence, q_st1 and q_st2 .

5. Assuming a suitable value of K (less than 1, say 0.9), determine X using Eq. (13.23). 6. Obtain h/D for computed values of X (step 5) and Z (step 3).
7. Obtain Q_e/Q₁ from Eq. (13.25) and, therefore, Q_e for the assumed value of Q₁.
8. New (revised) value of Q₁ is Q₂ + Q_e.
If the revised value of Q₁ matches with the assumed value of Q₁ in step 1, the values of h (step 5) and Q_e (step 7) can be accepted. Otherwise, repeat steps 2 to 8 with the new value of

Q₁.
13.11.3. Settling Basin
In case of canals carrying fine sediment, the variation of sediment concentration will be almost uniform, i.e., the sediment will be moving more as suspended load than bed load. In such situations, the height of the ejector platform will have to be raised. This would result in much larger escape discharge that may not be desirable. An effective way of removing fine sediment

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469

from flowing water in a canal is by means of a settling basin in which flow velocity is reduced considerably by expanding the cross-sectional area of flow over the length of the settling basin, Fig. 13.17. The reduction in velocity, accompanied with reduction in bed shear and turbulence, stops the movement of the bed material, and also causes the suspended material to deposit on the bed of the basin. The material on the bed of the settling basin is suitably removed. The settling basin, a costly proposition, is suitable for power channels carrying fine sediment which may damage the turbine blades. The design of such a settling basin involves estimation of the dimensions of the settling basin and suitable method for removing the material from the bed of the settling basin. For known size (and, hence, fall velocity w) of the sediment particle and the depth of flow D, the time required for the particle on the water surface to settle on the bed of the basin would be (D/w) and if the particle moves with a horizontal velocity of flow U, the required length of the basin should be equal to or more than UD/w. To account for the reduction in fall velocity due to turbulence, the length of the basin so obtained may be increased by about 20%.

	L
A	A
Flow	B2
B1

Plan

^qsi		^qse
		D
	h	U

Section AA
Fig. 13.17 Settling basin - definition sketch
The efficiency of removal of sediment η by a settling basin is defined as

η =	^q si ^− ^qse	= 1 −	^qse	(13.26)
^qsi	^qsi

Here, q_si and q_se are, respectively, the amount of sediment of a given size entering and leaving the settling basin in a unit time. Dobbins (15) obtained an analytical solution for the estimation of η by assuming : (i) the longitudinal concentration gradient zone, (ii) uniform velocity distribution for flow in the basin, and (iii) invariant diffusion coefficient over the flow section in the basin. Camp (16) presented Dobbins analytical solution in the form of a graph, Fig. 13.18, between η and (w/u_*) for various values of wL/UD. Here, u_* is the shear velocity
(= gDS in which S is the slope of the settling basin). Using Manning’s equation,

470								IRRIGATION AND WATER RESOURCES ENGINEERING
	U =		1		D2 /3 S1/ 2
			n
one obtains	DS =				Un
			D	1/ 6
and, therefore,		u = (Un/ D ^1\6 ) g
	*
Hence,	w	=		wD1/6
u*	Un g

Here, n is the Manning’s roughness coefficient.

se q

si

q

1–

1.0

0.8

0.6

0.4

0.2

0

oL/UD = 2.0	1.0
	.5
	1
	0.8
	.2
	1

0.7
0.6

0.5
0.4

0.3
0.2

_oL/UD = 0.1
0.01 0.1 1.0 10
1/6

_oD

Un g

Fig. 13.18 Sediment removal efficiency for settling basin
Sumer (17) assumed logarithmic velocity distribution for flow in the settling basin and also considered suitable variation of the diffusion coefficient and thus analysed the settling of a sediment particle to finally obtain,

F kλ I F	Lu* I
− G		J G		J
η = 1 − e ^H	6 K H	UD K	(13.27)

w

Here, k = 0.4 and λ is a parameter that depends on β (= _ku* ), Fig. 13.19.

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471

50

40

30

20

10

10

0	1	2		3	4	5

Fig. 13.19 Relation between λ and β
Based on dimensional analysis and experimental investigation, Garde et al. (18) obtained

η = η (1 – e^–^KL^/^D)	(13.28)
o

Here, η_o and k are related to w/u_* as shown in Fig. 13.20. The nature of the relationships of Eqs. (13.27) and (13.28) is such that the efficiency reaches 100 per cent only asymptocally.

0.24
				(%)
				100
0.18				90
				80
^K 0.12				70	0
				60
0.06				50
				40
0.0				30
0.6	1.0	1.4	1.8	2.2
		w/u*

Fig. 13.20 Variation of K and η₀ with w/u*

472 IRRIGATION AND WATER RESOURCES ENGINEERING
These methods can be used suitably for estimating the efficiency of sediment removal, η for sediment size d in a given settling basin. However, for designing a suitable settling basin to achieve the desired efficiency of sediment removal, η for sediment size d and given flow rate Q, one needs to select suitable combinations of L, B₂, and D for the settling basin and obtain the values of η for each of these combinations. The one which gives η higher than the desired value of η can be selected. At times, these different methods would give very different results and one should use the results judiciously.
The performance of a settling basin is adversely affected if the flow conditions in the basin are relatively turbulent or there is some amount of ‘short-circuiting’ of flow on account of separation due to expansion in cross-section of flow. Therefore, a suitable expanding transition with two (or more) splitter plates at the entrance of the basin and a contracting transition at the outlet end of the basin are always provided.
Further, a suitable provision to remove the deposited material from the bed of the basin is to be made. For this, one can have two settling basins parallel to each other so that while the material from one basin is removed, the other is in operation. Alternatively, the bed of the basin may be divided into suitable number of hopper-shaped chambers and a suitable pipe outlet in each of these chambers is provided. The deposited sediment may be flushed away through these outlets.
Example 13.3 Estimate the efficiency of removal of sediment of size 0.05 mm (fall velocity = 2 × 10^–3 m/s) by a settling basin (length = 40 m, width = 12 m and depth of flow = 3 m and Manning’s roughness coefficient, n = 0.014) provided in a power channel carrying a discharge, Q of 1.41 m³/s.

Solution:

U =

Q

=

141.

= 0.039 m/s

DB

3 × 12

2

u =

Un

g

= 0.039 × 0.014 ×

9.81

= 1.424 × 10^–3 m/s

*

D1/ 6

(3)^1/ 6

w

=

2 × 10^−^3

= 1.4

u*

1424. × 10^−^3

wL

=

2 × 10

^−^3 × 40

= 0.684

UD

0.039 × 3

Using Camp – Dobbins methods, Fig. 13.18,

η = 0.66 = 66%

For Sumer’s method,

β =

w

=

2 × 10^−^3

= 3.5

ku*

0.4 ×

1424. × 10^−^3

From Fig. 13.19,

λ = 38.

F k λ I F

Lu* I

F 0.4

×

38I F

40 × 1424. × 10

−3 I

Therefore, G

J G

J

=

G

^J G

J

= 1.23

6

0.039 × 3

H 6

K H

UD K

H

K H

K

∴

η = 1 – e^–1.23 = 0.70 = 70%

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473

Thus, Camp-Dobbin’s method and Sumer’s method give matching results.

For ^w = 1.4, Fig. 13.20 gives u_*




K = 0.08 and η_o = 57% Therefore, Eq. (13.28) gives
η = η_o (1 – e^–KL/D) = 57 (1 – e^{–0.08 × 40/3}) = 37.38%
Thus the method proposed by Garde et al. gives relatively smaller value of η for the given problem compared to the value of η obtained by either Camp-Dobbins method or Sumer’s method.