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Mechanical Properties of Fluids

CBSE · Class 11 · Physics

NCERT Solutions for Mechanical Properties of Fluids — CBSE Class 11 Physics.

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EXERCISES

9.1Explain whyShow solution
Blood pressure at the feet is greater than at the brain because of hydrostatic pressure. In a fluid at rest, pressure increases with depth according to

P=Pa+ρghP = P_a + \rho gh.

Since the feet are at a greater height below the heart/brain level than the brain, the blood there is under a larger pressure due to the weight of the blood column above it.

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9.1(a)The blood pressure in humans is greater at the feet than at the brainShow solution
The blood pressure is greater at the feet because of hydrostatic pressure. In a fluid at rest, pressure increases with depth according to P=Pa+ρghP=P_a+\rho gh. Since the feet are lower than the brain, the column of blood above the feet is taller, so the pressure there is larger.

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9.1(b)Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 kmShow solution
Atmospheric pressure decreases with height because air pressure at any level is due to the weight of the air column above it. Even though the atmosphere extends to more than 100 km100\,\text{km}, most of its mass lies near the Earth’s surface. So by about 6 km6\,\text{km} the weight of air above has already reduced a lot, making pressure nearly half of sea-level pressure.

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9.1(c)Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.Show solution
Hydrostatic pressure is a scalar because pressure has magnitude only; no direction can be assigned to it. Although it is defined as force per unit area, the force in the numerator is only the normal component to the surface, not a vector quantity.

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9.2Explain whyShow solution
A drop of liquid is spherical because surface tension makes a liquid try to have the least surface area for a given volume. A sphere has the minimum surface area among all shapes with the same volume, so a free drop naturally becomes nearly spherical when external forces like gravity are negligible.

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9.2(a)The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.Show solution
The angle of contact depends on the relative attraction between the liquid and the solid. For mercury and glass, attraction between mercury molecules is stronger than attraction to glass, so mercury does not wet glass and the angle of contact is obtuse. For water and glass, water molecules are attracted strongly to glass, so water wets glass and the angle of contact is acute.

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9.2(b)Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)Show solution
On a clean glass surface, water is attracted more strongly to glass than to itself, so it spreads out and wets the surface. Mercury is more strongly attracted to its own molecules than to glass, so it pulls together into drops instead of spreading.

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9.2(c)Surface tension of a liquid is independent of the area of the surfaceShow solution
Surface tension is a property of the interface and not of the total surface area. For a given liquid at a fixed temperature, it is the force per unit length or surface energy per unit area, so changing the area does not change the value of surface tension itself.

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9.2(d)Water with detergent dissolved in it should have small angles of contact.Show solution
Detergent acts as a wetting agent. It reduces the angle of contact, so the liquid spreads better over the solid surface and can penetrate more easily.

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9.2(e)A drop of liquid under no external forces is always spherical in shapeShow solution
A free drop tends to have the least surface area for a given volume because surface energy is associated with its surface. A sphere has the minimum surface area for a given volume, so the drop becomes spherical when external forces are absent.

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9.3Fill in the blanks using the word(s) from the list appended with each statement:Show solution
The correct word is decreases because the chapter states that the surface tension of a liquid usually falls with temperature.

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9.3(a)Surface tension of liquids generally ... with temperaturesShow solution
From the chapter, the surface tension of a liquid usually falls with temperature. So the blank is decreases.

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9.3(b)Viscosity of gases ... with temperature, whereas viscosity of liquids ... with temperatureShow solution
The chapter states that viscosity of gases increases with temperature, while viscosity of liquids decreases with temperature.

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9.3(c)For solids with elastic modulus of rigidity, the shearing force is proportional to ... , while for fluids it is proportional to ...Show solution
For solids, the shearing force is proportional to shear strain. For fluids, it is proportional to the rate of shear strain.

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9.3(d)For a fluid in a steady flow, the increase in flow speed at a constriction followsShow solution
In a steady flow of an incompressible fluid, the relation is Av=constantAv=\text{constant}, which comes from conservation of mass.

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9.3(e)For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual planeShow solution
For a wind tunnel model, turbulence occurs at a smaller speed than for the actual plane because the model has a smaller characteristic size, so the same Reynolds-number condition is reached at a lower speed.

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9.4Explain whyShow solution
A spinning cricket ball does not follow a perfect parabolic path because its spin changes the flow of air around it. Due to the Magnus effect, air moves faster on one side of the ball and slower on the other, producing a pressure difference. This creates a sideways or upward force, so the ball deviates from the simple path of a projectile.

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9.4(a)To keep a piece of paper horizontal, you should blow over, not under, itShow solution
If you blow over the paper, the air speed above it increases. By Bernoulli’s principle, higher speed means lower pressure above the paper, so the greater pressure below keeps it horizontal.

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9.4(b)When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingersShow solution
When fingers partially block the tap, the water passes through a smaller opening. By the equation of continuity Av=constantAv=\text{constant}, the speed must increase as area decreases, so fast jets come out between the fingers.

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9.4(c)The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
9.4(d)A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
9.4(e)A spinning cricket ball in air does not follow a parabolic trajectory
9.5A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?
9.6Toricelli's barometer used mercury. Pascal duplicated it using French wine of density 984 kg m⁻³. Determine the height of the wine column for normal atmospheric pressure.
9.7A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
9.8A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm². What maximum pressure would the smaller piston have to bear ?
9.9A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?
9.10In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = 13.6)
9.11Can Bernoulli's equation be used to describe the flow of water through a rapid in a river ? Explain.
9.12Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation ? Explain.
9.13Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10⁻³ kg s⁻¹, what is the pressure difference between the two ends of the tube ? (Density of glycerine = 1.3 × 10³ kg m⁻³ and viscosity of glycerine = 0.83 Pa s).
9.14In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s⁻¹ and 63 m s⁻¹ respectively. What is the lift on the wing if its area is 2.5 m² ? Take the density of air to be 1.3 kg m⁻³.
9.15Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
9.16The cylindrical tube of a spray pump has a cross-section of 8.0 cm28.0~\mathrm{cm}^2 one end of which has 40 fine holes each of diameter 1.0mm1.0\mathrm{mm}. If the liquid flow inside the tube is 1.5mmin−11.5\mathrm{m}\mathrm{min}^{-1}, what is the speed of ejection of the liquid through the holes?
9.17A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5×10−2 N1.5 \times 10^{-2} \mathrm{~N} (which includes the small weight of the slider). The length of the slider is 30 cm30 \mathrm{~cm}. What is the surface tension of the film?
9.18Figure 9.21 (a) shows a thin liquid film supporting a small weight =4.5×10−2 N= 4.5 \times 10^{-2} \mathrm{~N}. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c)? Explain your answer physically.
9.19What is the pressure inside the drop of mercury of radius 3.00mm3.00\mathrm{mm} at room temperature? Surface tension of mercury at that temperature (20∘C)(20^{\circ}\mathrm{C}) is 4.65×10−1Nm−14.65\times 10^{-1}\mathrm{Nm}^{-1}. The atmospheric pressure is 1.01×105Pa1.01\times 10^{5}\mathrm{Pa}. Also give the excess pressure inside the drop.
9.20What is the excess pressure inside a bubble of soap solution of radius 5.00mm5.00\mathrm{mm} given that the surface tension of soap solution at the temperature (20∘C)(20^{\circ}\mathrm{C}) is 2.50×2.50\times 10−2Nm−110^{-2}\mathrm{Nm}^{-1}? If an air bubble of the same dimension were formed at depth of 40.0cm40.0\mathrm{cm} inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is 1.01×105Pa1.01\times 10^{5}\mathrm{Pa}).

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Frequently Asked Questions

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Mechanical Properties of Fluids covers several key topics that are frequently asked in CBSE Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Understand the core concepts first, then work through the 125 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
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This page has free step-by-step NCERT Solutions for every exercise question in Mechanical Properties of Fluids (CBSE Class 11 Physics) — written the way examiners award marks: given, formula, working, answer.

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