Mechanical Properties of Fluids - Practice Questions with Answers

Q1.

Pressure at depth h in a fluid of density ρ is:

• A P₀ + ρgh
• B ρgh
• C P₀ - ρgh
• D ρg/h

Q2.

Pascal's law states:

• A Pressure applied to an enclosed fluid is transmitted equally in all directions
• B Pressure in a fluid increases linearly with depth below the surface as frequently described
• C The buoyant force equals the weight of fluid displaced by the body in most textbook accounts
• D Fluid usually flows from a region of high pressure to low pressure during normal conditions

Q3.

According to Archimedes' principle, the buoyant force on an object equals:

• A Weight of fluid displaced by the object
• B Weight of the object
• C Volume of fluid displaced times g
• D Density of fluid times volume of object

Q4.

An object floats when:

• A The buoyant force equals its weight
• B Its density equals the fluid density
• C Its volume exceeds the fluid volume
• D The fluid pressure equals atmospheric pressure

Q5.

The equation of continuity A₁ v₁ = A₂ v₂ represents conservation of:

• A Mass (for incompressible fluid)
• B Kinetic plus potential energy along the streamline
• C Linear momentum of the fluid element
• D Static pressure across the pipe cross-section

Q6.

In a narrower section of a pipe, the fluid flows:

• A Faster (by continuity equation)
• B Slower
• C At the same speed
• D Depends on fluid density

Q7.

Bernoulli's equation states that for steady flow of an ideal fluid:

• A P + ½ρv² + ρgh = constant along a streamline
• B P = ρgh holds at every point regardless of flow speed
• C P + ρv stays constant along the streamline
• D P equals ½ρv² with no dependence on height

Q8.

Torricelli's theorem gives the velocity of fluid efflux from a hole in a tank at depth h as:

• A v = √(2gh)
• B v = 2gh
• C v = √(gh)
• D v = gh

Q9.

Surface tension is defined as:

• A Force per unit length along the surface
• B Force per unit area
• C Energy per unit volume
• D Pressure difference across a surface

Q10.

In a hydraulic press with areas A₁ = 10 cm² and A₂ = 1000 cm², a force of 100 N on the small piston produces a force on the large piston of:

• A 10,000 N
• B 1 N
• C 100 N
• D 1000 N

Q11.

The excess pressure inside a soap bubble is:

• A 4T/r (two surfaces: inner and outer)
• B 2T/r, as for a single liquid drop with one surface
• C T/r, treating the film as having only one surface
• D 8T/r, double-counting both surfaces twice over

Q12.

Viscosity of a liquid generally:

• A Decreases with increasing temperature
• B Increases with increasing temperature
• C Is independent of temperature
• D Equals surface tension

Q13.

The buoyant force on a submerged object depends on:

• A The volume of the object (not its weight or density)
• B The weight of the object in air before submersion
• C The chemical composition or material of the object
• D Only the geometric shape of the object, regardless of size

Q14.

Capillary rise of water in a glass tube is due to:

• A Surface tension (adhesive forces between water and glass)
• B Atmospheric pressure acting only inside the narrow tube
• C Viscous drag dragging water along the tube walls
• D Gravitational attraction pulling water upward into the tube

Q15.

The density of water is 1000 kg/m³. The buoyant force on a 1 litre submerged object is:

• A 9.8 N
• B 1 N
• C 98 N
• D 10 N

Q16.

Relative density (specific gravity) of a material is:

• A Density of material / density of water
• B Density of water / density of material
• C Mass of material / mass of water
• D Volume of material / volume of water

Q17.

In streamline (laminar) flow, the fluid layers:

• A Flow smoothly in parallel without mixing
• B Mix chaotically as generally observed
• C Flow turbulently in typical laboratory settings
• D Create eddies and vortices under usual circumstances

Q18.

An airplane wing generates lift because:

• A Air flows faster above the wing (lower pressure) than below it
• B The wing's trailing edge pushes a downward jet of air with no pressure change
• C The wing is tilted so gravity components add to lift
• D Engine thrust is redirected vertically beneath the wing

Q19.

The angle of contact for water on a glass surface is:

• A Less than 90° (acute, water wets glass)
• B Greater than 90°, as for mercury on glass
• C Exactly 90°, where the meniscus is perfectly flat
• D Exactly 0°, where the surface is completely non-wetting

Q20.

Reynolds number determines:

• A Whether flow is laminar or turbulent
• B The absolute viscosity coefficient of the fluid
• C The static pressure head inside a pipe
• D The surface tension coefficient of the liquid

Q21.

Water flows in a pipe that narrows from diameter 4 cm to 2 cm. If water enters at 1 m/s, what is the speed in the narrow section?

• A 4 m/s
• B 0.25 m/s
• C 2 m/s
• D 1 m/s

Q22.

Water (ρ = 1000 kg/m³) flows in a horizontal pipe. At point 1: P = 4×10⁵ Pa, v = 2 m/s. At point 2 (same height): v = 6 m/s. Find P₂.

• A 2.4 × 10⁵ Pa
• B 4 × 10⁵ Pa
• C 5.6 × 10⁵ Pa
• D 3 × 10⁵ Pa

Q23.

A hole is made in a tank 1.25 m below the water surface. Water exits at speed:

• A 5 m/s
• B 2.5 m/s
• C 12.25 m/s
• D 1.25 m/s

Q24.

An object of mass 10 kg and density 2000 kg/m³ is submerged in water. The net downward force is:

• A 49 N
• B 98 N
• C 0 N
• D 24.5 N

Q25.

A capillary tube of radius 0.1 mm is dipped in water (T = 0.07 N/m, contact angle = 0, ρ = 1000 kg/m³). Height of capillary rise is:

• A 14.3 cm
• B 1.43 cm
• C 143 cm
• D 0.143 cm

Q26.

The velocity of efflux from a tank depends only on the depth of the hole below the water surface (not tank dimensions). This is called:

• A Torricelli's theorem
• B Bernoulli's principle
• C Pascal's law
• D Archimedes' principle

Q27.

A steel ball (density 7800 kg/m³) falls in water. As it reaches terminal velocity, the viscous drag force equals:

• A Weight - Buoyant force (net weight in fluid)
• B The full weight of the ball measured in air
• C Zero, since the ball is still accelerating at terminal velocity
• D The buoyant force alone, ignoring the ball's actual weight

Q28.

Two identical bubbles of soap merge. The radius of the resulting bubble (same temperature and pressure) is:

• A r_new = r × 2^1/3 ≈ 1.26r
• B r_new = 2r, as if the radii generally added together
• C r_new = r√2, as if the surface areas generally added
• D r_new = r/√2, shrinking instead of growing on merging

Q29.

The Venturi meter principle uses Bernoulli's equation. If a fluid of density ρ passes through a constriction of area A₂ (< A₁), the pressure drop ΔP is:

• A ΔP = ½ρ v₂²(1 - (A₂/A₁)²)
• B ΔP = ρ v₂² as frequently described
• C ΔP = ρg(h₁-h₂) in most textbook accounts
• D ΔP = ½ρ(v₂-v₁)² during normal conditions

Q30.

Terminal velocity of a sphere of radius r falling in a fluid of viscosity η (Stokes law) is:

• A v_t = 2r²(ρ-σ)g/9η
• B v_t = 6πηrv
• C v_t = r(ρ-σ)/η
• D v_t = 4πr³ρg/3

Q31.

In a dam, the force on the wall increases with depth because:

• A Pressure increases with depth, so average pressure × area gives total force
• B Water at every depth pushes on the wall with exactly equal pressure
• C Temperature variation with depth is what raises the hydrostatic pressure
• D The flow velocity of standing water increases with depth

Q32.

A boat carrying iron cubes floats in a pond. If the cubes are thrown overboard and sink, the water level:

• A Falls (iron displaced less water when submerged than when floating)
• B Rises, since the total mass of boat plus cubes hasn't changed
• C Stays exactly the same regardless of how the cubes are distributed
• D Depends only on the density of iron relative to the boat's hull

Q33.

The dynamic pressure of a fluid flowing at velocity v is:

• A ½ρv²
• B ρv²
• C ρv
• D 2ρv²

Q34.

Poiseuille's law for viscous flow through a tube states that flow rate Q is proportional to:

• A r⁴/L (fourth power of radius divided by length)
• B r²/L, as if flow rate scaled only with cross-sectional area
• C r/L, a linear dependence on radius alone
• D r³/L, an intermediate power between area and the true relation

Q35.

An ice cube floats in a glass of water. When it melts completely, the water level:

• A Stays the same
• B Rises
• C Falls
• D Depends on ice density

Q36.

The pressure difference between the inside and outside of a liquid droplet of radius r is:

• A 2T/r
• B 4T/r
• C T/r
• D T/2r

Q37.

A swimmer underwater feels a greater pressure than at the surface. At 10 m depth in sea water (ρ = 1025 kg/m³), the pressure is approximately:

• A 2 atm (1 atm atmospheric + 1 atm from water column)
• B 10 atm, mistakenly equating 10 m of depth to 10 atm directly
• C 1 atm, ignoring the added pressure of the overlying water column
• D 5 atm, from incorrectly halving the depth-to-pressure conversion

Q38.

A gas bubble rises from the bottom of a lake (depth 10 m). When it reaches the surface, its volume:

• A Doubles (pressure halves)
• B Stays the same as generally observed
• C Quadruples in typical laboratory settings
• D Halves under usual circumstances

Q39.

The work done to blow a soap bubble of radius R from zero is:

• A 8πR² T
• B 2πR² T
• C 4πR² T
• D 16πR² T

Q40.

The Magnus effect (a spinning ball curves in flight) is due to:

• A Pressure difference created by Bernoulli effect on two sides of spinning ball
• B Gravity alone curving the ball's path sideways during flight according to most researchers
• C Plain air resistance acting uniformly on a non-spinning ball in the majority of cases studied
• D A centrifugal force acting outward on the spinning ball's surface as widely reported

Q41.

A tank of large cross-section has a hole of area a at depth h. The range of the horizontal jet of water on the ground (if the hole is at height H from ground) is:

• A x = 2√(h(H-h))
• B x = √(2gH)
• C x = √(gh)
• D x = 2H

Q42.

Two holes are at depths h₁ and h₂ from the water surface of a tank. Their ranges on the ground are equal. The relationship is:

• A h₁ + h₂ = H (total tank height)
• B h₁ = h₂, meaning the two holes are at the same depth
• C h₁ × h₂ = H², an incorrect product relation with the tank height
• D h₁ = 2h₂, an arbitrary fixed ratio between the two depths

Q43.

A sphere of density ρ_s, radius r, falls in a liquid of density ρ_l and viscosity η. At terminal velocity, the coefficient of viscosity is:

• A η = 2r²(ρ_s - ρ_l)g/9v_t
• B η = 9v_t/(2r² g) in standard practice
• C η = 6πrv_t under most conditions encountered
• D η = 2r² v_t as frequently observed in practice

Q44.

Two soap bubbles of radii r₁ and r₂ are connected by a tube. If r₁ > r₂, what happens?

• A Smaller bubble (r₂) shrinks and larger (r₁) grows
• B The larger bubble shrinks while the smaller one grows instead
• C Both bubbles settle to exactly the same final equilibrium radius
• D Neither bubble's size changes once they are connected by the tube

Q45.

A siphon transfers liquid from a container to a lower level. The maximum height h the siphon can reach above the container level is:

• A h = P_atm/(ρg) ≈ 10.3 m for water
• B h = ∞, since a siphon can theoretically rise to any height
• C h = 5 m, a fixed value independent of atmospheric pressure
• D h = 1 m, a fixed value independent of fluid density or pressure

Q46.

Blood flows in an artery of diameter 4 mm with speed 0.4 m/s. If the artery narrows to 2 mm diameter, the speed becomes:

• A 1.6 m/s
• B 0.1 m/s
• C 0.8 m/s
• D 6.4 m/s

Q47.

The angle of contact θ of a liquid in a capillary tube determines the direction of capillary flow. For mercury on glass (θ ≈ 135°):

• A Capillary depression occurs (mercury is pushed down)
• B Capillary rise occurs, exactly as it does for water in a glass tube
• C No capillary effect occurs for an obtuse angle of contact
• D Mercury overflows out of the top of the capillary tube largely

Q48.

A fluid undergoes rotational flow where velocity v = ωr at all points (rigid rotation). The pressure increases radially as:

• A dP/dr = ρω²r
• B dP/dr = ρv
• C dP/dr = -ρω²r
• D dP/dr = ρg

Q49.

Two pistons in a hydraulic system have areas 1 cm² and 50 cm². For a load of 500 N on the large piston, the required force on the small piston is 10 N. If the small piston moves down by 50 cm, the large piston moves up by:

• A 1 cm
• B 50 cm
• C 100 cm
• D 0.02 cm

Q50.

The rate of flow through a capillary tube is measured by Poiseuille: Q = πr⁴ΔP/8ηL. If the tube radius is halved, the flow rate:

• A Decreases by factor 16
• B Decreases by factor 2
• C Increases by factor 16
• D Decreases by factor 4

Q51.

In Stokes' law, the drag force on a sphere of radius r moving at velocity v is F = 6πηrv. This gives terminal velocity ∝ r². If two spheres have radii in ratio 2:1, their terminal velocities are in ratio:

• A 4:1
• B 2:1
• C 1:4
• D 8:1

Q52.

A hollow sphere and a solid sphere of the same external dimensions are placed in water. The hollow sphere floats while the solid sphere sinks. This is because:

• A The hollow sphere has lower average density than water while solid sphere has higher density
• B The hollow sphere is generally lighter in absolute weight than the solid one in many documented cases
• C Water seeps into the hollow sphere's interior cavity through tiny pores according to conventional understanding
• D The hollow sphere has a larger exposed surface area than the solid one in routine practice

Q53.

The work done per unit area to create a new surface of liquid is the surface energy. For a soap film of area A, the total surface energy is:

• A 2TA (factor 2 for two surfaces)
• B TA, counting only a single surface of the soap film
• C 4TA, double-counting both surfaces of the film twice over
• D T/A, dividing the surface tension by the area instead of multiplying

Q54.

Bernoulli's equation breaks down for:

• A Turbulent, viscous, or compressible flows
• B Slow, steady laminar flows of an ideal incompressible fluid
• C Flows occurring at a uniformly low absolute pressure
• D Flows confined to perfectly horizontal pipes of constant area

Q55.

An object of density ρ = 0.6 g/cm³ floats in water. The fraction of its volume above water is:

• A 0.4 (40%)
• B 0.6 (60%)
• C 0.5 (50%)
• D 0.1 (10%)

Q56.

In a horizontal Venturi meter, the throat (narrow section) has area A_t = A/2 where A is pipe area. Fluid density ρ, velocity at pipe entrance v. The height difference Δh in the manometer (density ρ_m) is:

• A Δh = 3ρv²/(2(ρ_m - ρ)g)
• B Δh = ρv²/2ρ_m g overall
• C Δh = v²/2g in most cases
• D Δh = 4ρv²/ρ_m g under typical conditions

Q57.

Dimensional analysis shows that surface tension has dimensions of:

• A [MT⁻²] (force per length = energy per area)
• B [MLT⁻²], the dimensional formula for force itself
• C [ML⁻¹T⁻²], the dimensional formula for pressure or stress
• D [ML²T⁻²], the dimensional formula for energy or work

Q58.

The critical velocity above which flow becomes turbulent in a tube of diameter d is approximately (Reynolds number ≈ 2000):

• A v_c = 2000η/(ρd)
• B v_c = 2000ρd
• C v_c = η/(ρd)
• D v_c = ρd/η

Q59.

A barometer uses mercury (ρ = 13600 kg/m³). Atmospheric pressure 10⁵ Pa corresponds to a mercury column height of:

• A 0.735 m (73.5 cm)
• B 10 m according to standard textbooks
• C 13.6 m in general practice
• D 1 m as frequently described

Q60.

A steel needle can float on water even though steel is denser than water. This is due to:

• A Surface tension creating a curved water surface that supports the needle
• B Ordinary buoyant force alone, as with any floating dense object in most textbook accounts
• C The needle being hollow and filled with trapped air inside during normal conditions
• D A pocket of air trapped directly underneath the solid needle as generally observed

Q61.

Water flows out of a small hole in a tank at a depth of 5 m below the surface (g = 10 m/s²). The efflux speed is:

• A 5 m/s
• B 10 m/s
• C 20 m/s
• D 7 m/s

Q62.

Water flows through a pipe whose cross-sectional area changes from 4A to A. The ratio of speeds in the wide to the narrow section is:

• A 4:1
• B 1:4
• C 2:1
• D 1:2

Q63.

A spherical drop falls at terminal velocity through a viscous fluid. If its radius is doubled, its terminal velocity becomes:

• A 2×
• B 4×
• C 8×
• D unchanged

Q64.

A soap bubble of radius 2 mm has surface tension 0.03 N/m. The excess pressure inside it is:

• A 15 Pa
• B 30 Pa
• C 60 Pa
• D 120 Pa

Q65.

In a hydraulic press, the small piston has area 0.01 m² and the large piston 0.1 m². A force of 100 N on the small piston produces on the large piston a force of:

• A 100 N
• B 1000 N
• C 10 N
• D 10000 N

Q66.

The rate of laminar flow through a tube is proportional to the fourth power of its radius. If the radius is halved, the flow rate becomes:

• A 1/2
• B 1/4
• C 1/8
• D 1/16

Q67.

An iceberg floats in sea water with density 900 kg/m³ for ice and 1000 kg/m³ for water. The fraction of its volume below the surface is:

• A 0.1
• B 0.5
• C 0.9
• D 1.0

Q68.

A capillary tube of radius r shows a liquid rise h. If a tube of radius r/2 is used, the rise becomes:

• A h/2
• B h
• C 2h
• D 4h