or
yKxnH^1 n0.5x1.85H^ 0.85 (4.18b)
(curve a in Fig. 4.5 (Novak and Cˇábelka, 1981)). Note that the head above
the new crest (origin) His smaller than the head habove the crest of the
sharp-edged notch from which the shape of the overall spillway (equation
(4.18a)) was derived. As, for K0.5, the pressures acting on the surface
defined by equation (4.18) are atmospheric (p 0 ), for K0.5 (curve b) the
pressures acting on the spillway will be negative (pp 0 ), and for K0.5
(curve c) positive (pp 0 ).
For an overflow spillway we can thus rewrite equation (4.16) as
Q
2
3
2
g1/2bCdH3/2 (4.19a)
or
Qg1/2bC 1 H3/2 (4.19b)
or
QC 2 bH3/2 (C 2 has dimensions L1/2T^1 ). (4.19c)
(AsHhin equation (4.19), Cd0.62 for atmospheric pressures.)
There are three possibilities for the choice of the relationship
between the design head Hdused for the derivation of the spillway shape
and the maximum actual head Hmax:
HdHmax. (4.20)
ForHdHmaxthe pressure is atmospheric and Cd0.745. For HdHmax
the pressure on the spillway is greater than atmospheric and the coefficient
of discharge will be 0.578Cd0.745. (The lower limit applies for broad-
crested weirs with Cd1/ 3
, and is attained at very small values of
Hmax/Hd(say, 0.05). For HdHmaxnegative pressures result, reaching cavi-
tation level for H 2 HdwithCd0.825. For safety it is recommended not
to exceed the value Hmax1.65HdwithCd0.81, in which case the intru-
sion of air on the spillway surface must be avoided, as otherwise the over-
fall jet may start to vibrate.
Some further details of the standard overfall spillway with HdHmax
are shown in Fig. 4.6 (US Army Waterways Experimental Station, 1959;
US Bureau of Reclamation, 1987).
For gated spillways, the placing of the gate sills by 0.2Hdownstream
from the crest substantially reduces the tendency towards negative pres-
208 DAM OUTLET WORKS
