Hydraulic Structures: Fourth Edition

Note that the velocity potential satisfies u0 at the wall for which x0.

At the wall

 sint. (15.8)

Using equation (15.8) in the linearized energy equation (14.6), the pres-

sure distribution on the wall is given by

p (^)  Hc sint gy.
(The second term in the bracket on the right-hand side of the above
equation is the contribution from the hydrostatic pressure distribution.)
Withc/k, and c^2 given by equation (14.13), the pressure can be written
as
p (^)  gH sint gy. (15.9)
At the bed (yd), the maximum and minimum pressures are
p gd. (15.10)
The maximum and the minimum forces exerted on the wall may be esti-
mated assuming that the pressure varies linearly from 0 at the surface to
the value on the bed given by equation (15.10). The pressure profiles are
shown in Fig. 15.5. The maximum and minimum pressures at any depth, y,
below the still-water level are
pmax g  d (15.11)
and
pmin g d. (15.12)
The force on the wall per unit width due to the clapotis at the crest posi-
tion is
Fmax (dh 0 H) d. (15.13)

H



cosh(kd)

g



2

H



cosh(kd)

yh 0 H



dh 0 H

H



cosh(kd)

yh 0 H



dh 0 H

H



cosh(kd)

cosh[k(yd)]



cosh(kd)

cosh[k(yd)]



sinh(kd)

Hccosh[(k(yd)]



sinh(kd)

∂



∂t

638 COASTAL ENGINEERING