Hydraulic Structures: Fourth Edition

(generally, the opening of the filling system is non-linear). In the same way

we could derive the equation for the time to equalize the water levels

between two locks of areas A 1 andA 2. For an instantaneous full opening of

the filling system,

T. (11.15)

IfA 1 A 2 ,

T (11.16)

and for A 1 ∞we again obtain equation (11.10).

The time of filling of a lock by an overfall height h 1 over a gate width

Bis given approximately by

T. (11.17)

(Equation (11.17) neglects the change from a modular to non-modular

overflow at the end of the filling.)

If the opening of the filling system is gradual but not linear, we have

to compute the filling time by a step method, e.g. from equation (11.10) it

follows that

∆t (h1/2i 1 h1/2i); (11.18)

thus

hih1/2i 1 ∆t

2

. (11.19)

Equation (11.19) gives also the rate of change of the depth in the lock

(H hi), and it permits us to compute the change of discharge with time

from equation (11.9a):

Qicai(2ghi)1/2 (11.9b)

(in equations (11.18) and (11.19), ais a function of time).

Of particular interest, of course, is the maximum discharge Qmax. In

the special case of a linear opening of the filling (emptying) system we can

determineQmaxand the head at which it occurs analytically from the two

equations

c(2g)1/2a



2 A

2 A



ca(2g)1/2

AH



2/3CdB(2g)1/2h 1 3/2

AH1/2



ca(2g)1/2

2 A 1 A 2 H1/2



(A 1 A 2 )ca(2g)1/2

484 INLAND WATERWAYS