Introduction
Put some drops of water on one side on a slanting surface and some drops of honey on the other. Come back and observe the flow of both the liquids. You would note that the slowness of water was very quick whereas honey was not that easily movable. In this case, honey is considered to be Viscous.
So, 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 the 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.
The concept has significant importance for competitive exams like JEE and NEET. So the faculty at Vedantu has holistically covered the topic keeping in mind the need of every student. So in this article, we shall be learning about -
Table of Content
Introduction
What is the viscous gradient?
What is the Coefficient of Viscosity?
SI Unit of Coefficient of Viscosity
Unit of Coefficient of Viscosity
Coefficient of Viscosity Unit and Dimension
The viscosity of Water in SI Units
Do You Know?
Benefits of studying with Vedantu
Frequently asked questions
What is a Viscous Gradient?
The viscous gradient is the difference in the velocity between the adjacent layer of the fluid. If more force is applied by the upper layer to move forward the more will be the viscous gradient. It is represented by v/x, where v is the velocity difference and x will be the difference of distance between the two layers. So, the higher the value of v/x, the more will be the viscous gradient.
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.
The viscosity of gas is less than the liquid viscosity.
SI Unit of Coefficient of Viscosity
Every liquid has its 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 centimetre-gram-second or CGS unit of coefficient of viscosity, η is
dyne-sec/ cm2 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 = MLT−2 . L / L2 . LT −1
On solving we get,
The 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,
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,
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 250C are having various values mentioned below:
In the SI unit, the value of viscosity is 8.90 × 10- 4 Pa·s.
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.
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FAQs on Coefficient of Viscosity
1. What is meant by the coefficient of viscosity in Physics?
The coefficient of viscosity is a measure of the internal friction offered by a fluid when one layer moves over another. It quantifies the resistance to flow and is defined as the tangential force required per unit area to maintain a unit velocity gradient between parallel layers of the fluid.
2. State the SI unit and dimensional formula of coefficient of viscosity.
The SI unit of coefficient of viscosity is pascal-second (Pa·s) or Newton-second per square meter (N·s·m-2). Its dimensional formula is [M1 L-1 T-1].
3. How does temperature affect the coefficient of viscosity of a liquid?
When temperature increases, the coefficient of viscosity of a liquid generally decreases. This happens because higher temperatures provide more kinetic energy to molecules, reducing intermolecular forces and thereby lowering resistance to flow.
4. What is the physical significance of a high coefficient of viscosity?
A high coefficient of viscosity means that the fluid is very resistant to flow, or in other words, the fluid is 'thicker' and offers greater internal friction. Examples include honey and glycerin as compared to water.
5. Why is the coefficient of viscosity different for liquids and gases?
The coefficient of viscosity differs because in liquids, viscosity mainly arises from intermolecular attraction, while in gases it depends largely on molecular momentum transfer. As a result, the temperature dependence and magnitude of viscosity for gases and liquids are not the same.
6. Write the mathematical expression for coefficient of viscosity and explain each term.
The coefficient of viscosity (η) is given by: η = F ⋅ d / (A ⋅ v), where:
- F = Tangential force applied
- d = Distance between two layers
- A = Area of each layer
- v = Relative velocity between the layers
7. What happens to the viscosity of water when impurities are added?
The viscosity of water usually increases when impurities (especially salts or solutes) are dissolved in it, because the solute particles hinder the relative motion of water molecules, raising internal friction.
8. Describe how Poiseuille's law helps determine the coefficient of viscosity experimentally.
Poiseuille's law relates the rate of flow of a viscous fluid through a capillary tube to the pressure difference, length, and radius of the tube, and the fluid's viscosity. By measuring the volume of liquid flowing per second and knowing the tube's dimensions and applied pressure, the coefficient of viscosity can be calculated using Poiseuille's equation.
9. How is the coefficient of viscosity important in real-life applications?
The coefficient of viscosity is crucial in various fields such as:
- Lubricant design for machines and engines
- Blood flow analysis in medical science
- Piping and transport of fluids in industry
- Performance of hydraulic systems
10. Distinguish between viscosity and density of a fluid.
Viscosity measures the resistance to flow due to internal friction, whereas density is a measure of the mass per unit volume of a fluid. High viscosity means the fluid flows slowly, while high density means the fluid is heavier for the same volume.
11. What common misconceptions exist about viscosity in liquids and gases?
A common misconception is that all fluids behave the same with respect to temperature. Actually, liquids reduce their viscosity with increasing temperature, but gases generally increase in viscosity as temperature rises due to different molecular mechanisms in each case.
12. Why is knowledge of viscosity essential for CBSE board exams?
Understanding viscosity is crucial because it connects fundamental physics concepts with real-life scenarios, forms the basis for numerical problems, and is a frequently tested topic in CBSE board examinations under the mechanics and properties of fluids chapters.
