Viscosity MCQ Quiz - Objective Question with Answer for Viscosity - Download Free PDF

Explanation:

Viscosity

Definition: Viscosity is a measure of a fluid's resistance to deformation or flow. It describes the internal friction of a moving fluid. A fluid with high viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion.

Correct Option Analysis:

The correct option is:

Option 3: It is the same as specific gravity.

This option is incorrect because viscosity and specific gravity are two distinct physical properties. Viscosity, as mentioned, measures a fluid's resistance to flow, while specific gravity is a measure of the density of a substance compared to the density of water. The two properties are not the same and describe different characteristics of fluids.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: It is caused by friction within a fluid.

This statement is true. Viscosity is indeed caused by the internal friction within a fluid. The internal resistance to flow is what characterizes a fluid's viscosity.

Option 2: Its unit is N-s/m^2.

This statement is true. The SI unit of viscosity is the Pascal-second (Pa·s), which is equivalent to N·s/m² (Newton-seconds per square meter). This unit is used to quantify the internal friction in the fluid.

Option 4: It is defined as the fluid's resistance to deformation at a given flow.

This statement is true. Viscosity is a measure of how much a fluid resists flowing when a force is applied to it. It quantifies the resistance to deformation at a given rate of flow.

Conclusion:

Understanding viscosity is crucial in various applications, including engineering, fluid mechanics, and everyday life. Viscosity is not the same as specific gravity, and confusing the two can lead to misunderstandings about fluid behavior. Specific gravity relates to density, while viscosity relates to flow resistance. Correctly distinguishing these properties ensures accurate analysis and application in scientific and engineering contexts.

Concept:

\(\rm Kinematic~ viscosity\; (\nu)= \frac {Dynamic ~ viscocity}{Density ~of ~fluid}= \;\frac {μ}{ρ}\)

Density of fluid = specific gravity × 1000

1 stoke = 10-4 m2/s

1 Poise = 0.1 Ns/m2 or Pa-s.

Calculation:

Given:

viscosity = 0.06 Poise ⇒ 0.06 × 0.1  N-s/m2

Kinematic viscosity = 0.025 stokes ⇒ 0.025 × 10-4 m2/s.

Density of fluid = specific gravity × 1000

∴ ρ = 1.9 × 1000 = 1900 kg/m3.

\(\rm Kinematic~ viscosity\; (\nu)= \frac {Dynamic ~ viscocity}{specific gravity × 1000}= \;\frac {μ}{ρ}\)

\(0.025×10^{-4}=\;\frac {0.06 × 0.1}{{specific gravity × 1000}}\)

∴ S = 2.4

Viscosity: The property that represents the internal resistance of a fluid to motion (i.e. fluidity) is called viscosity. There are two ways to write viscosities:

(1) Dynamic viscosity: This is also termed as absolute viscosity. A common unit of dynamic viscosity is poise.

1 poise = 0.1 Pa.s = 0.1 N.s/m2

(2) Kinematic Viscosity: The ratio of dynamic viscosity to density appears frequently and this ratio is given by the name kinematic viscosity. Its unit is Stoke or m2/s (1 stoke = 0.0001 m2 /s).

Concept:

• Viscosity: It is a property of a fluid to oppose relative motion between its layer.
  • The coefficient of viscosity is “η“ and dimension is [ ML-1T-1].
• Kinetic Viscosity: It is a measure to the inherent resistance of the of a fluid to flow when no external force is acted expect gravity.
  • Kinetic Viscosity = coefficient of viscosity / fluid mass density
  • V = η / ρ

Explanation:

• Dimensional formula of viscosity is [ ML-1T-1].

Explanation:

Newton's law of viscosity:

• Viscosity is a property of fluid by virtue of which they offer resistance to shear or angular deformation.
• It is primarily due to cohesion and molecular momentum exchange between fluid layers, and as flow occurs, these effects appear as shearing stresses between the moving layers.
• According to Newton's law of viscosity, shear stress is Inversely proportional to the distance between two layers of fluid.

\(τ\propto\frac{du}{dy}\)

\(τ=μ\frac{du}{dy}\)

where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear strain).

Explanation:

According to Newton's law of viscosity, shear stress is directly proportional to the rate of angular deformation (shear strain) or velocity gradient across the flow.

\(τ\propto\frac{du}{dy}\)

\(τ=μ\frac{du}{dy}\)

where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear-strain).

Units of Dynamic viscosity:

\(\mu=\frac{\tau}{\frac{du}{dy}}\Rightarrow\frac{Shear\;stress}{\frac{Change\;in\;velocity}{Change\;in\;distance}}\)

\(\mu=\frac{\frac{Force}{Area}}{\frac{Length}{Time}\times\frac{1}{Length}}\Rightarrow\frac{Force\;\times\;Time}{(Length)^2}\)

\(\mu=\frac{Ns}{m^2}\)

∴ the unit of dynamic viscosity in SI unit is Ns/m² or Pa-s.

The unit of force in the CGS system is dyne, the unit of length is cm and the unit of time is sec.

\(\mu=\frac{dyne\;\times\;sec}{cm^2}\)

\(\because1\;P=\frac{dyne\;\times\;sec}{cm^2}\)

∴ the unit of dynamic viscosity in CGS system is 'Poise' and 1 Poise = 0.1 Ns/m² or Pa-s.

Additional Information

Kinematic viscosity:

It is defined as the ratio between the dynamic viscosity and density of the fluid.

\(\nu=\frac{\mu}{\rho}\)

Units of kinematic viscosity:

\(\nu=\frac{\mu}{\rho}\Rightarrow\frac{\frac{Force\;\times\;Time}{(Length)^2}}{\frac{Mass}{(Length)^3}}=\frac{Mass\times\frac{Length}{(Time)^2}\times{Time}}{\frac{Mass}{Length}}\)

\(∴\nu=\frac{(Length)^2}{Time}\)

∴ the SI unit of kinematic viscosity is m²/s and the CGS unit of kinematic viscosity is cm²/s or 'stoke'.

1 stoke = 10^-4 m²/s.

Explanation:

Viscosity: The property that represents the internal resistance of a fluid to motion (i.e. fluidity) is called viscosity. There are two types of viscosity:

Dynamic viscosity: It is the property of a fluid which offers resistance to the movement of one layer of fluid over an adjacent layer of the fluid.

• Its SI unit is N-s/m2 or Pa-s.
• Its C.G.S unit is Poise.
• 1 Poise = 0.1 Pa-s = 0.1 Ns/m2 

Kinematic Viscosity: The ratio of dynamic viscosity to density appears frequently and this ratio is given by the name kinematic viscosity.

\({\rm{Kinematic\;Viscosity\;}}\left( {\rm{\gamma }} \right) = {\rm{\;}}\frac{{{\rm{Dynamic\;viscosity\;}}\left( {\rm{\mu }} \right)}}{{{\rm{density\;}}\left( {\rm{\rho }} \right)}}\)

• Its SI unit  = m2/s.
• Its C.G.S unit = Stoke or cm2/s.
• 1 Stoke = 10-4 m2/s.

Explanation:

Viscosity: The property that represents the internal resistance of a fluid to motion (i.e. fluidity) is called viscosity. There are two ways to write viscosities:

(1) Dynamic viscosity: This is also termed as absolute viscosity. A common unit of dynamic viscosity is poise.

1 poise = 0.1 Pa.s = 0.1 N.s/m2

Dynamic viscosity is a function of temperature only.

(2) Kinematic Viscosity: The ratio of dynamic viscosity to density appears frequently and this ratio is given by the name kinematic viscosity. Its unit is m2/s.

Kinematic Viscosity is a function of temperature and pressure.

∴ C.G.S unit of kinematic viscosity is cm2/s or, Stoke. (1 stoke = 0.0001 m2/s)

Variation of viscosity with temperature:

(i) Increase in temperature causes a decrease in the viscosity of a liquid, whereas the viscosity of gases increases with temperature growth.

(ii) The reason for the above phenomenon is that; in liquids; viscosity is primarily due to molecular cohesion which decreases with increases in volume due to temperature increment, while in gases, viscosity is due to molecular momentum transfer which increases with increases in number of collision between gas and molecule.

Explanation:

Viscosity: The property that represents the internal resistance of a fluid to motion (i.e. fluidity) is called viscosity. There are two ways to write viscosities:

(1) Dynamic viscosity: This is also termed as absolute viscosity. A common unit of dynamic viscosity is poise.

1 poise = 0.1 Pa.s = 0.1 N.s/m2

(2) Kinematic Viscosity: The ratio of dynamic viscosity to density appears frequently and this ratio is given by the name kinematic viscosity. Its unit is Stoke or m2/s (1 stoke = 0.0001 m2 /s).

∴ C.G.S unit of kinematic viscosity is cm2/s.

Concept:

\(\rm Kinematic~ viscosity\; (\nu)= \frac {Dynamic ~ viscocity}{Density ~of ~fluid}= \;\frac {μ}{ρ}\)

Density of fluid = specific gravity × 1000

1 stoke = 10-4 m2/s

1 Poise = 0.1 Ns/m² or Pa-s.

Calculation:

Given:

Specific gravity = 1.9, Kinematic viscosity = 6 stokes ⇒ 6 × 10-4 m2/s.

Density of fluid = specific gravity × 1000

∴ ρ = 1.9 × 1000 = 1900 kg/m³.

\(\rm Kinematic~ viscosity\; (\nu)= \frac {Dynamic ~ viscocity}{Density ~of ~fluid}= \;\frac {μ}{ρ}\)

\(6×10^{-4}=\;\frac {μ}{1900}\)

∴ μ = 114 × 10^-2 Ns/m² = 1.14 Ns/m²

Concept:

\(kinematic~ viscosity= \frac {dynamic ~ viscocity}{density ~of ~fluid}\)

\(ν = \frac {μ}{ρ }\)

Density = specific gravity × 1000

Calculation:

Given:

Dynamic viscosity(μ) = 0.006 Ns/m²

kinematic viscosity(ν) = 0.025 × 10-4 m2/s

\(kinematic~ viscosity= \frac {dynamic ~ viscocity}{density ~of ~fluid}\)

\(​​0.025\ \times 10^{-4}= \frac {0.006}{density ~of ~fluid}\)

Density of fluid = 2400 kg/m³

Specific gravity = Density of fluid/1000

Specific gravity = 2.4

Explanation:

Capillary Tube Viscometer:

• Viscometer is an instrument used for measuring the viscosity of a fluid. In the capillary tube viscometer, the pressure needed to force the fluid to flow at a specified rate through a narrow tube is measured.
• This type of viscometer is based on laminar flow through a circular pipe.
• It has a circular tube attached horizontally to a vessel filled with a liquid whose viscosity has to be measured. Suitable head (hf ) is provided to the liquid so that it can flow freely through the capillary tube of certain length (L) into a collection tank as shown in figure.
• The flow rate (Q) of the liquid having specific weight wl can be measured through the volume flow rate in the tank.
• The Hagen-Poiseuille equation for laminar flow can be applied to calculate the viscosity (µ) of the liquid.

\(\mu = \left( {\frac{\pi }{{128}}} \right)\frac{{{W_l}{h_f}{d^4}}}{{QL}}\)

Explanation:

Viscosity:

• Viscosity is a property of fluid by virtue of which they offer resistance to shear or angular deformation.
• It is primarily due to cohesion and molecular momentum exchange between fluid layers, and as flow occurs, these effects appears as shearing stresses between the moving layers.
• According to Newton's law of viscosity, shear stress is directly proportional to the rate of angular deformation (shear strain) or velocity gradient across the flow.

\(τ\propto\frac{du}{dy}\)

\(τ=μ\frac{du}{dy}\)

where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear strain).

Additional Information

Dynamic viscosity:

Dimension μ = [ML-1T-1]

SI unit μ = Ns/m2 or Pa-s.

CGS unit of μ = Poise (P) where 1P = 0.1 Ns/m2. 

Explanation:

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.

Kinematic viscosity:

Kinematic viscosity is defined as the ratio of dynamic viscosity and density of the fluid.

\(kinematic~ viscosity= \frac {dynamic ~ viscocity}{density ~of ~fluid}\)

\(ν = \frac {μ}{ρ }\)

In the Numerator, Dynamic Viscosity is there. So, let's talk about it.

Dynamic Viscosity (µ):

• Viscosity can be defined as the measure of a fluid's resistance to deformation at a given flow.
• For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls.
• In such a case, experiments show that some stress (such as a pressure difference between the two ends of the tube) is
  needed to sustain the flow through the tube.
• This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion.
• So for a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity.

​∴ It represents the property of the fluid to maintain its momentum.

So, Option(1) is the Correct answer.