Table of Contents

## Coefficient of Viscosity

Coefficient of Viscosity

**Definition:**

The coefficient of viscosity, also known as dynamic viscosity or simply viscosity, is a property of fluids that measures their resistance to flow. It quantifies the internal friction or stickiness of a fluid as it flows, particularly in response to applied shear stress. The coefficient of viscosity is denoted by the symbol η (eta) and is measured in units of pascal-seconds (Pa·s) or poise (P).

Viscosity arises due to the interactions between the molecules or particles within a fluid. In fluids with high viscosity, the molecules or particles are strongly bonded or closely packed, leading to greater resistance to flow. In contrast, fluids with low viscosity have weaker intermolecular forces or looser particle arrangements, resulting in easier flow.

### SI Unit of Coefficient of Viscosity

- Every liquid has its specific viscosity and the measure of this attribute is called the coefficient of viscosity.
- The coefficient of viscosity η is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit area A.
- The SI unit of η is Newton-second per square meter (Ns. m
^{-2}) or - Pascal-seconds (Pa .s)
- Hence the coefficient of viscosity is a measure of the resistance of the fluid to deformation at a given rate due to internal friction.

### Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient of the fluid is called the coefficient of viscosity η.

Hence the coefficient of viscosity is given by,

η = F . d / A .ⅴ

Where F is the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

- ⅴ is the velocity.
- A is the area
- d is the distance between the two layers of liquid skidding over each other.

The difference in the stream of velocity between the adjacent layers of the fluid is measured in the velocity gradient.

The viscosity of gas is less than the liquid viscosity.

A coefficient of viscosity is a measure of the resistance of a fluid to flow. The higher the coefficient of viscosity, the slower the fluid will flow. Viscosity is determined by the thickness of the fluid and the amount of force required to move it. Liquids with a higher coefficient of viscosity will have a higher resistance to flow and will be thicker than liquids with a lower coefficient of viscosity.

**Examples Coefficient of Viscosity:**

Here are a few examples of the coefficient of viscosity for different fluids:

- Water: The coefficient of viscosity for water at 20°C is approximately 0.001 Pa·s (pascal-seconds) or 1 centipoise (cP). This relatively low viscosity allows water to flow easily and is one of the reasons why it is commonly used as a benchmark for viscosity comparisons.
- Honey: Honey has a significantly higher viscosity compared to water. Its coefficient of viscosity can range from 10 to 20 Pa·s or higher, depending on factors such as temperature and the type of honey. This high viscosity gives honey its thick, slow-flowing characteristic.
- Motor Oil: Motor oil is designed to have a higher viscosity compared to water to ensure effective lubrication of engine components. The viscosity of motor oil typically falls within a wide range, from 20 to 100 centistokes (cSt) or higher. Higher viscosity oils, such as those used in heavy-duty applications, have higher coefficients of viscosity.
- Air: Although gases are typically much less viscous than liquids, they still have a coefficient of viscosity. However, the viscosity of gases is considerably lower than that of liquids. The coefficient of viscosity for air at room temperature and atmospheric pressure is approximately 0.000018 Pa·s or 0.018 millipoise (mP). This low viscosity allows air to flow easily.
- Molten Glass: Molten glass has a relatively high viscosity compared to many other liquids. The coefficient of viscosity for molten glass can vary widely depending on its composition and temperature. It can range from around 10^2 to 10^8 Pa·s, indicating a high resistance to flow.

These examples demonstrate the range of viscosities observed in different fluids. The coefficient of viscosity determines how easily or difficultly a fluid flows under the influence of external forces, and it plays a significant role in numerous industrial, scientific, and everyday applications.