# Units of Viscosity

Last Updated: April 24, 2024

## Units of Viscosity

What is the Unit of Viscosity?

The unit of viscosity is the pascal-second (Pa·s) in the International System of Units (SI). Viscosity refers to the resistance of a fluid to flow, and it is a crucial property in fluid dynamics.

Viscosity (η) can be defined by the relationship between the shear stress (τ) and the shear rate (γ˙​​) with in a fluid, expressed by Newton’s law of viscosity:

τ=η × γ˙​

Where:
τ is the shear stress, measured in pascals (Pa).
η is the dynamic viscosity, measured in pascal-seconds (Pa·s).
γ˙​ is the shear rate, measured in reciprocal seconds (s⁻¹).

## SI Unit of Viscosity

The SI unit of viscosity is the pascal-second (Pa·s), also commonly expressed as the kilogram per meter per second (kg/(m·s)). Viscosity is a measure of a fluid’s resistance to flow. It describes the internal friction within a fluid as it flows.

Viscosity is often denoted by the symbol η (eta). It can be calculated using the formula:

η=F⋅d/A⋅v

Where:
η (eta) is the viscosity (in pascal-seconds, Pa·s)
F is the force (in newtons, N) applied perpendicular to the direction of flow
d is the distance (in meters, m) the fluid layer moves in the direction of the force
A is the area (in square meters, m²) through which the force is applied
v is the velocity (in meters per second, m/s) of the fluid

## CGS Unit of Viscosity

In the CGS (centimeter-gram-second) system, the unit of viscosity is the poise (P). Viscosity measures a fluid’s resistance to flow, with higher viscosity indicating greater resistance. The formula to calculate viscosity in CGS units is:

Viscosity (Poise) = Force (dyn)/Area (cm²) × Velocity (cm/s)

Where:

Force is measured in dynes (dyn), which is the CGS unit of force.
Area is measured in square centimeters (cm²).
Velocity is measured in centimeters per second (cm/s).

## Conversion of Viscosity Units

### Poise (P) to Pascal-seconds (Pa·s)

1 Poise (P) = 0.1 Pascal-seconds (Pa·s)

One poise (P) is equivalent to 0.1 pascal-seconds (Pa·s), serving as a conversion factor between viscosity units in the CGS and SI systems.

### Pascal-seconds (Pa·s) to Poise

1 Pascal-seconds (Pa·s) = 10 Poise (p)

One pascal-second (Pa·s) corresponds to 10 poise (P), facilitating the conversion of viscosity measurements from the SI system to the CGS system.

### Centipoise (cP) to Pascal-seconds (Pa·s)

1 Centipoise (cP) = 0.001 Pascal-seconds (Pa·s)

One centipoise (cP) is equal to 0.001 pascal-seconds (Pa·s), providing a conversion factor for viscosity measurements between smaller units in the SI system.

### Pascal-seconds (Pa·s) to Centipoise (cP)

1 Pascal-seconds (Pa·s) = 1000 Centipoise (cP)

One pascal-second (Pa·s) corresponds to 1000 centipoise (cP), facilitating viscosity conversions from the SI system to smaller units.

### Poise (P) to Centipoise (cP)

1 Poise(P) = 100 Centipoise (cP)

One poise (P) equals 100 centipoise (cP), facilitating viscosity conversions between CGS and SI units, particularly for larger values in the centipoise scale.

### Centipoise (cP) to Poise (p)

1 Centipoise (cP) = 0.01 Poise (p)

One centipoise (cP) is equal to 0.01 poise (p). This conversion factor simplifies transitioning between centipoise and poise, commonly used in measuring viscosity of fluids.

## Why is viscosity important?

Viscosity is crucial in various fields such as engineering, physics, and chemistry. It affects the behavior of fluids in processes like flow, mixing, and lubrication.

## How is viscosity measured?

Viscosity is typically measured using viscometers, instruments designed to determine the resistance of a fluid to flow under specific conditions.

## What are some real-world applications of viscosity?

Viscosity is applied in various industries, including automotive (engine oils), food and beverage (sauces and syrups), pharmaceutical (drug formulations), and petroleum (drilling fluids).

## Can viscosity change with time?

Yes, viscosity can change with time due to factors such as temperature variations, chemical reactions, and the aging of fluids. This phenomenon is known as viscosity variation or rheological behavior.

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