Question

the velocity of water wave depend on wavelenght density of water rho acceleration to gravity establised dimensionally the relation between this grabity?

Answer 1

Let  v = k * λ^a ρ^b g^c    v = [L] [T]⁻¹   λ = [ L]       ρ = density = [M] [L]⁻³     g = [ L] [T]⁻²
Hence   [L][T]⁻¹ = [M]^b [L]^{a-3b+c} [T]^{-2c}Comparing the dimensions:             b = 0.    c = 1/2       => a = 1/2
So   v = k √(gλ)