83 practice questions on Mechanical Properties of Fluids , sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Mechanical Properties of Fluids notes .
Continuity Equation: Narrow Pipe → Faster Flow A₁, v₁ (wide, slow) A₂, v₂ (narrow, fast) A₁v₁ = A₂v₂ (continuity) Smaller area → higher speed → (by Bernoulli) LOWER pressure Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Easy - 25 questions Q1.
The SI unit of the coefficient of viscosity is:
A N s m<sup>-2</sup>B kg m s<sup>-1</sup>C N m<sup>-1</sup>D Pa mShow answer & explanation →
Q2.
When the temperature of a liquid rises, its surface tension generally:
A increasesB decreasesC remains unchangedD first rises then fallsShow answer & explanation →
Q3.
Adding soap or detergent to water:
A leaves it unchangedB raises its surface tensionC lowers its surface tensionD raises its density sharplyShow answer & explanation →
Q4.
The pressure exerted by a fluid at rest at a point acts:
A only vertically downwardB only along the container wallsC only vertically upwardD equally in all directionsShow answer & explanation →
Q5.
Small liquid drops become spherical because surface tension tends to:
A minimise its surface areaB maximise its surface areaC increase its volumeD lower its densityShow answer & explanation →
Q7.
Pascal's law states:
A Pressure applied to an enclosed fluid is transmitted equally in all directionsB Pressure in a fluid increases linearly with depth below the surface as frequently describedC The buoyant force equals the weight of fluid displaced by the body in most textbook accountsD Fluid usually flows from a region of high pressure to low pressure during normal conditionsShow answer & explanation →
Q8.
According to Archimedes' principle, the buoyant force on an object equals:
A Weight of fluid displaced by the objectB Weight of the objectC Volume of fluid displaced times gD Density of fluid times volume of objectShow answer & explanation →
Q9.
An object floats when:
A The buoyant force equals its weightB Its density equals the fluid densityC Its volume exceeds the fluid volumeD The fluid pressure equals atmospheric pressureShow answer & explanation →
Q10.
The equation of continuity A<sub>1</sub> v<sub>1</sub> = A<sub>2</sub> v<sub>2</sub> represents conservation of:
A Mass (for incompressible fluid)B Kinetic plus potential energy along the streamlineC Linear momentum of the fluid elementD Static pressure across the pipe cross-sectionShow answer & explanation →
Q11.
In a narrower section of a pipe, the fluid flows:
A Faster (by continuity equation)B SlowerC At the same speedD Depends on fluid densityShow answer & explanation →
Q12.
Bernoulli's equation states that for steady flow of an ideal fluid:
A P + ½ρv² + ρgh = constant along a streamlineB P = ρgh holds at every point regardless of flow speedC P + ρv stays constant along the streamlineD P equals ½ρv² with no dependence on heightShow answer & explanation →
Q13.
Torricelli's theorem gives the velocity of fluid efflux from a hole in a tank at depth h as:
A v = √(2gh)B v = 2ghC v = √(gh)D v = ghShow answer & explanation →
Q14.
Surface tension is defined as:
A Force per unit length along the surfaceB Force per unit areaC Energy per unit volumeD Pressure difference across a surfaceShow answer & explanation →
Q15.
In a hydraulic press with areas A<sub>1</sub> = 10 cm² and A<sub>2</sub> = 1000 cm², a force of 100 N on the small piston produces a force on the large piston of:
A 10,000 NB 1 NC 100 ND 1000 NShow answer & explanation →
Q16.
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 surfaceC T/r, treating the film as having only one surfaceD 8T/r, double-counting both surfaces twice overShow answer & explanation →
Q17.
Viscosity of a liquid generally:
A Decreases with increasing temperatureB Increases with increasing temperatureC Is independent of temperatureD Equals surface tensionShow answer & explanation →
Q18.
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 submersionC The chemical composition or material of the objectD Only the geometric shape of the object, regardless of sizeShow answer & explanation →
Q19.
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 tubeC Viscous drag dragging water along the tube wallsD Gravitational attraction pulling water upward into the tubeShow answer & explanation →
Q21.
Relative density (specific gravity) of a material is:
A Density of material / density of waterB Density of water / density of materialC Mass of material / mass of waterD Volume of material / volume of waterShow answer & explanation →
Q22.
In streamline (laminar) flow, the fluid layers:
A Flow smoothly in parallel without mixingB Mix chaotically as generally observedC Flow turbulently in typical laboratory settingsD Create eddies and vortices under usual circumstancesShow answer & explanation →
Q23.
An airplane wing generates lift because:
A Air flows faster above the wing (lower pressure) than below itB The wing's trailing edge pushes a downward jet of air with no pressure changeC The wing is tilted so gravity components add to liftD Engine thrust is redirected vertically beneath the wingShow answer & explanation →
Q24.
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 glassC Exactly 90°, where the meniscus is perfectly flatD Exactly 0°, where the surface is completely non-wettingShow answer & explanation →
Q25.
Reynolds number determines:
A Whether flow is laminar or turbulentB The absolute viscosity coefficient of the fluidC The static pressure head inside a pipeD The surface tension coefficient of the liquidShow answer & explanation →
Medium - 25 questions Q26.
Water flows through a horizontal pipe of cross-section 6 cm<sup>2</sup> at 2 m/s. Where the pipe narrows to 1.5 cm<sup>2</sup>, the flow speed becomes:
A 4 m/sB 8 m/sC 6 m/sD 12 m/sShow answer & explanation →
Q27.
In a U-tube, oil of density 800 kg m<sup>-3</sup> in one arm balances a water column in the other. If the oil column is 10 cm, the balancing water column is:
A 12.5 cmB 8 cmC 6.4 cmD 10 cmShow answer & explanation →
Q28.
A wooden block floats in water with 80% of its volume submerged. Its density is:
A 600 kg m<sup>-3</sup>B 900 kg m<sup>-3</sup>C 800 kg m<sup>-3</sup>D 1250 kg m<sup>-3</sup>Show answer & explanation →
Q29.
Water flows at 4 m/s in a pipe of radius 2 cm. Where the pipe narrows to radius 1 cm, the speed becomes:
A 4 m/sB 8 m/sC 2 m/sD 16 m/sShow answer & explanation →
Q30.
Water (ρ = 1000 kg m<sup>-3</sup>) speeds up from 3 m/s to 5 m/s along a horizontal pipe. The pressure drop is:
A 4000 PaB 8000 PaC 16000 PaD 2000 PaShow answer & explanation →
Q31.
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/sB 0.25 m/sC 2 m/sD 1 m/sShow answer & explanation →
Q32.
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 P<sub>2</sub>.
A 2.4 × 10⁵ PaB 4 × 10⁵ PaC 5.6 × 10⁵ PaD 3 × 10⁵ PaShow answer & explanation →
Q33.
A hole is made in a tank 1.25 m below the water surface. Water exits at speed:
A 5 m/sB 2.5 m/sC 12.25 m/sD 1.25 m/sShow answer & explanation →
Q34.
An object of mass 10 kg and density 2000 kg/m³ is submerged in water. The net downward force is:
A 49 NB 98 NC 0 ND 24.5 NShow answer & explanation →
Q35.
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 cmB 1.43 cmC 143 cmD 0.143 cmShow answer & explanation →
Q36.
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 theoremB Bernoulli's principleC Pascal's lawD Archimedes' principleShow answer & explanation →
Q37.
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 airC Zero, since the ball is still accelerating at terminal velocityD The buoyant force alone, ignoring the ball's actual weightShow answer & explanation →
Q38.
Two identical bubbles of soap merge. The radius of the resulting bubble (same temperature and pressure) is:
A r<sub>new</sub> = r × 2<sup>1/3</sup> ≈ 1.26rB r<sub>new</sub> = 2r, as if the radii generally added togetherC r<sub>new</sub> = r√2, as if the surface areas generally addedD r<sub>new</sub> = r/√2, shrinking instead of growing on mergingShow answer & explanation →
Q39.
The Venturi meter principle uses Bernoulli's equation. If a fluid of density ρ passes through a constriction of area A<sub>2</sub> (< A<sub>1</sub>), the pressure drop ΔP is:
A ΔP = ½ρ v<sub>2</sub>²(1 - (A<sub>2</sub>/A<sub>1</sub>)²)B ΔP = ρ v<sub>2</sub>² as frequently describedC ΔP = ρg(h<sub>1</sub>-h<sub>2</sub>) in most textbook accountsD ΔP = ½ρ(v<sub>2</sub>-v<sub>1</sub>)² during normal conditionsShow answer & explanation →
Q40.
Terminal velocity of a sphere of radius r falling in a fluid of viscosity η (Stokes law) is:
A v<sub>t</sub> = 2r²(ρ-σ)g/9ηB v<sub>t</sub> = 6πηrvC v<sub>t</sub> = r(ρ-σ)/ηD v<sub>t</sub> = 4πr³ρg/3Show answer & explanation →
Q41.
In a dam, the force on the wall increases with depth because:
A Pressure increases with depth, so average pressure × area gives total forceB Water at every depth pushes on the wall with exactly equal pressureC Temperature variation with depth is what raises the hydrostatic pressureD The flow velocity of standing water increases with depthShow answer & explanation →
Q42.
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 changedC Stays exactly the same regardless of how the cubes are distributedD Depends only on the density of iron relative to the boat's hullShow answer & explanation →
Q44.
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 areaC r/L, a linear dependence on radius aloneD r³/L, an intermediate power between area and the true relationShow answer & explanation →
Q45.
An ice cube floats in a glass of water. When it melts completely, the water level:
A Stays the sameB RisesC FallsD Depends on ice densityShow answer & explanation →
Q47.
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 directlyC 1 atm, ignoring the added pressure of the overlying water columnD 5 atm, from incorrectly halving the depth-to-pressure conversionShow answer & explanation →
Q48.
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 observedC Quadruples in typical laboratory settingsD Halves under usual circumstancesShow answer & explanation →
Q50.
The Magnus effect (a spinning ball curves in flight) is due to:
A Pressure difference created by Bernoulli effect on two sides of spinning ballB Gravity alone curving the ball's path sideways during flight according to most researchersC Plain air resistance acting uniformly on a non-spinning ball in the majority of cases studiedD A centrifugal force acting outward on the spinning ball's surface as widely reportedShow answer & explanation →
Hard - 33 questions Q51.
A spherical water drop of radius 0.5 mm has surface tension 0.072 N/m. The excess pressure inside the drop is:
A 576 PaB 144 PaC 72 PaD 288 PaShow answer & explanation →
Q52.
Two solid spheres of the same material, radii in ratio 3:1, fall through the same viscous fluid. The ratio of their terminal velocities is:
A 3 : 1B 6 : 1C 9 : 1D 27 : 1Show answer & explanation →
Q53.
A hole is 0.5 m below the water surface of a tank, and 2 m above the ground (g = 10 m/s<sup>2</sup>). The horizontal range of the jet is:
Show answer & explanation →
Q54.
By Poiseuille law (Q ∝ r<sup>4</sup>/L), if a tube radius is doubled and its length is also doubled, the flow rate changes by a factor of:
A 4 timesB 8 timesC 16 timesD 2 timesShow answer & explanation →
Q55.
A tank has water 3.2 m deep with a hole of area 2 cm<sup>2</sup> at the bottom (g = 10 m/s<sup>2</sup>). The volume flow rate through the hole is:
A 0.8 L/sB 3.2 L/sC 1.6 L/sD 0.4 L/sShow answer & explanation →
Q56.
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 = 2HShow answer & explanation →
Q57.
Two holes are at depths h<sub>1</sub> and h<sub>2</sub> from the water surface of a tank. Their ranges on the ground are equal. The relationship is:
A h<sub>1</sub> + h<sub>2</sub> = H (total tank height)B h<sub>1</sub> = h<sub>2</sub>, meaning the two holes are at the same depthC h<sub>1</sub> × h<sub>2</sub> = H², an incorrect product relation with the tank heightD h<sub>1</sub> = 2h<sub>2</sub>, an arbitrary fixed ratio between the two depthsShow answer & explanation →
Q58.
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<sub>t</sub>B η = 9v<sub>t</sub>/(2r² g) in standard practiceC η = 6πrv_t under most conditions encounteredD η = 2r² v<sub>t</sub> as frequently observed in practiceShow answer & explanation →
Q59.
Two soap bubbles of radii r<sub>1</sub> and r<sub>2</sub> are connected by a tube. If r<sub>1</sub> > r<sub>2</sub>, what happens?
A Smaller bubble (r<sub>2</sub>) shrinks and larger (r<sub>1</sub>) growsB The larger bubble shrinks while the smaller one grows insteadC Both bubbles settle to exactly the same final equilibrium radiusD Neither bubble's size changes once they are connected by the tubeShow answer & explanation →
Q60.
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<sub>atm</sub>/(ρg) ≈ 10.3 m for waterB h = ∞, since a siphon can theoretically rise to any heightC h = 5 m, a fixed value independent of atmospheric pressureD h = 1 m, a fixed value independent of fluid density or pressureShow answer & explanation →
Q61.
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/sB 0.1 m/sC 0.8 m/sD 6.4 m/sShow answer & explanation →
Q62.
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 tubeC No capillary effect occurs for an obtuse angle of contactD Mercury overflows out of the top of the capillary tube largelyShow answer & explanation →
Q63.
A fluid undergoes rotational flow where velocity v = ωr at all points (rigid rotation). The pressure increases radially as:
A dP/dr = ρω²rB dP/dr = ρvC dP/dr = -ρω²rD dP/dr = ρgShow answer & explanation →
Q64.
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 cmB 50 cmC 100 cmD 0.02 cmShow answer & explanation →
Q65.
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 16B Decreases by factor 2C Increases by factor 16D Decreases by factor 4Show answer & explanation →
Q66.
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:
Show answer & explanation →
Q67.
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 densityB The hollow sphere is generally lighter in absolute weight than the solid one in many documented casesC Water seeps into the hollow sphere's interior cavity through tiny pores according to conventional understandingD The hollow sphere has a larger exposed surface area than the solid one in routine practiceShow answer & explanation →
Q68.
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 filmC 4TA, double-counting both surfaces of the film twice overD T/A, dividing the surface tension by the area instead of multiplyingShow answer & explanation →
Q69.
Bernoulli's equation breaks down for:
A Turbulent, viscous, or compressible flowsB Slow, steady laminar flows of an ideal incompressible fluidC Flows occurring at a uniformly low absolute pressureD Flows confined to perfectly horizontal pipes of constant areaShow answer & explanation →
Q70.
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%)Show answer & explanation →
Q71.
In a horizontal Venturi meter, the throat (narrow section) has area A<sub>t</sub> = 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 overallC Δh = v²/2g in most casesD Δh = 4ρv²/ρ_m g under typical conditionsShow answer & explanation →
Q72.
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 itselfC [ML⁻¹T⁻²], the dimensional formula for pressure or stressD [ML²T⁻²], the dimensional formula for energy or workShow answer & explanation →
Q73.
The critical velocity above which flow becomes turbulent in a tube of diameter d is approximately (Reynolds number ≈ 2000):
A v<sub>c</sub> = 2000η/(ρd)B v<sub>c</sub> = 2000ρdC v<sub>c</sub> = η/(ρd)D v<sub>c</sub> = ρd/ηShow answer & explanation →
Q74.
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 textbooksC 13.6 m in general practiceD 1 m as frequently describedShow answer & explanation →
Q75.
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 needleB Ordinary buoyant force alone, as with any floating dense object in most textbook accountsC The needle being hollow and filled with trapped air inside during normal conditionsD A pocket of air trapped directly underneath the solid needle as generally observedShow answer & explanation →
Q76.
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/sB 10 m/sC 20 m/sD 7 m/sShow answer & explanation →
Q77.
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:
Show answer & explanation →
Q78.
A spherical drop falls at terminal velocity through a viscous fluid. If its radius is doubled, its terminal velocity becomes:
Show answer & explanation →
Q79.
A soap bubble of radius 2 mm has surface tension 0.03 N/m. The excess pressure inside it is:
A 15 PaB 30 PaC 60 PaD 120 PaShow answer & explanation →
Q80.
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 NB 1000 NC 10 ND 10000 NShow answer & explanation →
Q81.
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:
Show answer & explanation →
Q82.
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:
Show answer & explanation →