Hydraulic Structures: Fourth Edition

The basic treatment of the hydraulics of shock waves can be found

for example in Henderson (1966) and of design considerations in Chow

(1983) (following the classical work of Ippen and Knapp). Briefly, for an

inclinationof the shock wave to the direction of flow and the ratio of the

downstream and upstream depths y 2 andy 1 close to 1, Fr 1 sin1. For

values of y 2 /y 1 appreciably bigger than 1,

Fr 1 sin

y

y

2

1

 (^1) 
1/2

. (4.31)

Substituting for y 2 /y 1 tan/tan ( ) (from continuity and momentum

equations) with as the wall deflection angle results in



1

2

[(1^8 Fr^21 sin^2 )1/2^ 1]. (4.32)

The above equations can be simplified to

y 2 /y 1  2

 Fr 1 sin 1/2, (4.33)

3/(2 2

 Fr 1 ). (4.34)

For small values of andy 2 /y 1 2 this may be written as

y 2 /y 1  1  2

 Fr 1 . (4.35)

tan



tan ( )

y 2



y 1

1



2

214 DAM OUTLET WORKS

Fig. 4.10 Interference waves at a chute spillway inlet (Cassidy and Elder,

1984)