Hydraulic Structures: Fourth Edition

SPILLWAYS 211

a free overfall over the entire horizontal spillway crest, so that the reservoir
level is not influenced by the flow in the channel. The width of the flume
may therefore increase in the direction of the flow (Fig. 4.8). From the
energy dissipation point of view, the deeper the channel and the steeper the
side facing the spillway, the better; on the other hand, this shape is in most
cases more expensive to construct than a shallow wide channel with a
gently sloping side. The result is usually a compromise, as shown in Fig. 4.9.
The flow in a side-channel spillway is an example of a spatially varied
non-uniform flow that is best solved by the application of the momentum
principle, assuming that the lateral inflow into the channel (Fig. 4.9) has no
momentum in the direction of flow, but that there is substantial energy dis-
sipation in the channel. Taking the slope of the channel, S 0 , and the resis-
tance (friction slope Sf) into account results, for a cross-section of the
channel,A, wetted perimeter, P, depth yof the centre of gravity of
sectionA, and length (in the direction of flow) ∆x, in

  AyA(S 0 Sf). (4.24)

Q^2



gA

d



dx

dM



dx

Fig. 4.8 Side-channel spillway: plan

Fig. 4.9 Side-channel spillway: section A–A