A wave tank is 120 ft long, 3 ft wide, and 4 ft deep and is fi lled with fresh water to a depth of 3 ft. The wave maker generates a wave which has a wave height of 0.75 ft and wave period of 1.1 s. The density of water is 1.94 slugs/ft3. Evaluate the wave celerity, length, group celerity, energy in one wavelength (EL), and power..

Solution

Wave height,Hm = 0.75ft

water depth = 3ft

For a case of deep water wave

Wave length,λ = g/2π*T2 where T is the period of the wave

= 32.174 /2π *( 1.1)2

=6.195 ft

λ is not much larger than the depth

Thus,

wave celerity ,Cp = ( gλ /2π) = 5.63 ft/s

Group celerity,Cg = Cp/2 = 2.816ft/s

Wave energy can be calculated according to the linear wave theory

E = 1/8 ρgHm2

= 1/8 * 1.94 *32.174 *32.174 * 0.75*0.75

=141.20 lb/s2

Power = E*Cg

=141.20*2.817

=397.62 lbft/s

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