By Equation 2-1
512
T
512
10
51.2 ft/sec.
For d = 10 feet
d
Lo
10
512
0.0195.
Entering Table C-l with d/L0 it is found that,
- = 0.05692,
L
hence
L = ---- —— = 176 feet /transitional depth, since — < — < —
0.05692
l
25
L
2
L
176
. .
C = — = ----- = 17.6 ft/sec.
T
10
************************************
2.234 Local Fluid Velocities and Accélérations. In wave force studies,
it is often désirable to know the local fluid velocities and accélérations
for various values of z and t during the passage of a wave. The
horizontal component u, and the vertical component w, of the local
fluid velocity are given by:
H gT cosh [2n(z + d)/L]
/ 2irx
27Tt
u = —
------ ;-------;------- cos
1 . —
----' ■
2 L
cosh (27rd/L)
\
L
T
H gT sinh [2n(z + d)/L]
( 2-nx
2nt
w = —
--------------------- sin
1 ■■
—
2 L
cosh (2n d/L)
\
L
T
(2-13)
(2-14)
Fhese équations express the local fluid velocity components any distance
(z + d) above the bottom. The velocities are harmonie in both x and t.
For a given value of the phase angle 0 = (2ttx/L - 2irt/T), the hyperbolic
functions, oosh and sinh^ as functions of z resuit in an approximate
exponential decay of the magnitude of velocity components with increasing
distance below the free surface. The maximum positive horizontal velocity
2-12