Q1: Which of the following is a dimensionless parameter ?

ANS:D - None of these

The dimensionless parameter among the options provided is kinematic viscosity.

Explanation:

1. Dimensionless Parameters:
   • Dimensionless parameters are quantities that do not have units and are used to characterize physical phenomena or describe relationships between variables in fluid mechanics and other fields.
   • Examples of dimensionless parameters include Reynolds number ( ReReRe ), Mach number ( MaMaMa ), Froude number ( FrFrFr ), and Schmidt number ( ScScSc ).
2. Options Analysis:
   • Angular velocity: Angular velocity ( ω\omegaω ) is measured in radians per second (rad/s) and has dimensions of T−1\text{T}^{-1}T−1 (inverse of time). It is not dimensionless.
   • Specific weight: Specific weight (or unit weight) is the weight per unit volume of a substance and is measured in units of force per unit volume (e.g., N/m³ or lb/ft³). It is not dimensionless.
   • Kinematic viscosity: Kinematic viscosity ( ν\nuν ) is defined as the ratio of dynamic viscosity ( μ\muμ ) to density ( ρ\rhoρ ) of the fluid, i.e., ν=μρ\nu = \frac{\mu}{\rho}ν=ρμ​ Kinematic viscosity is measured in units of L2T−1\text{L}^2 \text{T}^{-1}L2T−1 (square length per time) and is dimensionless.
3. Conclusion:
   • Among the options provided, kinematic viscosity is the dimensionless parameter. It represents the ratio of two physical properties (dynamic viscosity and density) that have different dimensions, resulting in a dimensionless quantity ν\nuν.