222 DAM OUTLET WORKS
Fig. 4.13 Shaft spillway
outlets or even a turbine tailrace. The main components and rating curve
of the spillway are shown schematically in Fig. 4.13.
The shape of the shaft spillway is derived in a similar manner to the
overfall spillway from the shape of the nappe flowing over a sharp-edged cir-
cular weir (Wagner, 1956; Fig. 4.14). Clearly, in this case the shape for atmos-
pheric pressure on the spillway is a function of Hs/Ds, where Hsis the head
above the notch crest of diameter Ds. For ratios Hs/Ds0.225 the spillway is
free-flowing (i.e. with crest control) and for Hs/Ds0.5 the overfall is com-
pletely drowned. For the free overfall the discharge is given by
Q
2
3
CdπDc 2
g1/2H3/2 (4.60)
(curve 1 in Fig. 4.13, and for the drowned (submerged) régime (with
orifice control) by
Q
1
4
Cd 1 πD^2 [2g(HZ)]1/2 (4.61)
(curve 3 in Fig. 4.13), where Dis the shaft diameter, Dcis the crest dia-
meter (DcDs), His the head of the reservoir level above the crest
(HHs),zis the height of crest above the outflow from the shaft bend,
andCdandCd 1 are discharge coefficients (Fig. 4.13).
Figure 4.15 is a plot of the discharge coefficient (in the form
m2/3Cdirrespective of the type of flow at the shaft inlet) for two values
ofs/Dsas a function of Hs/DsH/Dc(defined in Fig. 4.15). In equation
(4.60) in the range 0.1
D
H
c
0.25 the coefficient of discharge Cdmay be
