 # Coefficient of Viscosity

The viscosity is defined as the ratio of the force required to make adjacent layers of the liquid move over each other.

Figure .1 (a) shows an ideal or superfluid with no friction however, practically there is always some friction in the fluids as shown in the figure. 1(b).

Let’s take an example,

As you can see in figure.2 above, there is a variation in each horizontal layer of the liquid that is happening due to the presence of some internal friction (viscosity) between the layers of the fluid passing via two plates.

### Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient of the fluid is called the coefficient of viscosity η.

Hence the coefficient of viscosity is given by,

 η  = F . d / A .ⅴ

Where

• F is the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

• ⅴ is the velocity.

• A is the area

• d is the distance between the two layers of liquid skidding over each other.

The difference in the stream of velocity between the adjacent layers of the fluid is measured in the velocity gradient.

Basically, the viscosity of gas is less than the liquid viscosity.

### SI Unit of Coefficient of Viscosity

Every liquid has its own specific viscosity and the measure of this attribute is called the coefficient of viscosity.

The coefficient of viscosity η is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit area A.

The SI unit of η is Newton-second per square meter (Ns. m^ - 2) or

Pascal-seconds (Pa .s)

Hence the coefficient of viscosity is a measure of the resistance of the fluid to deformation at a given rate due to internal friction.

### Unit of Coefficient of Viscosity

The centimeter-gram-second or CGS unit of coefficient of viscosity,  η is

dyne-sec/ cm ^ 2 which is 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.

### Coefficient of Viscosity Unit and Dimension

Since, the formula for coefficient of viscosity is given by,

η  = F . d/ A .ⅴ  = [M  L T ^ - 2] . [L] / [L ^ 2] . [L T ^ - 1]

On solving  we get,

 Dimensional formula for η = [M L ^ -1 T ^ - 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.

The Poiseuille’s equation for the flow of liquid determines the volume of the liquid flowing through a capillary tube in a unit time.

Poiseuille's formula is given by,

 Ⅴ = π P ໗ ^ 4 / 8 η l

Here, the rate of flow of the viscous liquid 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.

The formula for the coefficient of viscosity of water is given by,

 η =  π P ໗ ^ 4 / 8 Ⅴ l

Here

Ⅴ  is the rate of flow of the volume of liquid.

P is the pressure that would be applied to the liquid.

໗ is the inner radius of the capillary tube.

l is the length of the capillary tube.

SI unit of viscosity of water is Ns.m^ -2 or Pa.s.

### Do You Know?

• The dynamic viscosity of water at room temperature  25°C are having various values mentioned below:

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/cm ^ 2 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.

Q1: Who Discovered Viscosity?

Ans: Jean-Louis-Marie Poiseuille discovered viscosity by setting up experiments where he tested the flow of liquids through varying sized narrow tubes in the year of 1929.

He was a French physicist and physiologist whose interest in the circulation of blood in the human body led him to discover viscosity.

Q2: Explain How Heat Affects Viscosity?

Ans: When the liquid is heated, the particles gain entropy. Therefore, the kinetic energy generated weakens the intermolecular forces between the particles leading to the separation between the molecules which decreases the thickness of the liquid as viscosity is the state of fluid being thick and sticky. Hence, the viscosity of the liquid also decreases.

Q3: What Causes Viscosity?

Ans: Viscosity is caused by friction within a fluid which is the result of intermolecular forces between particles within a fluid. These intermolecular forces obstruct the shearing movement of the fluid and the viscosity of a fluid is directly proportional to the strength of these forces. The more strong is the force of attraction between the molecules in the liquid, the more will be the internal friction. Hence the property of the friction in a fluid is called the viscosity. It is mostly expressed in centipoise (cP) which is equivalent to 1m Pa. s (millipascal second).

Q4: Write Some Examples of Viscosity.

Ans:  There are certain real-life examples to explain viscosity

• In your day-to-day life, you prefer using the products (dishwasher or hand wash) that have viscosity because the more viscous the fluid is, the more effective it is in washing your hands and the utensils.

• Another example you can consider is oil and if a drop of it falls on the surface, drop sticks on the surface in a small spherical shape.