“…To define Π 1 , we choose v i , l p , ρ t as the 3 repeating variables and δ t as the dependent variable (6) with the power law coefficients, α = 0, β = − 1, γ = 0. Therefore, eq 6 becomes, (7) To define Π 2 , v, l p , ρ t are the 3 repeating variables and ρ p is the dependent variable (8) with power law coefficients, α = 0, β = 0, γ = − 1.Eq 8 becomes (9) Buckingham Π Theorem relates the Π as (10) Eq 10 indicates that the penetration depth should scale with the ratio of the densities. Buckingham Π analysis does not explicitly define the exponent m, merely that one dimensionless group (Π 1 ) is related to another one (Π 2 ).…”