Hydraulic Structures: Fourth Edition

with intermediate reservoirs. The economy of handling water is achieved
at the cost of increased capital outlay and a longer time for the passage of
vessels through the given step. Another way of saving water are thrift
locks (see Section 11.9) and lifts (see Section 11.10).

11.8.4 Hydraulics of locks

The design parameters of major interest are the time of filling (emptying)
T, the maximum discharge Q, and the maximum forces acting on a vessel
during lockage. If we assume that the lock is filled from a large forebay
with a constant water level, we can write

Qdtca(2gh)1/2dtAdh (11.9a)

whereAis the lock area in plan, his the instantaneous head (the dif-
ference between the forebay and lock water levels), cis a coefficient and a
is the filling system area (valve area); both candaare functions of time,
butcis usually taken as a constant.
For an instantaneous complete opening of the filling system, equa-
tion (11.9a) yields, for the time of filling a lock with a total head H,

T

T

0

dt 

0

H

. (11.10)

For a linear opening of the system in time T 1 (aa 1 T 1 /t),



T 1

0

dt 

hT 1

1

H

 

hT 1

H

. (11.11)

Thus



T 1

0

tdt (H1/2 hT1/2 1 ) (11.12)

and

T 1 . (11.13)

The total filling time from equations (11.10) and (11.13) is then

TT 1  (11.14)

2 AH1/2



ca(2g)1/2

T 1



2

2 AhT 1 1/2



ca(2g)1/2

4 A(H1/2 hT 1 1/2)



ca(2g)1/2

2 AT 1



ca(2g)1/2

dh



h1/2

AT 1



cat(2g)1/2

dh



ath1/2

A



c(2g)1/2

2 A(H)1/2



ca(2g)1/2

dh



h1/2

A



ca(2g)1/2

LOCKS 483