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In: Physics

Dimensional analysis In deep water, the fact that the propagation velocity v for surface waves has...

Dimensional analysis

In deep water, the fact that the propagation velocity v for surface waves has been observed depends on the wavelength λ of the waves and the wave height h. It is also reasonable to believe that also the density ρ of the liquid and the acceleration of gravity g affect. Use dimensional analysis for to produce a possible connection. Note that the dimensional analysis can show that someone parameter actually has no effect. In that case, this must be justified.

Expert Solution

lets first list out the dimensional formulas of all the properties given,

velocity:
wavelength :
waveheight :
density of liquid :
acceleration of gravity :

now, lets assume velocity

let's compare dimensions of both the sides of equation

lets compare powers of M,L and T from both the sides

from these equations, we get,

lets assume ,

velocity does not depend upon the density of a liquid, as

genius_generous answered 2 years ago

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