Properties of Fluids MCQ Quiz - Objective Question with Answer for Properties of Fluids - Download Free PDF

Explanation:

Vapour Pressure:

• Vapour pressure is a fundamental concept in the study of liquids and their phase transitions. It is defined as the pressure exerted by the vapour in equilibrium with its liquid at a given temperature. This means that at a specific temperature, a certain number of liquid molecules will have enough kinetic energy to escape the liquid phase and enter the vapour phase, creating a dynamic equilibrium where the rate of evaporation equals the rate of condensation.
• When a liquid is placed in a closed container, molecules continuously move between the liquid and vapour phases. Initially, the rate of evaporation exceeds the rate of condensation because there are few molecules in the vapour phase. As more molecules enter the vapour phase, the rate of condensation increases. Eventually, a state of equilibrium is reached where the number of molecules evaporating equals the number of molecules condensing. The pressure exerted by the vapour at this equilibrium state is called the vapour pressure.

Factors Affecting Vapour Pressure:

• Temperature: Vapour pressure increases with temperature because higher temperatures provide more energy for molecules to escape the liquid phase.
• Nature of the Liquid: Different liquids have different vapour pressures at the same temperature. For example, volatile liquids like ether have higher vapour pressures compared to less volatile liquids like water.

Explanation:

Fluid Pressure

Definition: Fluid pressure is defined as the force per unit area exerted by a fluid at rest. It is a fundamental concept in fluid mechanics and is crucial for understanding how fluids behave in different conditions and systems.

Working Principle: The pressure in a fluid at rest is the same in all directions at a given point and increases with depth due to the weight of the fluid above. This principle is described by Pascal's law, which states that any change in the pressure of an enclosed fluid is transmitted undiminished to all parts of the fluid and the walls of its container.

Mathematical Expression: Fluid pressure (P) can be mathematically expressed as:

\(P = \frac{F}{ A}\)

where:

• P is the fluid pressure
• F is the force exerted by the fluid
• A is the area over which the force is exerted

This equation shows that fluid pressure is directly proportional to the force applied and inversely proportional to the area over which the force is distributed.

Applications:

• Hydraulics: Fluid pressure is extensively used in hydraulic systems, where it is utilized to transmit power and perform work, such as in hydraulic presses and brakes.
• Aerodynamics: Understanding fluid pressure is essential for analyzing air flow over objects, such as aircraft wings, to ensure proper lift and stability.
• Weather Forecasting: Atmospheric pressure measurements are crucial for predicting weather patterns and understanding phenomena like high and low-pressure systems.

Explanation:

The specific volume of a fluid is a fundamental property that is the reciprocal of its mass density. To understand this concept, let's delve into the definitions and relationships between specific volume and mass density.

Specific Volume: Specific volume is defined as the volume occupied by a unit mass of a substance. It is an intrinsic property of matter, indicating how much space one kilogram (or any other unit of mass) of the substance occupies. Specific volume is typically denoted by the symbol \( v \) and is expressed in units of cubic meters per kilogram (m³/kg).

Mass Density: Mass density, often simply referred to as density, is defined as the mass per unit volume of a substance. It is a measure of how much mass is contained in a given volume of the substance. Mass density is denoted by the symbol \( \rho \) and is expressed in units of kilograms per cubic meter (kg/m³).

The relationship between specific volume and mass density is given by the following equation:

Specific Volume (v) = 1 / Mass Density (ρ)

This equation highlights that specific volume and mass density are inversely related. As the mass density of a substance increases, its specific volume decreases, and vice versa. This inverse relationship is crucial in various engineering applications, especially in thermal and fluid engineering.

For example, in the study of thermodynamics, the specific volume is a key parameter in describing the state of a fluid. It is used in various thermodynamic equations and processes, such as the Ideal Gas Law, which relates the pressure, volume, and temperature of a gas.

Understanding the specific volume is also essential in fluid dynamics, where it helps in analyzing the flow properties of fluids. In particular, the specific volume is used to determine the compressibility and expansion of fluids under different pressure and temperature conditions.

Now, let’s analyze the incorrect options to further clarify why mass density is the correct answer.

Option 1: Surface Tension

Surface tension is a physical property that describes the elastic tendency of a fluid surface, which makes it acquire the least surface area possible. It is not related to the reciprocal of the specific volume of a fluid. Surface tension is more relevant in phenomena such as capillary action, droplet formation, and the behavior of liquids at interfaces.

Option 2: Viscosity

Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction between fluid layers as they move past each other. While viscosity is an important property in fluid dynamics and affects the flow behavior of fluids, it is not related to the reciprocal of the specific volume. Viscosity is typically measured in units such as Pascal-seconds (Pa·s) or poise.

Option 4: Dynamic Viscosity

Dynamic viscosity, also known as absolute viscosity, is another term for viscosity. It quantifies the fluid's internal resistance to shear flow. As with option 2, dynamic viscosity is not related to the reciprocal of the specific volume. It is a different physical property that plays a significant role in characterizing the flow behavior of fluids.

In summary, the specific volume of a fluid is the reciprocal of its mass density. This relationship is fundamental in understanding the behavior and properties of fluids in various engineering and scientific applications. The other options, such as surface tension and viscosity, are important fluid properties but do not describe the reciprocal of specific volume.

By understanding the correct relationship between specific volume and mass density, engineers and scientists can accurately analyze and predict the behavior of fluids in different conditions, leading to more efficient and effective designs in thermal and fluid systems.

Important Information:

In practical applications, the concept of specific volume is widely used in the fields of thermodynamics, fluid mechanics, and heat transfer. For example, in the design of heat exchangers, the specific volume of the working fluid is crucial for determining the required size and configuration of the exchanger to achieve efficient heat transfer.

In the study of gas dynamics, the specific volume is an essential parameter in the analysis of compressible flow, where changes in pressure and temperature can significantly affect the volume occupied by the gas. Engineers use the specific volume to calculate properties such as the Mach number, which describes the ratio of the fluid velocity to the speed of sound in the medium.

Additionally, in the field of refrigeration and air conditioning, the specific volume of refrigerants is a key factor in determining the efficiency and performance of refrigeration cycles. By accurately measuring and controlling the specific volume, engineers can optimize the cooling capacity and energy consumption of refrigeration systems.

Overall, the specific volume is a critical parameter that provides valuable insights into the behavior of fluids under various conditions. Its inverse relationship with mass density is a fundamental concept that underpins many engineering analyses and designs, making it an essential topic for students and professionals in the field of thermal and fluid engineering.

Explanation:

Specific volume is the volume occupied by a unit mass of a substance. It is the reciprocal of density.

• Density (ρ) has units of kg/m³ (kilograms per cubic meter), which represents mass per unit volume.

• Specific Volume (v) is the inverse of density, so its unit is m³/kg (cubic meters per kilogram), which represents the volume per unit mass.

Additional Information Units of Other Options:

• kg/m³: This is the unit of density, not specific volume.

• m³/N: This is the unit of specific compliance in material science or elasticity.

• N/m²: This is the unit of pressure, also known as Pascals (Pa).

Explanation:

Dimension of Surface Tension

Definition: Surface tension is a physical property of a liquid that causes its surface to behave like a stretched elastic sheet. It arises due to cohesive forces between the liquid molecules, which are more strongly attracted to each other than to the surrounding air molecules. Surface tension is responsible for phenomena such as the formation of water droplets and the ability of some insects to walk on water.

Formula for Surface Tension:

Surface tension (T) is mathematically defined as the force (F) acting per unit length (L) of a liquid surface:

T = F/L

Here,

• F is the force, with a dimensional formula of M × L × T^-2, where:
  • M represents mass
  • L represents length
  • T represents time
• L is the length, with a dimensional formula of L.

Dimensional Analysis:

To find the dimensional formula of surface tension (T), substitute the dimensions of force (F) and length (L) into the formula:

T = F/L

Dimensional formula of T:

[T] = [F]/[L]

Substituting [F] = M × L × T^-2 and [L] = L:

[T] = (M × L × T^-2) / L

Canceling L in the numerator and denominator:

[T] = M × T^-2

Thus, the dimensional formula for surface tension is:

M × T^-2

Concept:

Specific gravity

• Specific gravity is also termed as relative density.
• The relative density/specific gravity of a substance is defined as the ratio of the density, mass or weight of the substance to the density, mass or weight of water at 4° C

\(Specific~gravity,S = \frac{\rho }{{{\rho _{water}}}}\)

Calculation:

Given:

Volume, V = 1 liter = 10^-3 m³,   mass, m = 7.5 kg

\(\rho = \frac{m}{V} = \frac{{7.5}}{{{{10}^{ - 3}}}} = 7500~\frac{{kg}}{{{m^3}}}\)

\(Specific~gravity,S = \frac{\rho }{{{\rho _{water}}}} = \frac{{7500}}{{1000}} = 7.5\)

CONCEPT:

Surface tension (S):

• It is the property by virtue of which the free surface of a liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy the minimum surface area.
• Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.
  \(Surface\;tension (S) = \frac{{Force (F)}}{{length(l)}}\)

• A small liquid drop has a spherical shape, as due to surface tension the liquid surface tries to have the minimum surface area and for a given volume, the sphere has a minimum surface area. Therefore option 3 is correct.

Applications of Surface Tension

• The warm soup tastes tasty because its surface tension is low at high temperatures and the soup spreads on all parts of the tongue.
• The phenomenon of the rising or fall of liquid level inside a capillary tube, when it is dipped in the liquid, is called capillary action.
• The capillary actions are due to surface tension.
• Capillary action draws the ink to the tips of fountain pen nibs from a reservoir or cartridge within the pen.

Explanation:

• ​The surface tension of water provides the necessary wall tension for the formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into spherical shapes.
• The pressure difference between the inside and outside of a bubble depends upon the surface tension and the radius of the bubble.
• The relationship can be obtained by visualizing the bubble as two hemispheres and noting that the internal pressure which tends to push the hemispheres apart is counteracted by the surface tension acting around the circumference of the circle.
• For a bubble with two surfaces providing tension, the pressure relationship is:

\(P_i - P_o = \frac{4T}{r}\)

Bubble Pressure: The net upward force on the top hemisphere of the bubble is just the pressure difference times the area of the equatorial circle:

\(F_{upward} = (P_i - P_o)\pi r^{2}\)

• The force of the surface tension downward on the entire circumference of the circle is twice the surface tension times the circumference since two surfaces contribute to the force.

\(F_{downward}= 2T(2 \pi r)\)

This gives

\(P_i - P_o = \frac{4T}{r} \) for a bubble

\(P_i - P_o = \frac{2T}{r} \) for a droplet that has only one surface.

Surface tension on a liquid droplet (Spherical droplet of water):

Pressure intensity inside the droplet:

\(p = \frac{{4σ }}{d}\)

In the question surface tension for the liquid droplet = A

Replacing σ with A in the above equation we get

\(A = \frac{{pd }}{4}\)

Surface tension on a hollow bubble (Soap bubble): w

Pressure intensity inside the bubble:

\(p = \frac{{8σ }}{d}\)

In the question, the surface tension in a hollow bubble = B

Replacing σ with b ion the above equation we get

\(B = \frac{{pd }}{8}\)

Thus, A = 2B

Mistake PointsIn this question surface tension of the bubble and drop has been asked, Don't confuse it with the pressure comparison.

Concept:

Newtonian fluids defined as fluids for which the shear stress is linearly proportional to the shear strain rate

Newtonian fluids are analogous to elastic solids (Hooke’s law: stress proportional to strain)

Any common fluids, such as air and other gases, water, kerosene, gasoline, and other oil-based liquids, are Newtonian fluids

\(\tau = \mu \frac{{du}}{{dy}}\) where μ is shear viscosity of the fluid

Fluids for which the shear stress is not linearly related to the shear strain rate are called non-Newtonian fluids

\(\tau = \mu {\left( {\frac{{du}}{{dy}}} \right)^n} + A\)

For Newtonian Fluid: A = 0 and n = 1 (Example: Air, Water, Glycerin)

\(\tau = \mu \left( {\frac{{du}}{{dy}}} \right)\)

For Bingham Plastic: A = τ0 and n = 1(Fluid does not move or deform until there is critical stress. Example: Toothpaste)

\(\tau = \mu \left( {\frac{{du}}{{dy}}} \right) + {\tau _0}\)

For Dilatant: A = 0 and n > 1 (Fluid starts ‘thickening' with an increase in its apparent viscosity. Example: starch or sand suspension or shear thickening fluid)

\(\tau = \mu {\left( {\frac{{du}}{{dy}}} \right)^n};n > 1\)

For Pseudo plastic: A = 0 and n < 1 (Fluid starts ‘thinning' with an increase in its apparent viscosity. Example: Paint, polymer solutions, colloidal suspensions or shear-thinning fluid)

\(\tau = \mu {\left( {\frac{{du}}{{dy}}} \right)^n};n < 1\)

Concept:

Compressibility is the reciprocal of the bulk modulus of elasticity.

Compressibility (p) = 1/K, and K = bulk modulus of Elasticity

\({\rm{K}} = \frac{{{\rm{Increase\;of\;pressure}}}}{{{\rm{Volumetric\;strain}}}} = \frac{{{\rm{dP}}}}{{\frac{{ - {\rm{dv}}}}{{\rm{v}}}}} = \frac{{ - {\rm{dP}}}}{{{\rm{dv}}}} \times {\rm{V}}\)      ----(i)

For isothermal process:

\(\frac{{\rm{P}}}{{\rm{\rho }}} = {\rm{Constant}} \Rightarrow {\rm{P}} \times {\rm{V}} = {\rm{constant}}\)      ----(ii)

Differentiating equation (ii),

PdV + Vdp = 0

⇒ PdV = -Vdp

\(\Rightarrow {\rm{P}} = \frac{{ - {\rm{VdP}}}}{{{\rm{dV}}}}\)      ----(iii)

From equation (i) & (iii), we have

K = P

For adiabatic condition, \(\frac{{\rm{P}}}{{{{\rm{\rho }}^{\rm{k}}}}} = \) constant, where k = Ratio of specific heats.

Bulk modulus, K = Pk

Explanation:

The relation between shear stress and rate of deformation i.e. velocity gradient can be represented by:

\(\tau=m\left ( \frac{du}{dy} \right )^n\)

where n = flow behavior index, m = consistency index.

For Newtonian fluid:

• Fluids for which shear stress (τ) is directly proportional to the deformation rate or velocity gradient are Newtonian fluid.
• m = μ and n = 1.

For non-Newtonian fluid:

• Fluids for which shear stress (τ) is not directly proportional to the deformation rate or velocity gradient are non-Newtonian fluid.
• It can be written as \(\tau=m\left ( \frac{du}{dy} \right )^{n-1}\left ( \frac{du}{dy} \right )=\mu\frac{du}{dy}\)
• where \(\mu=m\left ( \frac{du}{dy} \right )^{n-1}\)is apparent viscosity.
• As per the value of n, the non-Newtonian fluid is of various types which can be shown in the graph.

Ideal fluid:

• A fluid that is incompressible and is having no viscosity is known as an ideal fluid.
• Ideal fluid is an imaginary fluid as all the fluids, which exist, have some viscosity.

Real fluid:

• A fluid that possesses viscosity, is known as real fluid.
• All the fluid in practice is real fluids.

Newtonian fluid:

• Fluids for which shear stress (τ) is directly proportional to the deformation rate or velocity gradient are Newtonian fluid.

Non-Newtonian fluid:

• Fluids for which shear stress (τ) is not directly proportional to the deformation rate or velocity gradient are non-Newtonian fluid.

Pseudoplatsic: 

• Fine particle suspension, gelatine, clay, blood, milk, paper pulp, polymeric solutions such as rubbers, paints.

Dilatant fluids: 

• Ultrafine irregular particle suspension, sugar in water, aqueous suspension of rice starch, quicksand, butter printing ink.

Ideal plastics or Bingham plastic fluids:

• Sewage sludge, drilling muds, toothpaste.

Thixotropic: 

• Printer’s ink, crude oil, lipstick, certain paints and enamels

Rheopectic fluids: 

• Very rare liquid-solid suspensions, gypsum suspension in water and bentonite solutions.

Viscoelastic fluids: 

• Liquids solid combination in pipe flow, bitumen, tar, asphalt, polymerized fluids with drag reduction features.

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.
• The SI unit of viscosity is poiseiulle (Pl). Its other units are Nsm-2 or Pa s.

EXPLANATION:

• Surface tension is the property by virtue of which liquid tries to minimize its free surface area and it is measured as the force acting per unit length of an imaginary line drawn on the liquid surface. Therefore option 1 is incorrect.
• The force of attraction between molecules of same substance is called the force of cohesion. Therefore option 2 is incorrect.
• From above it is clear that the property by virtue of which liquid opposes relative motion between its different layers is called viscosity. Therefore option 3 is correct.
• If a tube of the very narrow bore (called capillary) is dipped in a liquid, it is found that the liquid in the capillary either ascends or descends relative to the surrounding liquid. This phenomenon is called capillarity. Therefore option 4 is incorrect.

• Cause of Viscosity: It is due to cohesion and molecular momentum exchange between fluid layers.
• C.G.S Unit of viscosity is Poise = dyne-sec/cm²
• One Poise = 0.1 Pa.s
• 1/100 Poise is called centipoises.

CONCEPT:

Surface Tension (σ) of a liquid:

• It is defined as the force per unit length in the plane of the liquid surface at right angles to either side of an imaginary line drawn on that surface.
• The SI unit of surface tension is N/m.

Mathematically, σ = F/L

where, σ = surface tension of liquid, F = force , L = length.

EXPLANATION: 

• Surface tension is the result of the cohesive force among the liquid molecules, which always tries to make the surface area of the liquid droplet minimum.
• The spherical shape of the drop is also the reason for surface tension.
• Detergent is sparingly soluble in water.
• The surface tension decreases when detergent is added to water.

Effect of impurities and temperature on surface tension:

Concept:

\(ρ=\frac{mass}{volume}⇒\frac{m}{V}\) kg/m³

Specific gravity (S.G): The specific gravity of a liquid is the relative weight of that liquid compared to an equal volume of water.

\(S.G= \frac{{Density\;of\;liquid}}{{Density\;of\;water}}⇒\frac{ρ}{ρ_w}\)

Specific volume (ν): It is the ratio of volume per unit mass.

\(\nu=\frac{volume}{mass}⇒\frac{V}{m}=\frac{1}{ρ}\) m³/kg

Calculation:

Given:

v = 0.000112 m3/kg.

\(\nu=\frac{V}{m}=\frac{1}{ρ}\)

\(0.000112=\frac{1}{ρ}\)

\(112\times10^{-6}=\frac{1}{ρ}\)

\(\rho=\frac{1}{112\times10^{-6}}=\frac{10^6}{112}\) kg/m³.

\(S.G= \frac{{Density\;of\;liquid}}{{Density\;of\;water}}⇒\frac{ρ}{ρ_w}\)

\(S.G= \frac{{Density\;of\;liquid}}{{Density\;of\;water}}⇒\frac{\frac{10^6}{112}}{1000}=\frac{1000}{112}=8.928\)

Concept:

The excess pressure inside the soap bubble is given by,

\({\rm{\Delta }}P = \frac{{4σ }}{R}\) 

where σ = Surface tension, R = Radius of bubble

Calculation:

Given:

D = 10 mm, R = 5 mm = 0.005 m σ = 0.04 N/m

\({\rm{\Delta }}P = \frac{{4\sigma }}{R} = \frac{{4 \times 0.04}}{{0.005}} = 32~Pa\)

Important Points

Excess pressure inside the droplet is given by,

\({\rm{\Delta }}P = \frac{{2\sigma }}{R}\)

Pressure in case of the liquid jet.

\({\rm{\Delta }}P = \frac{\sigma }{R}\)