STILLING BASINS 251
Fory 2 y 0 no stilling basin is necessary, and a horizontal apron protecting
the river bed downstream of the dam is sufficient, as a submerged jump will
result naturally. The stilling basin design for case 4 has to be based on the
maximum discharge (the same as for case 1) and, for case 5, on the dis-
charge giving a maximum difference between y 2 andy 0 (withQdQmax); this
can result in a small stilling basin at the toe of the dam followed by a hori-
zontal apron (or vice versa), or in a sloping apron design.
Where the result of the first computation shows that a stilling basin is
required, the procedure is repeated for a new value of E(in equation
(5.7)) which takes into account the lowering of the energy datum by a suf-
ficient amount (see Worked example 5.1).
The values of the coefficients andKin equations (5.9) and (5.10)
can be taken (Novak and Cˇábelka, 1981) as 1.11.25 and
4.5K5.5, where the lower value of Kapplies for Fr 1 10 and the
higher for Fr 1 3. Because at low supercritical Froude numbers the jump
is not well developed and can be unstable, it is rather difficult to design an
economically dimensioned basin in these cases without model studies.
Equations (5.8) and (5.10), and thus the design under discussion,
apply to basins with a horizontal floor only. In sloping channels the value
ofy 2 /y 1 increases with the slope; for a slope S 0 0.2,y 2 /y 1 is twice the value
of a horizontal channel, with the same Froude number.
The quoted values of K, and particularly of , are fairly low (as dic-
tated by economy) and dependent on a good assessment of the coefficient
!, and particularly of the downstream depth y 0 which, in turn, depends
usually on an assumed value of Manning’s nfor the river. If conservative
values of nand!are assumed (i.e. low nand high !) then a small value of
(say, 1.1) is sufficient, otherwise a higher value may have to be selected.
It is also very important to assess the possible long-term river-bed degra-
dation downstream of the dam, which could result in a lowering of the
downstream water levels and of y 0.
A simple end sill with a 1 in 3 slope is usually as good as more com-
plicated sills (Section 5.3.3).
It is evident from equations (5.7)–(5.10) that the lower the value of!
(the higher the value of ) the smaller will be the required stilling basin;!
in equation (5.7) refers to the total losses between the spillway crest and
entry into the stilling basin, i.e. to !1–3(equation (5.5)).
The energy loss in the fourth and fifth phases of energy dissipation
(Section 5.1) can be expressed as
e4,5(y 2 y 1 )^3 /4y 2 y 1. (5.11)Downstream of the jump at the outflow from the basin there is still a
substantial proportion of excess energy left, mainly due to the high
turbulence of flow which can be expressed (Novak and Cˇábelka, 1981) as
e 5 ( )V^20 /2g (5.12)