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Dimensions of Viscosity

Last updated date: 27th Nov 2023
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What is Viscosity?

Viscosity is the internal resistance to flow that is possessed by a liquid. The liquids that flow slowly have high internal resistance. This happens because of the strong intermolecular forces. Thus, the dimension of the viscosity of liquid of these kinds are more viscous and hold high Viscosity.

The dimension of viscosity in physics is conceptualized as quantifying the internal frictional force which arises between the adjacent layers of fluid, which are in relative motion. For example, when a fluid is forced through a tube, it flows quickly near the axis of the tube than near its walls.

The liquids that flow rapidly have low internal resistance. This happens because of the weak intermolecular forces. Therefore, they have low viscosity or are less viscous.

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Working of Viscosity

Let us know how viscosity works with an example.

Consider a liquid flowing via a narrow tube. All parts of the liquids do not pass through the tube with similar velocity. Imagine the liquid is to be made of a large number of the thin cylindrical coaxial layers. The layers that are in contact with the walls of the tube are mostly stationary. As we travel from the wall towards the centre of the tube, the cylindrical layers’ velocity keeps on increasing until it is maximum at the centre.

This is called laminar flow and is a type with a regular gradation of velocity in going from one to the layer besides to it. As we travel from the centre towards the walls, the layers’ velocity keeps on decreasing. Especially, every layer offers some friction or resistance to the layer present behind it immediately.

Viscosity is the force of friction that one part of the liquid offers to another part. The force of friction ‘f’ between two layers, each separated with a distance of ‘dx’ cm, having area ‘A’ sq cm, and having a velocity difference of ‘dv’ cm/sec, is given as follows.

f ∝ A ( dv / dx )

f = η A ( dv / dx)

Where η  is a constant, which is called the coefficient of viscosity, and ‘dv/dx’ is the velocity gradient. If A = 1 sq cm, dx =1, dv = 1 cm/sec, then f = η. Hence the coefficient of viscosity can be defined as the force of friction needed to maintain a velocity difference of 1 cm/sec between the two parallel layers, apart 1 cm and each having an area of the same 1 sq cm.

Dimensional Formula of Viscosity

The dimensional formula for Viscosity (η) can be given as follows.

M1 L-1 T-1

Where M is Mass, L is Length and T is the Time

Units of Viscosity

As we know that, the dimensional unit of viscosity is, η = f .dx / A .dv

Hence, η = dynes × cm / cm2 ×cm/sec.

Therefore, we can write as,

η = dynes cm-2 sec or the viscosity units are, dynes sec cm-2.

This quantity is known as 1 Poise.

f = m × a

η =  \[\frac{(m×a×d_x)}{(A . dv)}\]

Hence, η = g cm-1 s-1

Therefore, η = 1 poise

In S.I. units, η = f .dx / A .dv

= \[\frac{(N×m)}{(m^2 × ms^{-1})}\]

Therefore we can write, η = N m-2 or Pas

1 Poise = 1 g cm-1s-1 = 0.1 kg m-1 s-1

Derivation of Viscosity

Viscosity = Tangential Force × Distance between layers  [Area × Velocity] -1 ---- (1)

Since, the Tangential Force = M × a = M × [L T-2]

Therefore, the dimensional formula of Tangential Force = M1 L1 T-2 ---- (2)

And, the dimensions of the area and velocity = M0L2 T0 and M0 L1 T-1 ---- (3)

On substituting the equations (2), (3) in (1), we get,

Viscosity = Force [Area × Velocity]-1 × Distance between the layers

Or, η = [M1 L1 T-2] × [M0 L2 T0]-1 × [M0 L1 T-1]-1 × [M0 L1 T0] = [M1 L-1 T-1]

Therefore, the viscosity is dimensionally represented as [M1 L-1 T-1]

Applications of Viscosity

While viscosity seems to be minor importance in daily life, it actually can be very important in many different fields. Let us discuss a few viscosity applications of daily life.

  • Lubrication in Vehicles

When we pour oil into the truck or car, we should be aware of its viscosity. Because viscosity affects friction and friction, in turn, it affects the heat. In addition, it also affects the rate of oil consumption and the ease with which our vehicle will start in either hot or cold conditions.

  • Cooking

Viscosity plays a vital role in the preparation and food serving. Cooking oils may not change viscosity as they heat, while many become very viscous as they cool. Fats that are moderately viscous when heated becomes solid when cooled.

  • Medicine

Viscosity can be of critical importance in medicine as the fluids are intravenously introduced into the body. Blood viscosity is a primary issue: blood that is too thin will not clot, whereas the blood that is too viscous can form dangerous internal clots; it can lead to dangerous blood loss and even death sometimes.

Relevance of Studying Dimensions of Viscosity for IIT JEE

Dimensions of Viscosity is an interesting topic and is one of the important topics for IIT JEE competitive exams.  It needs to be understood well by the students before they attempt questions on this topic.  The formula for dimensional viscosity also needs to be known so that the problems that come based on them can be easily resolved. The units, derivation are important too. IIT JEE is a challenging exam that only the most brilliant and hardworking students are able to crack. Studying all the topics well will be advantageous for the students before they sit for the main test.

Does Vedantu Have Anything on  Dimensions of Viscosity?

Vedantu has apt study material on Dimensions of Viscosity. Students can read from Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs and understand the topic in its entirety.  It has useful insights on the topic that can be used by all students to prepare for a test that’s on the topic.

FAQs on Dimensions of Viscosity

1. Why is the viscosity of Oil greater compared to Water?

Vegetable oils are the more viscous ones because they are the esters of glycerol, which holds three chains of fatty acids in a 3D branched formation, which makes the sliding of molecules past each other rather more difficult to that of when water molecules do it.

Mineral oils are also branched but comparatively less.

Some oily substances, like the dimethyl esters of dibasic acids, for example, sebacic, have a much lower viscosity to that of water. They are the straight-chain molecules with a little intermolecular attraction. Water molecules form longish chains through hydrogen bonding.

2. Explain the cause of viscosity in a Fluid?

In very simple terms, the viscosity of any fluid is its inherent nature to oppose the flow. Every fluid is made up of some kind of particles such as molecules and atoms clubbed together because of the internal forces acting between them. 

Now the extent up to which these viscous forces can resist any deformation that is caused in the fluid due to any external forces, or maybe due to the fluid flow, is marked as the viscosity of that fluid. In solids, the particles are bounded firmly because the inter-particle forces are most strong, whereas in liquids, the forces are weak, and similarly in gases, it is the weakest.

3. What are the units of viscosity?

The dimensional unit of viscosity is denoted by  η = f .dx / A .dv
More about the topic has been elaborated upon in Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs on Vedantu. This page has relevant information on the dimension of viscosity that the students must go through. That way, they will understand what viscosity is and what its units are.  To be able to solve problems that come from this part of the chapter, it is important for them to know the units.

4. Where is viscosity applied in everyday life?

Viscosity is of great significance in everyday life. It is used in the lubrication of vehicles, in the cooking oils that people use, in medicine when it comes to blood. Students can find out more about Viscosity if they read from Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs on Vedantu’s online tutoring platform. This page has relevant information on Viscosity and how it is applied in the regular lives of people. Sound knowledge about the dimensions of viscosity can be gathered if they study well from this page.

5. How can students derive the formula for the dimension of viscosity?

The formula of dimensions of viscosity depends on mass, length and time and can be derived if the students read up the chapter on it well. Understanding any topic instead of just mugging up the details will assist them in answering all questions that come from the chapter. Any student who wishes to get their concepts clear or are looking to revise Dimension of Viscosity can do so by going to  Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs on Vedantu. This page will guide them in the right manner.

6. Is the chapter Dimensions of Viscosity an important chapter for IIT JEE?

Yes, all chapters for IIT JEE are equally important and need to be studied well. The chapter on Dimensions of Viscosity is also important as it sheds light on some of the interesting concepts such as the internal resistance to flow that is possessed by any liquid. Questions can come from any portion of this chapter and so, reading it in a thorough manner will benefit all students. The material on this page has been designed by expert Science teachers who understand the topic well. They have included only the most relevant bits here. They can check out Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs on Vedantu.

7. How are viscosity and friction related?

Friction refers to those forces that resist relative motion whereas viscosity refers to resistive forces that occur between layers of fluid when these fluids attempt to flow. More about viscosity and its relation to other concepts have been stressed upon in Dimensions of Viscosity –Working, Units, Derivation, Applications and FAQs on Vedantu’s e-learning portal. This page will guide them in an ideal manner by explaining viscosity in depth. It has all those inputs that will be needed by the students to know before a test on the topic. Students must be careful in not skipping any portion that's on the page as that could affect their overall marks.