1. Homework #1 Coastal Engineering
Let: wave Period (T) = 8s, Wave height (H) = 1.5m, Water depth (d) = 6 m
a) Wave length in 6 m of water
𝑔𝑔𝑇𝑇 2 9.81( 𝑚𝑚⁄ 𝑠𝑠 2 ) × �8(𝑠𝑠)�
2
Assuming that the waves in the deep water
𝐿𝐿0 = = = 99.923 𝑚𝑚
2𝜋𝜋 2𝜋𝜋
Check the value 𝑑𝑑⁄L = 99.923 = 0.06 Unusable
6
Assuming that the waves in the Shallow water
𝐶𝐶 = �𝑔𝑔𝑔𝑔 = √9.81 × 6 = 7.6720
𝐿𝐿 = 𝐶𝐶𝐶𝐶 = 7.6720 × 8 = 61.37
𝑑𝑑⁄ 𝐿𝐿 = 6⁄61.37 = 0.09 Available
Wave length (L) = 61.37 m.
2𝜋𝜋 2𝜋𝜋
𝑘𝑘 = = = 0.10
b) Wave number (k)
𝐿𝐿 61.37
c) Velocity of propagation (c)
𝑔𝑔𝑔𝑔 9.81 × 61.37
𝐶𝐶 = � tanh 𝑘𝑘𝑘𝑘 = � tanh(0.10 × 6) = 7.17
2𝜋𝜋 2𝜋𝜋
𝐶𝐶 𝐺𝐺 = 𝐶𝐶 = 7.17
d) Group velocity (CG)
1 1
𝐸𝐸 = 𝜌𝜌𝑔𝑔𝐻𝐻2 = × 1025 × 9.81 × 1.52 = 2828.039 𝑗𝑗/𝑚𝑚 2
e) Energy density (Density of sea water=1025)
8 8
𝑃𝑃 = 𝐸𝐸𝐸𝐸 = 2828.039 × 7.17 = 20277.040 𝑤𝑤/𝑚𝑚
f) Wave power
𝜋𝜋𝐻𝐻 cosh 𝑘𝑘 ( 𝑧𝑧 + 𝑑𝑑)
𝑢𝑢 = cosh( 𝑘𝑘𝑘𝑘 − 𝜔𝜔𝑡𝑡)
g) Horizontal component of orbital velocity at bottom (at bottom z = 0)
𝑇𝑇 sinh 𝑘𝑘𝑘𝑘
𝜋𝜋 × 1.5 cosh 0.10(0 + 6)
= × cosh(0.10 × 0 − 0.785 × 8) = 293.67
8 sinh(0.10 × 6)
h) Amplitude of the orbital motion at bottom (at bottom z = 0)
𝐻𝐻 cosh 𝑘𝑘 ( 𝑧𝑧 + 𝑑𝑑) 1.5 cosh 0.10(0 + 6)
𝐴𝐴 = = = 1.3965 𝑚𝑚
2 sinh 𝑘𝑘𝑘𝑘 2 sinh(0.10 × 6)
Surawut Nimtim 5310501355 E 21-3