Viscosity MCQ - Practice Questions with Answers

• Viscosity-

 Ideal fluids are non-viscous. But for real fluids, there is a viscous force between the adjacent layers of fluids which are in contact.

In case of a steady flow of a fluid when a layer of fluid slips or tends to slip on adjacent layers in contact, the tangential force/viscous force acting between two adjacent layers try to stop the relative motion between them.

So The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity. 

Viscosity is also known as fluid friction or internal friction.

• Velocity gradient -

It is defined as the ratio of change in velocity to change in height.

I.e Velocity gradient $=\frac{\text { chane in velocity }}{\text { change in height }}$

For the above figure

Layer AB is at rest

While Layer CD is having velocity v and is at a distance x from layer AB

Similarly, Layer MN has velocity (v+dv) and is at a distance (x+dx)  from Layer AB

Then Velocity gradient is given as Velocity gradient $=\frac{d v}{d x}$

This means Velocity gradient denotes the rate of change of velocity with distance x. 

• Viscous Force-

In the case of a steady flow of fluid, the force between the fluid layers opposing the relative motion is called viscous force.

1. Viscous force directly proportional  to the area

I.e

Where A is the area 

2. Viscous force directly proportional  to the Velocity gradient

1.e $F \alpha A$

Where A is the area
2. Viscous force directly proportional to the Velocity gradient

$$
F \alpha \frac{d v}{d x}
$$

So we can write

$$
F \alpha \frac{A d v}{d x}=F=-\eta A \frac{d v}{d x}
$$

Where A-Area
F-Viscous force
$\eta=C o-e f$ ficient of viscosity
$v-$ Velocity of liquid
$x$ - Distance from reference point

Here Negative sign shows viscous force acts opposite to the flow of liquid

• Coefficient of viscosity-

From the equation

So the coefficient of viscosity is defined as the viscous force acting per unit area between two layers moving with a unit velocity gradient.

1. The coefficient of viscosity shows the nature of liquids.

2.  The unit of viscosity is $d y n e-s-\mathrm{cm}^{-2}$ or Poise in the CGS system

   And Newton $-S-m^{-2}$ or Poiseuille or decapoise ${ }_{\text {in the slem }}$
   And 1 decapoise $=10$ Poise
   The dimension of viscosity is $M L^{-1} T^{-1}$

3. The cause of viscosity in liquids is cohesive forces among molecules whereas, in gases, it is due to the diffusion of molecules.

4. The viscosity of the liquid is much greater (about 100 times more) than that of gases.

5. With an increase in pressure, the viscosity of liquids (except water) increases while For gases viscosity is practically independent of pressure. The viscosity of water decreases with an increase in pressure.

6. The viscosity of gases increases with the increase of temperature because on increasing temperature the rate of diffusion increases.

7. The viscosity of a liquid decreases with the increase in temperature because the cohesive force between the liquid molecules decreases with the increase in temperature

 

• Poiseuille’s Formula

For the stream-line flow of liquid in a capillary/narrow tube, If a pressure difference (P) is maintained across the two ends of a capillary tube of length 'l ' and radius r as shown in figure

Then according to Poiseuille’s Formula

V= the volume of liquid coming out of the tube per second is

1. Directly proportional to the pressure difference (P).

2. Directly proportional to the fourth power of radius (r) of the capillary tube

3. Inversely proportional to the coefficient of viscosity $(\eta)$ of the liquid.

4. Inversely proportional to the length (l) of the capillary tube.

With the help of the Dimension formula we get

$$
V=\frac{K P r^4}{\eta l}
$$

Where $K$ is the constant of proportionality
And experimentally it is found that $K=\frac{\pi}{8}$
So Poiseuille's Formula is given as

$$
V=\frac{\pi P r^4}{8 \eta l}
$$