Question

A dimensionless group formed with the variables ρ (density), ω (angular velocity), μ (dynamic viscosity) and D (characteristic diameter) is
1. ρμD/ω
2. ρωμ/D²
3. ωμD²/ρ
4. μ/ρωD²

Answer 1

Correct Answer - Option 4 : μ/ρωD²

Explanation:

Dimensions:

Density (ρ) = [ML^-3]

Angular velocity (ω) = [T^-1]

Dynamic viscosity (μ) = [ML^-1T^-1]

Characterstic diameter (D) = [L]

By Buckingham π - method:

π = [ρ^a, ω^b, D^c] μ 

Where,

π = dimensionless number

π = [ML^-3]^a [T^-1]^b [L]^c [ML^-1T^-1]

Equating the dimention of both side;

a = -1

b = -1

c = -2

μ/ρωD² is the dimensionless term.