Hydraulic Structures: Fourth Edition

SPILLWAYS 209

sures for outflow under partially raised gates. The discharge through par-
tially raised gates may be computed (Fig. 4.7(a)) from

Q

2

3

 2

 g1/2bCd 1 (H3/2 H 1 3/2) (4.21a)

withCd 1 0.6 or, better, from

QCd 2 ba(2gHe)1/2 (4.21b)

whereais the distance of the gate lip from the spillway surface, and Hethe
effective head on the gated spillway (H) (0.55Cd 2 0.7).
For slender dam sections, e.g. in arch dams, it may be necessary to
offset the upstream spillway face into the reservoir in order to gain suffi-
cient width to develop the spillway shape (Fig. 4.7(b)); the effect on the
coefficient of discharge is negligible. For details of discharge coefficients
for irregular overfall spillways see, for example, Bradley (1952).
In equations (4.19) and (4.21a), brefers to the spillway length. In the
case of piers on the crest (e.g. gated spillways) this length has to be
reduced to

bcb knH (4.22)

wherenis the number of contractions and kis a coefficient which is a
function of Hand pier shape; (0k0.09 with the upper limit for
semicircular-nosed piers and H/Hd0.2). For further details see, e.g.,
Lencastre (1987), Hager (1988), ASCE (1995) and Vischer and Hager
(1998).
In the case of concrete gravity dams, the spillway shown in Fig. 4.6 is
continued by a plane surface (forming a tangent to it and coinciding with the
downstream dam face) to the foot of the dam and into the stilling basin.

Fig. 4.7 Overfall spillway with (a) gates and (b) offset