Viscosity (Basic Concept of Fluid Mechanics Part-3)

Viscosity: It is the resistance provided by one layer of the fluid over other layer.

We know that

shear stress = Shear force/shear area

τ = F/A

As the molecules are taken into same area 

τ↑ α F↑

If dθ/dt is large

→Flow is easy

→Resistance is less

→μ is less

If dθ/dt is less

→Flow is not easy

→Resistance is more

→μ is more

μ represents resistance to the flow, it is known as coefficient of viscosity.

If the velocity profile is linear

τ = μv/y

We know that 

τ = F/A


Above derived expression is only valid for linear profile only

Unit of viscosity μ, is Pa-s or kg/m-s

** 1 Poise = 0.1 kg/m-s

Kinematic viscosity (ν): In fluid mechanics, the term μ/ρ appears frequently & for convenience, this term is known as kinematic viscosity(v).


μ = dynamic viscosity

ρ = density.

unit of kinematic viscosity is cm²/sec or stroke.

Variation of viscosity with temperature:

In case of liquid, intermolecular distance is a small and hence cohesive force is large with rise in temperature, Cohesive forces decreases & hence resistance to the flow also decreases. Hence in case of liquids with rise in temperature viscosity decreases.

In case of gases, cohesive forces are negligible & with rise in temperature molecular disturbance ( agitation) increases. Hence there is resistance to the flow also increases i.e. In case of gases with rise in temperature viscosity increases.

Note: Viscosity varies very little with pressure but at very very high-pressure viscosity increases because at very very high-pressure movement of fluid will be difficult.

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