# Dimensions of Viscosity

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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.

### 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 = M0 L2 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 the critical importance in medicine as the fluids 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 a dangerous blood loss and even death sometimes.

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

Ans. 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?

Ans. 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.