Contents preface (VII) introduction 1—37

Fig. 17.23 Trajectory bucket
The horizontal range of the jet at the level of the lip (i.e., y = 0) is given by
x = 4k₁E tan θ cos² θ = 2k₁E sin 2θ
The maximum value of x will be 2 k₁E when θ is 45°. The lip angle depends on the radius of the bucket and the height of the lip above the bucket invert. It usually varies from 20° to 45°. The bucket radius should be large enough to ensure a concentric flow along the bucket (10).
(ii) Roller (or Submerged) Bucket: A roller bucket is used when the tail-water depth is greater than 1.1 times the required conjugate depth for the formation of the hydraulic jump and the river bed rock is good (10). Roller buckets can be either solid or slotted (Fig. 17.24). The

Flow
^R –45°

1:1
0.6 R

(a) Solid bucket

	0.05 R
	radius
Flow
	0.125R
R	45°
	0.05R
	16°
	8°

0.5R
(b) Slotted bucket

Fig. 17.24 Roller buckets

SPILLWAYS

595

general hydraulic action responsible for the dissipation of energy is shown in Fig. 17.25. The energy dissipates through the formation of two rollers; one is on the surface of the bucket and moves anticlockwise (considering that the flow is to the right), and the other is a ground roller moving in a clockwise direction and which forms immediately downstream of the bucket (Fig. 17.25). The intermingling of the incoming flow with the roller as well as the movements of the latter dissipate the energy of the water effectively and prevent excessive scouring down-stream of the bucket.

Boil

Bucket roller	Ground roller

(a) Solid bucket

Standing wave

Bucket roller

Ground roller

(b) Slotted bucket

Fig. 17.25 Roller formation in roller buckets
Although the hydraulic action of the two buckets is similar, there are some differing flow features as well. The deflector lip of a solid bucket directs upward the high-velocity flow and thus creates a high boil on the water surface and a violent ground roller moving clockwise immediately downstream of the bucket. This ground roller picks up the loose material and keeps some of it in a constant state of agitation. There may be unwanted abrasion on the concrete surfaces because of the loose material which is brought back towards the lip of the bucket by the ground roller. Further, the more violent water surface created by surface boil is carried downstream causing objectionable eddy currents which may adversely affect the river banks. In the slotted bucket, the high-velocity jet leaves the lip of the bucket at a relatively flatter angle and only a part of the high-velocity flow finds its way to the water surface. Thus, a relatively less violent surface boil forms and there is better dispersion of the flow in the region above the ground roller. Therefore, there is less concentration of high-energy flow throughout the bucket and a smoother downstream flow.