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# Coefficient of Viscosity Formula, Examples and Units - Viscosity Measurement & Viscosity of Water Units

## Definition

Viscosity is the resistance of a fluid to flow under an applied force. Under streamline flow conditions, the ratio of the tangential frictional force acts per unit area to the velocity gradient. Liquids with high velocity move slower than low viscous solutions. High viscous solutions have a lower spread than low viscous liquids. Low viscous liquids like water, petrol, lemonade, etc., spread more than higher viscous liquids like glycerine, oil, and honey.

The food industry is one of the major industries where viscosity measurements are used to improve the overall cost-effectiveness and maximize production efficiency. Besides the food industry, viscosity is significantly used in other industries such as adhesives, petroleum, concrete, and cosmetics.

## Examples

• In our daily life, we prefer the products that are more viscous, like dishwashers or hand wash, because the more viscous the fluid is, the more effective it is in washing the utensils and our hands.
• Another example we see in our daily life is oil. If a drop of oil falls on the surface, the drop sticks in a small spherical shape. This is due to the viscous force present within the oil.

## Viscosity measurement

Viscosity is measured in terms of the coefficient of viscosity. It does not change for a particular liquid and depends upon the nature of the liquid. Viscosity is measured through Poiseuille's apparatus. In this, the liquid is allowed to flow at different pressures. The resistance is measured, which denotes the coefficient of viscosity.

The coefficient of viscosity decreases with an increase in temperature in liquids. When the liquid is heated, the particles gain entropy. As a result, the kinetic energy generated weakens the intermolecular forces between the particles, leading to the separation between the molecules, decreasing the liquid's thickness as viscosity is the state of fluid being thick and sticky. Therefore, with the increase in temperature, the bonds in liquid are deliberate, due to which the coefficient of viscosity decreases. This condition is inverse in gases of gases. The coefficient of viscosity increases with an increase in temperature.

## Coefficient of viscosity formula

Viscosity = shear stress / shear rate

The force of friction between two layers of a liquid is directly proportional to the velocity gradient-
f ∝ A (dv/dt)
f = η A (dv/dt)
where, η = coefficient of viscosity
A = cross-sectional area through which the liquid flows

When A = 1cm2, dv/dt = 1, then f = η.
This means the viscosity coefficient is the force of friction required to maintain the velocity gradient between two layers in a unit cross-sectional area. η is measured in Poise or centipoise. 1 centipoise is equal to 1mPa (milli Pascal second).

## Units of coefficient of viscosity

SI Unit of Coefficient of Viscosity
The SI unit of η is Newton-second per square meter (Ns. m-2) or
Pascal-seconds (Pa.s)

The centimeter-gram-second or CGS unit of coefficient of viscosity, η, is
dyne-sec/ cm2, equal to Poise.
Where one Poise is exactly 0.1 Pa·s.
The meter-kilogram-second or MKS unit is: Kilogram per meter per second or
Kg m-1 s - 1.

Since, the formula for coefficient of viscosity is given by,
η = F . d/ A .ⅴ = MLT−2MLT−2 . LL / L2 L2 . LT−1LT−1
Simplifying this, we get,

Dimensional formula for η = ML−1T−1ML−1T−1, and it is equivalent to Kg m-1 s -1

## Viscosity of Water in SI Units

The coefficient of viscosity of water can be determined by using Poiseuille's law.
Poiseuille's equation for the flow of liquid determines the volume of the liquid flowing through a capillary tube in a unit of time.

Poiseuille's formula is given by,
Ⅴ = π P ໗ ^ 4 / 8 η l
Here, the viscous liquid's flow rate through a tube of length 'l' and radius '໗' is proportional to the applied pressure P.
The rate of flow of the viscous liquid is proportional to the fourth power of the inner radius of the tube and inversely proportional to the viscosity of the liquid and the length of the tube.

## Do You Know?

• The dynamic viscosity of water at room temperature 25°C has the following values-
1. In the SI unit, the value of viscosity is 8.90 × 10 - 4 Pa·s.
2. In CGS unit, the value of viscosity is 8.90 × 10- 3 dyn·s/cm2 or 0.890 cP.
Therefore, water has a viscosity of 0.0091 poise.
• Viscosity and density are two different terms where viscosity is the thickness of fluid and density refers to the space between its particles.      Talk to our expert
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