Stoke’s Law and Application of Viscosity

We have studied various states of matter like solids, liquids, gases, and plasma. In solids, molecules are tightly packed, and in liquids, molecules are less loosely arranged than the solids. Solids have fixed volume and shape. Liquids have fixed volume but no fixed shape, and it takes the shape of the container which holds them. The density of the liquid is constant. These are some of the properties of liquid we have studied. One of the properties that differentiate one liquid from another is viscosity. Viscosity denotes opposition to flow. Let us now discuss viscosity in detail and also one of the key laws – Stoke’s law.

Even though rainwater falls from greater height from the clouds, it does not hurt or harm us. This concept is explained through Stoke’s Law. This law deals with the settling velocities of the small spherical particles in a fluid medium. Let us know more about Stoke’s law.

What is Viscosity?

Viscosity is the most commonly heard term in our daily life. Have you observed some liquids like honey, water, oil, and alcohol? Other than the composition of these liquids, their flow is different from each other. Honey flows slower than water. Have you thought about what makes honey flow slower than water and oil? Viscosity is the reason behind this.

Viscosity is defined as the measure of a fluid’s resistance to flow. Viscosity is the resistance offered by the liquid to objects passing through it or the fluid’s thickness. Here the thicker liquids like honey and water are classified as highly viscous liquids. Water, gasoline, and glycerol are classified as low viscous liquids. Viscosity arises when there is relative motion between layers of the fluid.

The SI unit of viscosity is poiseuille (PI). Other units are Newton-second per square metre (N s m-2) or pascal-second (Pa s.) The dimensional formula of viscosity is [ML-1T-1]. There are many ways to measure viscosity, and viscometer is the device used to measure the viscosity of a given liquid.

Viscosity plays a major factor in finding the forces that are needed to control when fluids are used in lubrication and transported in pipelines. Viscosity aids in controlling the liquid flow while surface coating, spraying, and injection moulding.

There are two ways to measure the fluid’s viscosity:

• Dynamic Viscosity (Absolute Viscosity)
• Kinematic Viscosity

Force of Viscosity

The drag force which opposes the fall of small spherical particles through a fluid medium is explained in Stoke’s law. This law is mainly used to find the settling of sediment in freshwater and to measure the viscosity of fluids.

This law was first put forth in 1851 by the British scientist George G. Stokes. He explained Stoke’s law equation that explains the viscous drag force. The force that opposes a sphere moving through a fluid that is viscous is proportional to the radius of the sphere, the velocity, and the fluid’s viscosity. Stoke’s law equation is given as F = 6πηrv. Where r is the sphere radius, η is the fluid viscosity, and v is the sphere’s velocity.

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