Question

The kinematic viscosity is the

• A. ratio of absolute viscosity to the density of the liquid
• B. ratio of density of the liquid to the absolute viscosity
• C. product of absolute viscosity and density of the liquid
• D. product of absolute viscosity and mass of the liquid

Hint:

To remember the units and formulas:
$\text{Kinematic Viscosity } (\nu) = \frac{\text{Dynamic Viscosity } (\mu)}{\text{Density } (\rho)}$.
Dimensional formula: $[\nu] = [L^2 T^{-1}]$. Units are $\text{m}^2/\text{s}$ or Stokes.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the mathematical definition of kinematic viscosity ($\nu$), which is a fundamental property describing a fluid's resistance to shear flow under the influence of gravity.

Step 2: Key Formula or Approach:

• Kinematic viscosity ($\nu$) is defined as the ratio of dynamic (absolute) viscosity ($\mu$) to the fluid density ($\rho$): \[ \nu = \frac{\mu}{\rho} \]
• The units of kinematic viscosity in the SI system are $\text{m}^2/\text{s}$, and in the CGS system, the unit is Stokes ($\text{cm}^2/\text{s}$).

Step 3: Detailed Explanation:

• Dynamic viscosity ($\mu$) represents the internal friction or force required to deform a fluid at a given rate.

• Density ($\rho$) represents the mass per unit volume of the fluid.

• When a fluid flows under gravitational forces, its inertia (represented by density) resists acceleration, while its viscous forces resist shear.

• Kinematic viscosity combines these two effects. It represents the rate of diffusion of momentum through the fluid.

• Comparing the options:
Option (A) accurately states that kinematic viscosity is the ratio of absolute viscosity to density.

Step 4: Final Answer:
Kinematic viscosity is the ratio of absolute viscosity to the density of the liquid.