where a full analysis of the flow conditions and factors influencing them is
really necessary.
The most important factors on which flow over and under the gates
will depend are the geometry of the upstream and downstream water
passage, the geometry and position of the gate and its accessories such as
seals, supports, etc., the upstream head, whether the flow through the gate
is free with atmospheric pressure downstream of it or submerged, the flow
Froude and Reynolds – and possibly even Weber – numbers, the degree of
turbulence of the incoming flow and aeration of the space downstream of
the gates. A detailed treatment of the subject of the prediction of flow con-
ditions and related hydrodynamic forces acting on gates is outside the
scope of this book, but can be found, for example, in Naudascher (1987,
1991). For an example of conditions in case of wicket gates with a partial
opening, see de Bejar and Hall (1998).
Generally the gate design is a difficult area partly because of the com-
plexity of hydraulic conditions indicated above and partly because the
design has to satisfy conflicting demands: vibration damping may conflict
with keeping the forces for the gate operation to a minimum; the need
to avoid vibrations may conflict with the optimum shape and strength
required by the flow conditions and loading; the optimum shape of the
edges and seals may conflict with water tightness of the closed gate, etc.
It is often useful to carry out a potential flow analysis and use this for
the determination of the hydrodynamic force (Rouse, 1950), which (in
some simpler cases) can also be obtained by using the momentum equa-
tion (see Worked example 6.1).
For gates with overflowthe discharge coefficient can be expressed by
the same equation as for an overfall spillway, i.e.CdQ
2
3
(2g)1/2bh3/2 (6.2)wherehis the head of the upstream water level above the crest (or top
edge) of the gate. The total head, H, can also be used in equation (6.2) with
an appropriate change of Cd(for dam crest gates Hh). The coefficient
will depend largely on the geometry of the overflow and the amount of air
which has access to ventilate the nappe. Very broadly, the range of Cdis
similar to that for overfall spillways, i.e. 0.55Cd0.8; for further details
see, for example, Hager (1988) and Naudascher (1987, 1991).
For gates with underflowthe discharge and flow field will depend pri-
marily whether the outflow is free(modular) or drowned. For free flow the
form of equation (4.21b) may be used:QCdba(2gH)1/2 (6.3)(ais the gate opening and Hthe upstream head), where the coefficients of
dischargeCdand contraction Ccare related by