Co-efficient of Viscosity of viscous liquid by measuring terminal velocity

Viscosity is a physical term that defines the resistance of a liquid or gas to flow or to be in motion. The term was first coined by French physicist Jean Leonard Marie Poiseuille in 1929. Lower the viscosity, more is the flow rate of the liquid/gas. The greater the viscosity, the lower will be the flow rate of the liquid/gas. To understand, consider the example of water, which has a very low viscosity. On the other hand, consider the example of molasses, which has high viscosity.

To understand the concept of viscosity, knowledge of some important terms is necessary: 

• Shear stress: It is the amount of force that is required to move one layer of fluid onto another, in per unit area.
• Shear rate: The measure of the amount of change in speed of movement of intermediate layers concerning each other.
• Newtonian fluids: The fluids whose viscosity remains constant at a given temperature and shear stress irrespective of the shear rate. For example, water and honey.
• Non-Newtonian fluids: Fluids whose viscosities change, depending upon the change in shear stress are called Non-Newtonian fluids.
• Types of Non-Newtonian fluids: Rheopectic, dilatant, plastic, pseudoplastic, thixotropic are five types of Non-Newtonian fluids. However, each requires different types of methods to measure their viscosities.

Viscosity measurement:

Viscosity represents the opposition to flow. The opposite of viscosity is called “fluidity“. It can be assumed that viscosity is a result of internal frictions between the fluid. It is important to measure the viscosity of fluids that are used for lubrication purposes to determine the forces that must be required to overcome the internal friction. Also, to manufacture spray, surface coating, etc., it is necessary to determine the viscosity. For example, if the toothpaste manufacturer does not have enough knowledge of the viscosity of toothpaste, toothpaste will either pump out too much or will not even come out.

The shearing stress is directly proportional to the rate of deformation, also called as shearing rate, for most of the fluids.

Issac Newton was the first to formulate the mathematical description of viscosity.

Coefficient of Viscosity Formula: 

The coefficient of viscosity in mathematical terms can be represented as: 

η = F . d / A . v

where,

F = is the amount of force required to maintain velocity gradient in between two consecutive layers of liquid per unit area.

A = area

d = distance between two consecutive layers of liquid present over each other

v = velocity

Generally, the viscosity of gas is less than that of liquid.

a. Terminal velocity and its formula

The maximum velocity attained by any object when it falls on a liquid is known as its terminal velocity. Terminal velocity is observed when the sum of buoyancy and drag force of an object is equal to the gravitational force.

b. Formula for terminal velocity

The formula for terminal velocity can be written as:

v = 2 r² (ρ−σ) g / 9η

where r = radius of the object

v = terminal velocity of the object

g = gravitational force

ρ = density of the object

σ = density of liquid and

η = coefficient of viscosity

 Units of coefficient of viscosity

• SI Unit: The Si unit of the coefficient of viscosity “η” is Ns.m-2 or Pa.s, that is, Newton-second per square meter or Pascal-seconds.
• CGS Unit: The centimeter-gram-second unit of the coefficient of viscosity “η” is Poise, or we can also say dyne-sec / cm2.
• 1 poise = 0.1 Pa.s
• MKS Unit: The meter-kilogram-second unit of the coefficient of viscosity “η” is kg m-1s-1

Dimension of Coefficient of Viscosity:

The formula of coefficient of viscosity is written as

η = F . d / A . v

   = M L T-2. L / (L². L T-1)

after solving we get, 

η = M L-1 T-1 

which is equal to kg m-1s-1

 Viscosity Examples :

1. In the food industry: Food production involves various steps in processing where it has to be passed out from various pipelines. So measurement of viscosity helps in determining how much time is required for the movement of product from long pipes, how much time it will take to become dry, or the time required by the product to set. This increases the efficiency of the product and its cost-effectiveness.
2. In adhesives: It is very necessary to determine the viscosity of adhesives as if an adhesive will have high viscosity, it will flow slowly and vice-versa. Adhesives having low viscosity will flow more readily than required. A high-viscosity adhesive is preferred, mostly.
3. In the petroleum industry: Viscosity measurement here is used to determine the design of the elements in the construction of pipelines and to measure the effectiveness of lubricating oil.
4. In the cosmetics industry: In the cosmetics industry, the viscosity of a product is determined to know the feel and flow of the cosmetic product.
5. In concrete: Here, the measurement of viscosity provides an idea about the pumping behavior of a concrete mix. 

Conclusion:

Viscosity is simply defined as the resistance to the flow of a fluid.

Viscosity = shear stress/shear rate

Shear stress is the amount of force required to move one layer of fluid and shear rate is the measure of change in speed of movement of intermediate layers.

Issac Newton was the first to discover the formula of viscosity. He assumed that the viscosity of fluid remains constant regardless of shear rate at a given temperature and shear stress. The fluids that behave as said by Newton are referred to as Newtonian fluids, whereas fluids whose viscosity changes concerning shear rate are referred to as Non-Newtonian fluids.