Viscosity MCQ Quiz in मल्याळम - Objective Question with Answer for Viscosity - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

The correct answer is option 4) i.e. shearing stress to the velocity gradient

CONCEPT:

• Viscosity: The viscosity is the resistance offered to the flow of fluids.
  • At the molecular level of fluids, it is the internal friction between molecules of the fluids.
  • A fluid with low viscosity will easily flow as the internal friction is less.
  • Under the application of a force F, the gradual deformation due to shear is resisted by the fluid. 

The force acting between the different layers of a fluid is given by –

\(F = - \eta A\frac{{dv}}{{dy}}\)

Where η = coefficient of viscosity, A = area of the plane and dv/dy = velocity gradient.

The viscosity of a fluid depends on shear stress and Velocity gradient (\(\frac{dv}{dy}\))

Viscosity, \(\eta = \frac{\tau}{dv/dy}\)     (For unit area)

EXPLANATION:

We know that viscosity, \(\mu = \frac{\tau}{dv/dy}\)

• Therefore, the viscosity of a fluid is the ratio of shearing stress to the velocity gradient of the fluid.

option(4)

CONCEPT:

• Coefficient of Viscosity (η): The tangential viscous force required to maintain the unit velocity gradient between its two parallel layers each of unit area is called the coefficient of viscosity.

EXPLANATION:

•  The coefficient of viscosity (η) of a fluid can be defined as the ratio of shearing stress to the strain rate.

η =\(\frac{F/A}{v/x}\) where v/x is dx.x/t ( velocity = dx/dt) = \(\frac{ Shearing stress}{Shear Strain/t} \)

• Coefficient of Viscosity is a constant term which only depends on the nature of the fluids and gives measures of viscosity
• Shearing Stress is the internal restoring force set up per unit area of cross-section of the deformed body is called stress.
• Shearing Strain the ratio of change in length to the original length.

The correct answer is option 2) i.e. m²/s.

CONCEPT:

• Kinematic Viscosity: The measure of a fluid's internal resistance to flow under the influence of gravitational forces is called kinematic viscosity.
  • It is the ratio of Dynamic Viscosity to the fluid's mass density.
• Dynamic Viscosity: It is the measure of the internal resistance developed in the fluid against the force that can cause the liquid to flow.
  • Its SI unit is pascal-seconds.
• Mass Density: It is the ratio of the mass of fluid to the volume of the fluid. Its SI unit is kg/m³.

EXPLANATION:

• Kinematic Viscosity is the ratio of dynamic viscosity to mass density.

Hence, the unit of kinematic viscosity will be = \(\frac{N/m^{2}-s}{kg/m^3} = \frac{kg\times m/s^{2}\times s}{m^{2}\times kg/m^{3}}=\frac{m^{2}}{s}\)

Additional Information

• m/s is the SI unit of speed or velocity of the flowing fluid.
• m³/s is the SI unit of rate of flow of fluid or also called discharge rate of the fluid.

Important Points

• The kinematic viscosity is often expressed in the C.G.S system as Poise.
• 1 poise = 10^-4 m²/s.
• The difference between kinematic and dynamic viscosity is that dynamic viscosity is the measure of force needed to make the fluid flow at a certain rate whereas, kinematic viscosity is the measure of the rate at which the fluid is flowing under the influence of a certain force.

Viscosity:

• When a fluid moves relative to a solid or when two fluids move relative to each other. The property that represents the internal resistance of a fluid to motion (i.e. fluidity) is called as viscosity.
• The fluids for which the rate of deformation is proportional to the shear stress are called Newtonian fluids and the linear relationship for a one-dimensional system is shown in the figure. The shear stress(τ ) is then expressed as,​

          \({\rm{\tau }} = {\rm{\mu }}\frac{{{\rm{du}}}}{{{\rm{dy}}}}\) ;

• where  \( \frac{{{\rm{du}}}}{{{\rm{dy}}}}\) is the shear strain rate and µ is the dynamic (or absolute) viscosity of the fluid.
• The dynamic viscosity has the dimension ML-1T-1 and the unit of kg/m.s or, \((N-sec)/m^2 \) or Pa-s . A common unit of dynamic viscosity is Poise which is equivalent to 0.1 Pa.s.

CONCEPT:

Terminal velocity:

• The maximum constant velocity acquired by a body while falling through a viscous medium is called terminal velocity.
• The terminal velocity of a spherical body of radius r is given as,

⇒ \(V=\frac{2}{9}\times\frac{r^2(ρ-σ)g}{η}\)

Where ρ = density of the body, σ = density of the fluid and η = viscosity of the fluid

EXPLANATION:

Given r_A > r_B

We know that the  terminal velocity of a spherical body of radius r is given as,

​⇒ \(V=\frac{2}{9}\times\frac{r^2(ρ-σ)g}{η}\)

⇒ V ∝ r²     -----(1)

• By equation 1 it is clear that the terminal velocity is proportional to the square of the radius of the body.
• Therefore we can say that if the radius of the body is more, then its terminal velocity will also be more.
• Since the radius of ball A is larger than the ball B, therefore the terminal velocity of ball A will be more than ball B. Hence, option 1 is correct.

Concept:

Viscous force is the resistive force acting between the layers of the fluid. It opposes the relative motion of the layers.

This force is also known as fluid friction.

Calculation:

Let F_v be the viscous force and F_B be the Bouyant force acting on the ball.

Then, when body moves with constant velocity

Mg = F_B + F_v [a = 0]

F_v = Mg – F_B

=dVg - \(\frac{d}{2}\).Vg         (where, M = dVg  and V = volume of the ball )

=\(\frac{d}{2}\).Vg

Hence, F_{V =} \(\frac{M}{2}g\)

CONCEPT:

Viscosity:

• In the case of a steady flow of a fluid when a layer of fluid slips or tends to slip on adjacent layers in contact, the two-layer exert tangential force on each other which tries to destroy the relative motion between them.
• The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force.

EXPLANATION:

• The viscosity of the liquid increases if the density of the liquid increases. Therefore option 1 is correct. 
• We know that the density of the liquid decreases as the temperature increases and hence viscosity also decreases.
• So we can say that the viscosity of liquid depends on the density and temperature both. Hence, option 3 is correct.

CONCEPT

Viscosity: It is the property of a fluid, by virtue of which it opposes the relative motion between its different layers is known as viscosity.

This force is known as the viscous force.

Mathematically, \(F = - η A\frac{{dv}}{{dx}}\;\)

where, η = coefficient of viscosity, A = area, dv/dx = velocity gradient.

EXPLANATION

Fluid means any liquid or gas that can flow.

As described above, 

• It opposes relative motion between adjacent layers therefore option 1 is correct.
• Viscosity is the property of fluid (liquid/gas) therefore, option 2 is incorrect.
• \(F = - η A\frac{{dv}}{{dx}}\; ⇒ η = - \frac{F}{A}\frac{{dx}}{{dv}} = \;P\frac{{dx}}{{dv}}\)
• η ∝ P ⇒ viscosity increases pressure increases and vice versa therefore option 3 is incorrect
• For the ideal fluid viscosity is zero therefore option 4 is correct.

∴ Option 4 is correct

CONCEPT:

• Viscous force (F): When a layer of fluid slips or tends to slip on adjacent layers in contact, the two layers exert tangential force on each other which tries to destroy the relative motion between them.
  • The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force.

The force acting between the different layers of a fluid is given by:

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

Where η = coefficient of viscosity, A = area of the plane and dv/dx = velocity gradient.

• A negative sign is employed because viscous force acts in a direction opposite to the flow of liquid.

EXPLANATION:

The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time, and ampere.

Above equation can be written as,

\(\eta = - \frac{{F\;\left( {\frac{{dx}}{{dv}}} \right)}}{A}\)

Now,

Force = mass × acceleration

∴ Dimensional formula of force (F) = [M] × [LT^-2] = [MLT^-2]

Dimensional formula of velocity (v) = [LT^-1]

Dimensional formula of distance (x) = [L]

Dimensional formula of (dx/dv) = [T]

Dimensional formula of area (A) = [L²]

Dimensional formula of viscosity (η) –

\(\eta = \frac{{\left[ {{M^1}{L^1}{T^{ - 2}}} \right]\left[ T \right]\;}}{{\left[ {{L^2}} \right]}} = \left[ {M{L^{ - 1}}{T^{ - 1}}} \right]\)

CONCEPT:

• Viscosity: The state of being sticky, thick, and semi-fluid inconsistency, due to internal friction of fluids is called viscosity.
  • The viscosity of a material is affected by temperature, pressure, nature of fluid, velocity gradient  , etc.

EXPLANATION:

• The following factors affect viscosity:
• Temperature: Generally, the viscosity of a liquid decreases with an increase in temperature.
  • With an increase in temperature, the average speed of the molecules increases. So, the amount of time they spend "in contact" with their nearest neighbors decreases.
  • So With an increase in temperature, the average intermolecular forces decrease.
  • Thus the stickiness and thickness decrease and hence viscosity decreases.
  • Syrups and Honey can be made to flow more readily when heated.
• The viscosity of gases increases with an increase in temperature.
• Pressure: Viscosity is normally independent of pressure.
  • But when extreme pressure is applied the fluids often experience an increase in viscosity.
  • The extra pressure increases stickiness and thickness. So viscosity increases.
• Nature of fluids: Every fluid behaves in a different manner. So different fluids will have different viscosity.
• So the viscosity depends on all the given options.
• Hence the correct answer is option 4.