Unit of Viscosity: Formula, Coefficient of Viscosity, and Sample Questions

Unit of Viscosity of a fluid is Poise (P) or pascal-seconds (Pa-s).

• The viscosity of a fluid is a measure of its resistance to flow.
• It is a property of fluid such as liquids and gases.
• Fluids with high viscosity move slowly to that of the fluids having low viscosity.
• Examples of high-viscosity fluids are sauce, jam, honey, etc.
• Examples of low-viscosity fluids are water, milk, fruit juice, etc.
• It can be defined as the resistance offered by a fluid against its flow when there is relative motion between the internal layers of the

Read More: Mechanical Properties of Fluids

Key Terms: Viscosity, SI Unit, CGS Unit, Kinematic Viscosity, Dynamic Viscosity, Poise, Dimensional Formula, Poiseuille, Coefficient of Viscosity

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Unit of Viscosity

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The coefficient of viscosity is regarded as the measure of viscosity, the unit of coefficient of viscosity is considered as the unit of viscosity.

From Newton's formula,

\(\eta =\frac {F}{A} \times \frac{dx}{dv}\)

Note: neglecting the negative sign for the sake of convenience.

Here

• η- viscosity
• F- force applied
• A- cross-sectional area
• dx- change in distance
• dv- change in volume

From the equation, we can determine the dimension of \(\eta\) as ML^-1T^-1. Now we can substitute the individual units and find the units in SI and CGS.

SI Unit of Viscosity

In SI standards, the unit of \(\eta\) is Kg/ms, and Nsm^-2. The unit is generally called Decapoise or Poiseulle.

CGS Unit of Viscocity

• In the CGS standard, the unit of viscosity is poise (P) which is used in honor of a French physiologist Jean Léonard Marie Poiseuille. 
• It is also widely used in ASTM standards, as centipoise (cP).
• The cgs unit for kinematic viscosity is stoke (St) which was named after Irish mathematician and physicist Sir George Gabriel Stokes. 
• Sometimes the unit centistokes (cSt) is also used.

Other Common Viscosity Units

Some non-standard units of viscosity are the Reyn which is a British unit of dynamic viscosity.

• Earlier, the kinematic viscosity was measured by using Saybolt viscometer where the units were expressed in Saybolt universal seconds (SUS).
• Furthermore, other abbreviations are sometimes used such as SUV (Saybolt universal viscosity) or SSU (Saybolt seconds universal).

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What is Viscosity?

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Viscosity is referred to as the ratio of the force required to make adjacent layers of the liquid move over each other.

• Viscosity is a peculiar property exhibited by the fluids due to which an internal frictional force comes into action when the fluid starts moving, and this very friction opposes the relative motion between the layers of the fluid.
• The backward dragging frictional force is called Viscous drag or Viscous Force, which acts tangentially on the layers of the fluid.
• Viscosity is symbolized by \(\eta\), “eta”, and the use of the Greek letter mu (μ) is also quite common.

Example of Viscosity in Fluids

In general, we normally deal with two types of viscosity,

• Dynamic Viscosity
• Kinematic Viscosity

Dynamic viscosity is the measure of the resistance to flow offered by the fluid when an external force is applied, whereas Kinematic viscosity is the inherent resistance offered by the fluid against its flow.

The video below explains this:

Viscosity Detailed Video Explanation:

Also Read: 

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Coefficient of Viscosity

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The coefficient of viscosity of fluid gives the measure of the viscosity of the fluid. It is defined as the frictional force acting tangentially per unit area of fluid divided by the velocity gradient of the fluid.

As shown in the figure, consider two parallel layers P & Q of a fluid in motion.

P and Q are at distances x and x+dx from the solid surface.

They are moving with velocities v and v+dv. We also know that the rate of change of velocity with distance is called the velocity gradient and it is denoted by, dv/dx.

Schematic for Coefficient of Viscosity Derivation

Consider the dragging force F tangentially between the layers of the fluid, and it is proportional to,

The area of contact between the layers A is directly proportinal to the dragging force,

F α A

The velocity gradient between the layers in contact is hence,

F α dv/dx

Therefore, 

F α Adv/dx

F = -\(\eta\)Adv/dx

Where \(\eta\) is the coefficient of viscosity, the negative sign implies that the viscous force is acting in the opposite direction of the fluid flow. The above equation is known as Newton's formula for viscous force.

Also Download: PDF on Viscosity

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Things to Remember 

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• In general, thick liquids are more viscous than thin liquids. For example, Blood is more viscous compared to water.
• The viscosity of liquids decreases with the increase in temperature, whereas in gases viscosity increases with an increase in temperature.
• Viscosity is the fluid resistance against its flow and it comes into action due to the relative motion of the internal layers of the fluid.
• The coefficient of viscosity is considered as the measure of viscosity.
• The unit of viscosity in SI units is Kg/ms and in CGS it is dyne s cm^-2.

​Also Check:

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Previous Year Questions

1. If the excess pressure inside a soap bubble is balanced by oil column of height…? [JKCET 2004]
2. Bernoulli’s principle is based on the law of conservation of…? [UPSEEE 2010]
3. A sphere of radius R is gently dropped into liquid of viscosity η in a vertical uniform tube…? [JKCET 2008]
4. If the work done in blowing a bubble of volume V is W, then the work done in…? [BCECE 2003]
5. A solid sphere falls with a terminal velocity of 20m/s in air. If it is allowed to fall in vacuum…? [AMUEEE 2015]
6. A cylindrical capillary tube of 0.2mm radius is made by joining two capillaries…? [JEE 2019]
7. A square wire frame of size L is dipped in a liquid. On taking out, a membrane is formed…?[DUET 2004]
8. A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water…? [JEE 2018]
9. An open U-tube contains mercury. When 11.2cm of water is poured into one of the arms…? [BCECE 2006]
10. A water drop is divided into 8 equal droplets. The pressure difference between… [BHU UET 2008]
11. A tank is filled with water. There is a hole in the bottom. At the bottom total pressure…? [BCECE 2014]
12. Which one of the following equation is Torricelli law?  [JKCET 2014]
13. At what speed, the velocity head of water is equal to pressure head of 40cm of Hg…? [BCECE 2008]
14. A rain drop of radius 0.3mm has a terminal velocity of 1m/s and the viscosity of…? [BCECE 2003]
15. If the potential energy of a body on a planet is numerically U and the escape velocity…? [BHU UET 2008]
16. A closed compartment containing gas is moving with some acceleration in horizontal direction…? [JCECE 2010]
17. Work done in increasing the size of a soap bubble from a radius of 3cm to 5cm is nearly…? [AMUEEE 2016]
18. Two capillary of lengths L and 2L and of radii R and 2R are connected in series…? [JCECE 2010]
19. Consider a soap film on a rectangular frame of wire of area 4×4cm². If the area of the soap…? [AMUEEE 2016]
20. If two soap bubbles of different radii are connected by a tube…? [BCECE 2004]

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