faces, at the expense of allowing small negative pressures to develop on
them. To prevent the formation of vortices in the water level upstream of
the inlet, its axis should be submerged sufficiently and/or vortex suppres-
sion devices (e.g. floating rafts) should be used (Knauss, 1987). It may be
advantageous to combine the outflow part of bottom outlets with the spill-
way energy dissipator; in many cases, however, a separate outlet energy
dissipator is provided (Section 5.5). For further details of bottom outlet
model testing and design, see Novak and Cˇábelka (1981); for details of the
protection of inlets against ice and their operation in winter conditions, see
Ashton (1988).
The flow in the outlet downstream of a gate can be free with or
without a hydraulic jump (see also Fig. 4.17). In their study of the jump
in circular conveyancies, diameter D, with a free downstream surface
Stahl and Hager (1999) defined the supercritical Froude number as
Fr 1 Q/(gDy 14 )1/2and obtained experimentally a simple relationship for
the sequent depths ratio for 1.5Fr 1 6.5 and 0.2y/D0.7:
y 2 /y 1 1.00Fr 1 0.9 (4.70)
The important choking discharge can be approximated from equation 4.70
by putting y 2 DandD/y 1 Fr 1.
The air demand of a hydraulic jump in a conduit where the flow
downstream of the jump is under pressure has been well researched and
the original Kalinske and Robertson (1943) equation has been shown to
be valid for a range of conditions (Qa/Q):
0.0066 (Fr 1 1)1.4 (4.71)
However, Haindl (1984) points to an increase of the entrainment capacity
of a jump with increasing conduit size and quotes a coefficient 0.015 in
equation (4.71) for the envelope of field data.
For further details of flow at tunnel bends see Gisonni and Hager (1999).
For a comprehensive discussion of air demand and entrainment in
bottom outlet tunnels, see Speerli (1999) and Hager (1999) (see also
Section 6.6).
Worked Example 4.1
The inflow hydrograph into a reservoir is given by the first two columns in
the lower table on this page. The relationship between the storage volume
in the reservoir (taking storage at crest level as zero) and the head above
the crest is given by the first two columns of the upper table (this was
obtained from equation (4.5)). A simple overfall spillway is to be designed
which would limit the maximum head on the spillway crest to 3.00 m.
234 DAM OUTLET WORKS
