360
CHAPTER 7. LABORATORY WAVE GENERATION
Fr^a.) = y/h + F] + ^(h- I?
(7.98)
Similarly, the maximum force when there is water of the same height
on both sides of the wave board is
Ftoo (max) — 2
+
(7.99)
Wave Board Power
Instantaneous power per unit width of board required to operate a variabledraft flap-type wave board with water on one side (neglecting friction and
mechanical losses) can be formulated as
/
o
p0(z,/) uo(z,t)dz
■(h-l)
(7.100)
where uo for this type of wave board is
n’iS /
z \
Uo =
( 1 + -—J ) cos at
(7.101)
After performing the integration, the instantaneous power equation
when water is on only one side of the wave board becomes
(
pa2SoA\ F. , ,,
(cosh kl — cosh khY\
9
— sinh kh + i------ —---- - ----------cos2 at +
2k /
k(n — I)
^pa2S0^^Cn [ ** । l f (cos
— cos
t
± ,n 1AM
+ I —-— ? — sinfcnh4-------- -——---- - ----- - sin at cos at (7.102)
\ 2 J
kn
kn(h - /)
. / P9°S0 \ .
>2
j
+ ( —Î2— ) (" ~ ‘) cosat
where A and Cn are determined from Eqns. 7.89 and 7.90, respectively. In
abbreviated form Eqn. 7.102 can be written as
f’o(t) = Pr cos2 at + Pj sin at cos at 4- P$ cos at
(7.103)
The instantaneous power for a wave board with water on both sides is
found by substituting Eqn. 7.64 into Eqn. 7.100 to obtain
P= Ï-Pr cos2 at + 2Pj sin at cosat
(7.104)
A relatively simple expression for maximum instantaneous wave power can
be found for the case with water on both sides of the wave board. First,