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# Homework 1 river

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• 1. Homework #1 Coastal EngineeringLet: 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