Hydraulic Structures: Fourth Edition

Worked Example 11.1

A navigation lock, 200 m12 m in plan and with a 9.00 m head, is filled
through two longitudinal conduits with rectangular gates 3.00 m wide con-
trolling the flow. The overall coefficient of discharge of the filling system is
0.65 and the gates open 8.5 mm s^1 at a uniform speed in 4.5 min. Deter-
mine the maximum discharge entering the lock and the total time of filling.

Solution

The time of opening of the gates is T4.5 60 270 s. The flow area of a
fully open gate is 30.0085 270 6.885 m^2. The flow area of the filling
system is 26.88513.77 m^2. From equation (11.14), for a linear opening
of the filling system the total time of filling is

T 

27

2

0

496 s.

The head on the lock at the end of the opening of the gates, hT 1 , is from
equation (11.13)

270 

4 A

c

(H

a(

1

2

/2

g

)1/

h

2

1/2

T^1 ).

ThushT 1 3.55 m. Qmaxoccurs at either hT 1 or 4/9H, whichever is greater;
in this case 4/9H4/9 9 4m3.55 m.
The time at which h4 m can be obtained from the equation



t

0

tdt 

ht

H

 (H1/2 ht1/2)t^2 /2;

forht4m

t^2  ( 9

4

 )65 370 s^2.

Thust256 s (270 s) and the maximum discharge occurs before the
filling system is fully open. At time t256 s, the area of opening of the
system is (13.77256)/27013.056 m^2. Therefore (from equation (11.9b))
Qmax0.6513.056(419.6)1/275.19 m^3 s^1.

4  200  12  270



0.6513.77 1

9

 .6 

2

2 AT 1



ca(2g)1/2

dh



h1/2

AT 1



ca(2g)1/2

4  200 12(3 h1/2T 1 )



0.6513.77 1

9

 .6 

2

2  200  (^129)

0.6513.77 1
9
.6
2

2 AH1/2



ca(2g)1/2

T 1



2

WORKED EXAMPLES 493