# What is Viscosity? | Definition, Formula, Units – Hydrodynamics

Viscosity Definition Physics:
The property of a fluid by virtue of which an internal frictional force acts between its different layers which opposes their relative motion is called viscosity.

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## What is Viscosity? | Definition, Formula, Units – Hydrodynamics

This internal frictional force is called viscous force.

Viscous forces are intermolecular forces acting between the molecules of different layers of liquid moving with different velocities.

Viscous Force Formula:

Viscous force (F) = -η A$$\frac{d v}{d x}$$
or
η = –$$\frac{F}{A\left(\frac{d v}{d x}\right)}$$

where,
$$\frac{d v}{d x}$$ = rate of change of velocity with distance called velocity gradient,
A = area of cross-section and
η = coefficient of viscosity.

Viscosity Units:
SI unit of η is Nsm-2 or pascal-second or decapoise.

Viscosity Dimensional Formula:
Dimensional formula is [ML-1T-1].

1. The knowledge of the coefficient of viscosity of different oils and its variation with temperature helps us to select a suitable lubricant for a given machine.

2. The cause of viscosity in liquid is due to cohesive force between liquid molecules, while in gases, it is due to diffusion.

3. Viscosity is due to transport of momentum. The value of viscosity (and compressibility) for ideal liquid is zero.

4. The viscosity of air and of some liquids is utilised for damping the moving parts of some instruments.

5. The knowledge of viscosity of some organic liquids is used in determining the molecular weight and shape of large organic moleculars like proteins and cellulose.

6. In any layer of liquid, the pulling of lower layers backwards while upper layers forward direction is known as laminar flow.

### Variation of Viscosity

1. The viscosity of liquids decreases with increase in temperature

ηt = $$\frac{\eta_{0}}{\left(1+\alpha t+\beta t^{2}\right)}$$

where,
η0 and ηt are coefficient of viscosities at 0°C and t°C, α and β are constants.

2. The viscosity of gases increases with increase in temperatures as

η ∝ $$\sqrt{T}$$

3. The viscosity of liquids increases with increase in pressure but the viscosity of water decreases with increase in pressure.

4. The viscosity of gases increases with increase of temperature because when temperature of gas increases, then rate of diffusion increases.

Hydrodynamics:
In physics, hydrodynamics of fluid dynamics explains the mechanism of fluid such as flow of liquids and gases. It has a wide range of applications such as evaluating forces and momentum on aircraft, prediction of weather, etc.