We were discussing the basic definition and significance of fluid mechanics and various properties of fluid in our previous post.

Now we will understand here the term “Viscosity” of fluid with the help of this post.

### Viscosity or Dynamic viscosity

Viscosity, also termed as dynamic viscosity, is basically defined as the resistance provided to a layer of fluid when it will move over another layer of fluid.

Let us consider two parallel plates of area A of each plate and separated by a distance y with each other as displayed in following figure. Let us consider that bottom plate is fixed and liquid is filled between both parallel plates.
Let us consider that a force F is required to move the top plate in a direction parallel with fluid flow.
When Reynold’s Number Re will be less than 2000, the flow will be considered as laminar flow and we will have one linear velocity distribution and such a parallel flow of uniform velocity gradient will be termed as Couette flow.

Force per unit area, required to move the upper plate in a direction parallel with fluid flow, will be termed as shear stress and this shear stress will be directionally proportional to fluid flow velocity and inversely proportional to gap between both plates.

Shear stress α (Fluid flow velocity/Gap between plates)
Shear stress, τ α (U/y)
Shear stress, τ = μ (U/y)

Where, μ is the constant of proportionality and this constant of proportionality will be termed as dynamic viscosity of fluid or simply viscosity of fluid.

### Understanding the viscosity in simple way

If we consider one layer of fluid of thickness y flowing over a fixed surface as displayed in following figure. Fluid which will be in contact with fixed surface will have zero velocity. As we will go away from fixed surface, fluid flow velocity will be increasing. At top most surface i.e. at a distance y from the fixed surface, velocity of fluid will be maximum.

Considering these two values of fluid velocity i.e. velocity at fixed surface and velocity at top most surface, we will draw the velocity profile as displayed in following figure.
Let us consider a small layer of fluid of thickness dy as displayed in above figure. Velocity of fluid will be u at bottom of small layer of thickness dy. Velocity of fluid will be u + du at top of small layer of thickness dy.

In simple, we can say that fluid layers will have different velocity according to its distance from the fixed surface. Hence, there will be possibilities of shearing action when fluid layers flowing over each other with different velocity.

Shear stress will be directionally proportional to the velocity gradient and therefore we will have following equation as mentioned here.

Shear stress α (du/dy)
Shear stress, τ = μ (du/dy)

Where, μ is the constant of proportionality and this constant of proportionality will be termed as dynamic viscosity of fluid or simply viscosity of fluid.

Above expression was given by Newton through experiment and therefore above expression is also termed as Newton’s law of viscosity.

### Unit of viscosity

Unit of viscosity in S.I system will be N.s/m2 or Pa.s
Viscosity is also provided with unit Poise or Centipoise.
1 Poise = 100 Centipoise = 0.1 N-s/m2

Viscosity is also given in terms of centistokes in various engineering applications such as hydraulic oil viscosity will be provided in terms of centistokes or cSt.

### Viscosity Vs temperature

Viscosity will be increased with increase in temperature in case of gases. While in case of liquid, viscosity will be decreased with increase in temperature. Relation between viscosity and temperature is reversed for liquid and gas.

Let us see here the curve indicating the change in viscosity with temperature for liquid and gas.

We will now discuss the basic concept of kinematic viscosity in the category of fluid mechanics in our next post.
Do you have suggestions? Please write in comment box.

### Reference:

Fluid mechanics by Y. Nakayama and R F Boucher