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

Explanation:

Specific Gravity

Dimensional Formula: [M⁰ L⁰ T⁰] 

• Definition: It is the ratio of the density of a fluid to the density of a reference fluid (typically water for liquids).

• It is a pure number — has no units or dimensions because it is a ratio of two densities.

• Importance: It indicates how heavy or light a fluid is compared to water, useful in many hydraulic and civil engineering applications.

 Additional InformationCoefficient of Viscosity (Dynamic viscosity, μ)

Dimensional Formula: [M L⁻¹ T⁻¹] 

• Definition: It measures a fluid’s internal resistance to flow when subjected to a shear force.

• Units: Pascal-second (Pa·s) or Ns/m² — higher viscosity = more resistance (e.g., honey vs water).

 Kinematic Viscosity (ν)

Dimensional Formula: [L² T⁻¹] 

• Definition: It is the ratio of dynamic viscosity to fluid density.​

• Represents how fast a fluid flows under gravity’s effect, not just internal resistance.

• Units: m²/s — higher ν means fluid spreads faster (e.g., air vs oil).

Stress

Dimensional Formula: [M L⁻¹ T⁻²] 

• Definition: It is force per unit area acting inside a material due to externally applied forces.​

• Types: Normal stress (tension/compression), shear stress.

• Units: Pascal (Pa) = N/m² — crucial in strength and structural design.

Explanation:

• Dynamic viscosity (μ), also called absolute viscosity, is defined as the measure of the internal resistance of a fluid to flow when an external force is applied.
• It expresses the relationship between shear stress and velocity gradient within the fluid.

• It quantifies the force required to move one layer of fluid over another.

• A fluid with high dynamic viscosity (such as honey) resists flow more than a fluid with low dynamic viscosity (such as water).

• SI Unit: Pa·s or Ns/m²

 Additional Information

•  Kinematic viscosity (ν) is defined as the ratio of dynamic viscosity (μ) to the density of the fluid (ρ). It measures the fluid’s resistance to flow under the effect of gravity rather than an applied force.

• It describes how easily a fluid flows in a gravitational field.

• Important in flow problems where both viscosity and density influence motion (e.g., in calculating Reynolds number).

• SI Unit: m²/s

Explanation:

Viscosity

• It is the property of a fluid that resists motion or flow.

• It measures the internal friction within the fluid as different layers move past one another.

• Higher viscosity means a thicker fluid (like honey), lower viscosity means a thinner fluid (like water).

• Mathematically related to shear stress and velocity gradient in fluid mechanics.

 Additional Information

Surface Tension

• It is the property of the surface of a liquid that causes it to behave like a stretched elastic membrane.

• Responsible for the spherical shape of droplets and phenomena like insects walking on water.

• Caused by cohesive forces between liquid molecules at the surface.

Compressibility

• It measures the ability of a fluid to change its volume under the effect of pressure.

• Gases are highly compressible, liquids are only slightly compressible.

• Important in aerodynamics, hydraulics, and designing pressurized systems.

Capillarity (Capillary Action)

• It is the ability of a fluid to rise or fall in a narrow tube against gravity.

• Caused by the combination of adhesive forces between fluid and surface and cohesive forces within the fluid.

• Commonly seen in soils, plant roots, and thin tubes (capillary tubes).

Explanation:

• Dynamic viscosity of water decreases with increase in temperature.

• As temperature rises, intermolecular forces weaken, making fluid layers slide more easily.

• For gases like air, dynamic viscosity increases with temperature.

• Higher temperature leads to more molecular motion, increasing momentum transfer between layers.

 Additional Information Dynamic Viscosity (μ)

• It measures a fluid’s resistance to flow when an external force is applied.

• Represents internal friction between fluid layers moving at different velocities.

• SI unit: Pascal-second (Pa·s) or N·s/m².

• For liquids, μ decreases as temperature increases.

• For gases, μ increases with temperature.

• Used in calculating shear stress and analyzing force in fluid motion.

Kinematic Viscosity (ν)

• It is the ratio of dynamic viscosity to fluid density.

• Describes how easily a fluid flows under gravity.

• SI unit: m²/s.

• $\nu = \mu / \rho$ — higher ν means more sluggish flow.

• Depends on both viscosity and density of fluid.

• Useful in flow problems where gravity and motion dominate over external forces.

Explanation:

Density:

• The density of a substance is defined as its mass per unit volume. Mathematically, it can be expressed as:

Density (ρ) = Mass (m) / Volume (V)

Water, one of the most studied substances, has a well-documented density. At room temperature, which is generally considered to be around 25°C (298 K), the density of pure water is approximately:

• 1 gram per cubic centimeter (1 gm/cm³) in the CGS (Centimeter-Gram-Second) system.
• 1000 kilograms per cubic meter (1000 kg/m³) in the SI (International System of Units).

These values are widely accepted and utilized in both scientific and engineering calculations. It is important to note that the density of water can vary slightly depending on temperature and pressure, but at room temperature, the values mentioned above are accurate and standardized.

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

$Specificgravity,S=\frac{\rho }{{\rho }_{water}}$

Calculation:

Given:

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

$\rho =\frac{m}{V}=\frac{7.5}{{10}^{-3}}=7500\frac{kg}{m^3}$

$Specificgravity,S=\frac{\rho }{{\rho }_{water}}=\frac{7500}{1000}=7.5$

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.
  $Surfacetension(S)=\frac{Force(F)}{length(l)}$

• 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:

$p=\frac{4\sigma }{d}$

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:

$p=\frac{8\sigma }{d}$

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

$\mathrm{K}=\frac{\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}}{\mathrm{V}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}}=\frac{\mathrm{d}\mathrm{P}}{\frac{-\mathrm{d}\mathrm{v}}{\mathrm{v}}}=\frac{-\mathrm{d}\mathrm{P}}{\mathrm{d}\mathrm{v}}\times \mathrm{V}$      ----(i)

For isothermal process:

$\frac{\mathrm{P}}{\rho }=\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\Rightarrow \mathrm{P}\times \mathrm{V}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$      ----(ii)

Differentiating equation (ii),

PdV + Vdp = 0

⇒ PdV = -Vdp

$\Rightarrow \mathrm{P}=\frac{-\mathrm{V}\mathrm{d}\mathrm{P}}{\mathrm{d}\mathrm{V}}$      ----(iii)

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

K = P

For adiabatic condition, $\frac{\mathrm{P}}{{\rho }^{\mathrm{k}}}=$ 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:

$\rho =\frac{mass}{volume}\Rightarrow \frac{m}{V}$ 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.

$S.G=\frac{Densityofliquid}{Densityofwater}\Rightarrow \frac{\rho }{{\rho }_w}$

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

$\nu =\frac{volume}{mass}\Rightarrow \frac{V}{m}=\frac{1}{\rho }$ m³/kg

Calculation:

Given:

v = 0.000112 m3/kg.

$\nu =\frac{V}{m}=\frac{1}{\rho }$

$0.000112=\frac{1}{\rho }$

$112\times {10}^{-6}=\frac{1}{\rho }$

$\rho =\frac{1}{112\times {10}^{-6}}=\frac{{10}^6}{112}$ kg/m³.

$S.G=\frac{Densityofliquid}{Densityofwater}\Rightarrow \frac{\rho }{{\rho }_w}$

$S.G=\frac{Densityofliquid}{Densityofwater}\Rightarrow \frac{\frac{{10}^6}{112}}{1000}=\frac{1000}{112}=8.928$

Concept:

The excess pressure inside the soap bubble is given by,

$\mathrm{\Delta }P=\frac{4\sigma }{R}$ 

where σ = Surface tension, R = Radius of bubble

Calculation:

Given:

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

$\mathrm{\Delta }P=\frac{4\sigma }{R}=\frac{4\times 0.04}{0.005}=32Pa$

Important Points

Excess pressure inside the droplet is given by,

$\mathrm{\Delta }P=\frac{2\sigma }{R}$

Pressure in case of the liquid jet.

$\mathrm{\Delta }P=\frac{\sigma }{R}$