Short Answer:

Kinematic viscosity is defined as the ratio of dynamic viscosity to the density of a fluid. It represents the fluid’s resistance to flow under the influence of gravity, without considering any external force. It helps determine how easily a fluid moves or spreads in space.

In simple terms, kinematic viscosity measures how thick or thin a fluid is when it flows naturally. It is denoted by the symbol ν (nu) and its SI unit is m²/s. For example, the kinematic viscosity of water at 20°C is approximately 1.003 × 10⁻⁶ m²/s.

Detailed Explanation :

Kinematic Viscosity

Kinematic viscosity is a fundamental property of fluids that describes how easily a fluid can flow due to gravity, without being affected by external pressure or force. It is defined as the ratio between dynamic viscosity (μ) and density (ρ) of the fluid.

Mathematically, it is expressed as:

Where,

ν (nu) = Kinematic viscosity (m²/s)
μ (mu) = Dynamic viscosity (N·s/m² or Pa·s)
ρ (rho) = Density of the fluid (kg/m³)

Kinematic viscosity gives a measure of the fluid’s internal resistance to flow under its own weight. It plays a very important role in fluid mechanics and engineering applications such as lubrication, flow measurement, and hydraulic design.

Concept of Kinematic Viscosity

When a fluid flows, the internal friction or resistance between its layers determines how easily it can move. The dynamic viscosity (μ) measures this internal resistance directly. However, since the density of the fluid also influences how it flows, kinematic viscosity gives a more complete picture by including the effect of density.

Kinematic viscosity thus measures how fast momentum is transferred through the fluid compared to its mass. It is particularly useful when studying the behavior of fluids moving under gravity, such as in open channels, lubrication, and air or water flow analysis.

If two fluids have the same dynamic viscosity but different densities, the one with a higher density will have a lower kinematic viscosity. This means that denser fluids move more easily under gravity than lighter ones with the same dynamic viscosity.

Units of Kinematic Viscosity

The SI unit of kinematic viscosity is m²/s.
In the CGS system, it is measured in stokes (St), where:

A smaller unit, the centistoke (cSt), is commonly used in industries, and:

Example:
If a fluid has a dynamic viscosity (μ) of 0.001 Pa·s and a density (ρ) of 1000 kg/m³,

This value represents the kinematic viscosity of water at 20°C.

Factors Affecting Kinematic Viscosity

Temperature:
Temperature has the greatest effect on kinematic viscosity.
- For liquids, as temperature increases, viscosity decreases because molecules move more freely, reducing internal friction.
- For gases, viscosity increases with temperature since faster-moving molecules collide more often and transfer momentum more efficiently.
Density:
Since kinematic viscosity is inversely proportional to density, fluids with higher density tend to have lower kinematic viscosity, provided their dynamic viscosity remains constant.
Pressure:
The effect of pressure is usually small, but at very high pressures, viscosity may increase slightly, particularly in liquids.
Nature of Fluid:
The molecular structure and chemical composition of a fluid also influence its kinematic viscosity. Fluids with long-chain molecules (like oils) have higher viscosity than simple fluids (like water or air).

Measurement of Kinematic Viscosity

Kinematic viscosity can be measured using instruments that determine the time taken by a fluid to flow through a narrow tube or orifice under the influence of gravity. The most commonly used instruments are:

Capillary Tube (Ostwald) Viscometer:
This device consists of a U-shaped glass tube with two marks. The time taken for a specific volume of fluid to flow between these marks under gravity is measured. The kinematic viscosity is then calculated based on the flow time and calibration constant of the instrument.
Saybolt Viscometer:
Commonly used for oils, this instrument measures the time (in seconds) required for a fixed volume of liquid to flow through a standard orifice at a specific temperature. The result is expressed in Saybolt Seconds Universal (SSU).
Redwood Viscometer:
This instrument works similarly to the Saybolt viscometer and is used to measure the viscosity of lubricating oils.

These instruments help in determining viscosity values accurately for industrial and research purposes.

Importance of Kinematic Viscosity in Engineering

Kinematic viscosity is extremely important in various engineering fields, particularly in fluid mechanics, lubrication, and thermal systems. Some of its key applications are:

Lubrication:
Kinematic viscosity determines how effectively a lubricant can form a film between moving surfaces. A lubricant with too high viscosity causes frictional losses, while one with too low viscosity cannot maintain a protective layer.
Hydraulic Systems:
In hydraulic systems like pumps, valves, and actuators, fluid viscosity affects energy transfer, flow rate, and efficiency. Proper viscosity ensures smooth operation and minimizes wear.
Flow Analysis:
The flow behavior of fluids (laminar or turbulent) is analyzed using the Reynolds number, which depends on kinematic viscosity. It helps in predicting flow patterns and energy losses in pipes and channels.
Heat Transfer and Cooling:
Kinematic viscosity affects heat transfer in fluids. Lower viscosity allows better convection and improves cooling in systems such as engines and heat exchangers.
Design of Pipes and Channels:
Engineers use kinematic viscosity in calculating the friction factor, head losses, and velocity profiles of fluids in pipes and ducts.

Examples of Kinematic Viscosity Values

Water (20°C): 1.003 × 10⁻⁶ m²/s
Air (20°C): 1.48 × 10⁻⁵ m²/s
Mercury: 1.12 × 10⁻⁷ m²/s
Engine Oil (40°C): 1.00 × 10⁻⁴ m²/s
Glycerin (20°C): 1.00 × 10⁻³ m²/s

These examples show that thicker fluids like oil and glycerin have higher kinematic viscosity than lighter fluids like water or air.

Relation Between Dynamic and Kinematic Viscosity

Dynamic viscosity (μ) and kinematic viscosity (ν) are directly related by the density (ρ) of the fluid, given by:

This means if the density of the fluid increases, its kinematic viscosity decreases for a given dynamic viscosity. Hence, both quantities are important in understanding the flow characteristics of fluids.

Conclusion

In conclusion, kinematic viscosity is the ratio of dynamic viscosity to the density of a fluid and measures the fluid’s resistance to flow under gravity. It helps in understanding how easily a fluid can move or spread without the influence of external forces. Kinematic viscosity plays a vital role in engineering applications such as lubrication, fluid flow design, and hydraulic systems. By knowing kinematic viscosity, engineers can design efficient systems that ensure smooth, safe, and effective fluid movement.