Dynamic Viscosity vs. Kinematic Viscosity: Key Differences

This article explores the concepts of dynamic viscosity and kinematic viscosity, highlighting their differences and relationships.

What is Viscosity?

At its core, viscosity is a fluid’s inherent property that resists flow. Think of it as the “thickness” or “stickiness” of a liquid or gas. Here are some key points to remember about viscosity:

• Temperature’s Impact: The viscosity of liquids generally decreases as temperature rises. Imagine how honey flows more easily when warmed up. Conversely, the viscosity of gases tends to increase with higher temperatures.
• Resistance to Flow: Viscosity quantifies a fluid’s internal resistance to flow at a specific temperature.
• Measurement Methods: There are primarily two methods to measure a fluid’s viscosity: dynamic viscosity and kinematic viscosity.

Dynamic Viscosity (μ)

Dynamic viscosity, often represented by the Greek letter μ (mu), describes a fluid’s resistance to flow under an applied force.

• Resistance to Deformation: It can also be understood as a fluid’s resistance to deformation when subjected to a force. Think about how a thick syrup resists being stirred compared to water.

• Formula: Dynamic viscosity is calculated as:

  Dynamic Viscosity (μ) = Shear Stress / Velocity Gradient

• Units:

  • The SI unit for dynamic viscosity is Newton-second per square meter (N·s/m²).
  • A common unit used is Poise (P) or Centipoise (cP).
  • Conversion: 1 cP = 1 mPa·s (millipascal-second)

• Example: Water at 20°C has a dynamic viscosity of approximately 1.0020 cP, or 0.001002 kg/(m·s).

Kinematic Viscosity (ν)

Kinematic viscosity, denoted by the Greek letter ν (nu), also relates to a fluid’s resistance to flow but factors in the fluid’s density.

• Measurement: It’s often measured by observing the time it takes for a fluid sample to flow through a small opening (orifice) in a capillary tube under the influence of gravity.

• Time Conversion: The measured time is then converted to kinematic viscosity.

• Units:

  • The cgs unit is the stokes (St).
  • It’s also commonly expressed in Centistokes (cSt) or square meters per second (m²/s).
  • Conversions:
  • 1 St = 1 cm²/s = 10⁻⁴ m²/s
  • 1 cSt = 1 mm²/s

• Example: Water at 20°C has a kinematic viscosity of approximately 1 cSt.

• Momentum Diffusivity: Kinematic viscosity is also referred to as the diffusivity of momentum within the fluid.

The Relationship Between Dynamic and Kinematic Viscosity

Both dynamic and kinematic viscosity are related and can be converted using the fluid’s density:

• Formula:

  Kinematic Viscosity (ν) = Dynamic Viscosity (μ) / Fluid Density (ρ)

• Conversion: 1 SI unit of kinematic viscosity = 10⁴ stokes

In essence, dynamic viscosity focuses solely on the fluid’s resistance to flow due to internal friction, while kinematic viscosity also considers how that resistance is affected by the fluid’s inertia (density). This distinction is why both concepts are crucial in various fields like fluid mechanics and materials science.