Hydraulic Structures: Fourth Edition

t^2  (H1/2 ht1/2)

and

Q.

ForQmax, dQ/dht0, giving

ht

4

9

H. (11.20)

The maximum discharge occurs at 4/9Hif the filling system is not fully
open yet by the time this level is reached, i.e. the criterion is the value of
hT 1 computed from equation (11.13). If hT 1 4/9Hthe maximum discharge
occurs at 4/9H; if hT 1 4/9Hthen the maximum discharge occurs at the
head of hT 1 corresponding to the end of opening of the filling (emptying)
system. The real time of filling can be up to 12% shorter than the com-
puted one owing to inertia effects in the filling system.
The coefficient of discharge usually varies between 0.6 and 0.9 and is
a function of the geometry of the system. Although also a function of time,
an average value of c, best determined by field or model experiments, is
usually used in the computation. Typical shapes of the Q,aandhvalues as
functions of time (Novak, 1994) are shown in Fig. 11.14.
During lockage the vessel is tied by hawsers to bollards, with the
ropes at an angle between 20° and 40° to the longitudinal axis of the lock
(vessel). Because of inertia, during the small movements of the vessel the
force in the ropes, R, is about 35% larger than the force, P, acting on the
vessel. The resultant tension in the rope is then

cat(2ght)1/2



T 1

4 AT 1



ca(2g)1/2

LOCKS 485

Fig. 11.14 Variation of Q,aandhwith time