According to first-order theory, a crest occurs at z = H/2,
cos 6=1 and a trough at z = - H/2, cos 0 = - 1. Equation 2-13
therefore implies
Hg T cosh [2ît(z + d)/L]
c’^
2 L
cosh (2ird/L)
with
H
z = —
2
and,
HgT cosh [2n(z + d)/L]
Ut,i
2L
cosh (27rd/L)
with
H
Z ” ~ 2
According to second-order theory, a crest occurs at z =
=
2.48 feet, cos 0 = cos 20 = 1 and a trough at z = ru g = - 1.52
feet, cos 0 = - 1, cos 20 = 1. Equation 2-51 therefore implies
HgT cosh [2rr(z + d)/L]
Uc>2 ~ ~2L
cosh (2rrd/L)
3 /nH\2
cosh [4n(z + d)/L]
4 \L j
sinh4 (2rrd/L)
with
z = rit 2 = — 1.52 feet .
3 /ttHY1
cosh [4rr(z + d)/L]
4 \L /
sinh (2rrd/L)
with
3 4
z = rj 2 = + 2.48 feet
and,
HgT cosh [2rr(z + d)/L]
t>2
2L
cosh (2rrd/L)
2-43