Hydraulic Structures: Fourth Edition

ENERGY DISSIPATION ON SPILLWAYS 249

The key parameters for the flip bucket design are the approach flow
velocity and depth, the radius rof the bucket, and the lip angle . For a
two-dimensional circular bucket the pressure head can be computed for
irrotational flow; experimental data confirm these values for the maximum
pressure head but (in contrast to the theory) show a non-uniform pressure
distribution (Fig. 5.3). At low flow the bucket acts like a stilling basin with
water flowing over the lip and the downstream face; the foundation of the
flip bucket has, therefore, to be protected against erosion. As the flow
increases a ‘sweep-out’ discharge is attained at which point the flip bucket
starts to operate properly with a jet.
The jet trajectory is hardly affected by air resistance for velocities
below 20 m s^1 , but for velocities of 40 m s^1 the throw distance can be
reduced by as much as 30% from the theoretical value, given by (^2 /g) sin 2.
The designer’s main concern is usually to have the impact zone as far
as possible from the bucket to protect the structure against retrogressive
erosion. Many designs with skew jets and various three-dimensional forms
of flip buckets have been developed. Heller et al. (2005) give an analysis of
ski-jump hydraulics and Locher and Hsu (1984) discuss further the flip
bucket design.

5.3 Stilling basins

5.3.1 Hydraulic jump stilling basin

The stilling basin is the most common form of energy dissipator converting
the supercritical flow from the spillway into subcritical flow compatible
with the downstream river régime. The straightforward – and often best –
method of achieving this transition is through a simple submerged jump
formed in a rectangular cross-section stilling basin. Vischer and Hager
(1995) give an overview of the hydraulics of various energy dissipators.
Hydraulic jumps have been investigated by many researchers, more
recently by Rajaratnam (1967) and Hager, Bremen and Kawagoshi (1990),
who also extended this investigation to a jump with a control sill (Hager and
Li, 1992). The implications of the hydraulics of the jump for the submerged
jump stilling basin have been studied by Novak (1955).
Referring to the notation in Fig. 5.4 and to equations (5.1) and (5.2)
we can write

Ey 1 . (5.7)

y 2 

y

2

1

^1 ^1 ^8 

1/2

. (5.8)

q^2



gy^31

q^2



2 g!^2 y^21