Understanding Newton’s Law of Viscosity

Viscosity is defined as the ability of a fluid or solid to resist the change in its shape and structure concerning stress or force from the adjacent layer; in other words, it is the opposite of fluidity. 

Viscosity is divided into two types: dynamic viscosity and kinematic viscosity. The SI unit of viscosity is pascal-second or poiseuille. The viscosity of any substance depends on the temperature and the state of the matter. For liquids, viscosity decreases with an increase in temperature, and for gases, viscosity increases with an increase in temperature.

Newton’s Law of Viscosity

Newton’s law of viscosity tells us about the relationship between the shear stress and velocity gradient of fluids. Shear stress refers to the amount of force acting per unit area on a particular fluid parallel to the surface of the fluid. The velocity gradient is defined as the velocity difference between the layers of fluid that are adjacent to each other.

Newton’s law of viscosity says that the shear stress is directly proportional to the velocity gradient.

The equation of newton’s law of viscosity is τ = μ du/dy

Where τ= shear stress, μ= viscosity, and du/dy= velocity gradient.

Newton’s Law of Viscosity Derivation

Shear stress (τ ) = Force(F)/ Area(A)

Velocity gradient = du/dy. Here, du is the velocity difference, and dy is the distance between the layers.

According to Newton’s law of viscosity, shear stress is proportional to velocity gradient.

τ ∝ du/dy

∴ τ= μ du/dy 

Here, μ is viscosity.

Types of Viscosity

Viscosity is divided into two types: dynamic viscosity and kinematic viscosity.

• Dynamic viscosity – A way to measure a fluid’s resistance to its flow under the influence of any external force or stress. In other words, it is defined as the force needed by a fluid to overcome its internal molecular friction so that it can flow. In simple words, it is a fluid’s viscosity that is referred to as dynamic viscosity. The SI unit of dynamic viscosity (μ) is the Pascal-second. Its formula is similar to that of viscosity.

The formula is τ= μ du/dy

Where τ = shear stress, μ = viscosity, and du/dy = velocity gradient.

The dynamic viscosity of a fluid is measured using a rotational viscometer. It rotates a probe in the liquid sample, and the viscosity is determined by measuring the force used to turn the probe.

• Kinematic viscosity – It is the measure of a fluid’s internal resistance to flow under gravity. It is determined by measuring the time required for a fixed volume of fluid to flow across a known distance under the influence of gravity through a capillary action within a calibrated viscometer in a fixed temperature range. In simpler words, kinematic viscosity is the measure of any fluid’s internal resistance to the flow across the cross-section area per unit of time.

The formula for kinematic viscosity is v=μ/ρ

Here, v = kinematic viscosity

μ = dynamic viscosity

ρ = density

Significance of Newton’s Law of Viscosity

Newton’s law of viscosity tells us about the relation between shear stress and the velocity gradient between the layers of the fluid.

It also helps to find the shear stresses at different positions in the moving fluid.

Types of Fluids

According to Newton’s law of viscosity, fluids can be divided into two categories: Newtonian fluids and non-newtonian fluids.

Newtonian fluids are those fluids that work according to Newton’s law of viscosity. In such fluids, the viscosity μ remains constant even under the influence of shear stress. 

Therefore, for viscosity and shear stress, the graph is linear. 

Some examples of Newtonian fluids are water, alcohol, mineral oil, and many more.

Non-newtonian fluids are those fluids that do not obey Newton’s law of viscosity. In such fluids, viscosity μ changes with shear stress. Examples of such fluids are toothpaste, cosmetics, paints, etc.

Conclusion

Viscosity is the ability of a fluid to resist the change in its shape concerning stress or force from the adjacent layer. Viscosity is divided into two types: dynamic viscosity and kinematic viscosity. The SI unit of viscosity is pascal-second. Newton’s law of viscosity tells us about the relationship between the shear stress and velocity gradient of fluids. According to Newton’s law of viscosity, fluids can be divided into two categories: newtonian fluids and non-newtonian fluids.