GATE 2019 MT – Question 17
The terminal rise velocity U of a spherical solid in a liquid obeys f(U,d,W,μ,ρ)=0, where d is diameter, W apparent weight, μ dynamic viscosity and ρ liquid density. How many independent dimensionless variables are required by Buckingham’s Π theorem?
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Correct answer: (B) 2
Explanation
There are five dimensional quantities. Their dimensions involve independent M,L,T: U=LT⁻¹, d=L, W=MLT⁻², μ=ML⁻¹T⁻¹ and ρ=ML⁻³. The dimensional matrix has rank three. Buckingham’s theorem therefore gives 5−3=2 independent groups, B.