State the standard units for kinematic viscosity in the SI system.
The correct answer and explanation is :
Correct Answer:
The standard unit for kinematic viscosity in the SI (International System of Units) is square meter per second (m²/s).
Explanation (Approx. 300 words):
Kinematic viscosity is a physical property of fluids that describes the fluid’s internal resistance to flow under the influence of gravity. It is defined as the ratio of dynamic viscosity (μ) to density (ρ) of the fluid:
[
\nu = \frac{\mu}{\rho}
]
Where:
- ( \nu ) is the kinematic viscosity,
- ( \mu ) is the dynamic viscosity (in pascal-seconds, Pa·s),
- ( \rho ) is the density (in kilograms per cubic meter, kg/m³).
Let’s derive the SI unit:
- Dynamic viscosity (μ) has the unit Pa·s, which is equivalent to:
[
\text{Pa·s} = \frac{\text{N·s}}{\text{m}^2} = \frac{\text{kg·m/s}^2 \cdot \text{s}}{\text{m}^2} = \frac{\text{kg}}{\text{m·s}}
] - Density (ρ) has the unit kg/m³
Therefore, kinematic viscosity (ν) becomes:
[
\nu = \frac{\mu}{\rho} = \frac{\frac{\text{kg}}{\text{m·s}}}{\frac{\text{kg}}{\text{m}^3}} = \frac{\text{m}^2}{\text{s}}
]
So, the standard SI unit of kinematic viscosity is m²/s (square meters per second).
In practical applications, especially in fluid dynamics and engineering, a smaller non-SI unit called the Stokes (St) is often used:
- ( 1 \, \text{St} = 10^{-4} \, \text{m}^2/\text{s} )
- Commonly used subunit: centistokes (cSt), where ( 1 \, \text{cSt} = 10^{-6} \, \text{m}^2/\text{s} )
Understanding the unit of kinematic viscosity is essential in analyzing fluid behavior in systems like pipelines, lubrication, and air or water flow. It helps engineers and scientists determine how fluids will behave when moving through or around objects.
