Q2: The average water height of an ocean area is 2.5 m high and each wave lasts for an average period of 7 s. Determine (a) the energy and power of the wave per unit area and (b) the work and average power output of a wave power plant on this ite with a plant efficiency of 35% and a toltal ocean wave area of 1 km2. Take the density of the seawater to be 1025 kg/m3.

(a) 561.12 W / m² (b) 196.39 MW

Explanation:

Solution

(a) Determine the energy and power of the wave per unit area

The energy per unit are of the wave is defined as:

E = 1 / 16ρgH²

= 1/16 * 1025 kg / m3 * 9.81 m/s² * (2.5 m) ²

=3927. 83 J/m²

Thus,

The power of the wave per unit area is,

P = E / t

= 3927. 83 J/m² / 7 s = 561.12 W / m²

(b) The average and work power output of a wave power plant

W = E * л * A

= 3927. 83 J/m² * 0.35 * 1 * 10^6 m²

= 1374.74 MJ

Then,

The power produced by the wave for one km²

P = P * л * A

= 5612.12 W/m² * 0.35 * 1 * 10^6 m²

=196.39 MW