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Physics · Class 11 Science

Ch 9Mechanical Properties of Fluids — Class 11 Physics, concept-first.

This opening section lays the conceptual foundation for the entire chapter. It answers a fundamental question: what makes a fluid different from a solid, and what do liquids and gases have in common that lets us study them together?

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Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

9.1

Introduction

This opening section lays the conceptual foundation for the entire chapter. It answers a fundamental question: what makes a fluid different from a solid, and what do liquids and gases have in common t…

9.2

Pressure

The idea of pressure explains why a sharp needle pierces skin while a blunt spoon does not, even when pushed with the same force.

9.2.1

Pascal's Law

Pressure is defined as the normal force acting per unit area. When you press a sharp needle against your skin, the force is concentrated over a very small area, producing a large pressure that pierces…

9.2.2

Variation of Pressure with Depth

When you swim to the bottom of a pool, you feel a pressure in your ears. That sensation is the weight of the water above you pressing down.

9.2.3

Atmospheric Pressure and Gauge Pressure

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A sharp needle pressed into the skin pierces it easily, while a blunt spoon pressed with the same force does not.

9.2.4

Hydraulic Machines

2 Q

The principle that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid — Pascal's law — has a direct and powerful application in hydraulic machines.

9.3

Streamline Flow

Fluids in motion can behave in strikingly different ways. Pour honey from a jar — it flows smoothly, in a steady, predictable stream.

9.4

Bernoulli's Principle

Fluid flow is a complex phenomenon, but for steady or streamline flows we can extract powerful relationships using the conservation of energy.

9.4.1

Speed of Efflux: Torricelli's Law

Efflux simply means the outflow of a fluid from a container. Torricelli’s law gives the speed at which a liquid emerges from a small hole in an open tank.

9.4.2

Dynamic Lift

When a body moves through a fluid, it experiences a force perpendicular to its motion called dynamic lift.

9.5

Viscosity

When a fluid flows, different layers of the fluid move at different speeds. Think of water flowing through a pipe: the layer right next to the pipe wall is almost stationary, while the layer at the ce…

9.5.1

Stokes' Law

When a solid object moves through a fluid, the fluid exerts a resistive force that opposes the motion. This force arises from viscosity — the internal friction between layers of the fluid.

9.6

Surface Tension

The behaviour of a liquid at its free surface is strikingly different from its behaviour in the bulk. A liquid surface behaves as if it were a stretched elastic membrane under tension.

9.6.1

Surface Energy

When you stretch a rubber band, you do work against the elastic forces, and that work gets stored as elastic potential energy. A liquid surface behaves in a strikingly similar way.

9.6.2

Surface Energy and Surface Tension

The molecules inside a liquid experience equal attractive forces from all directions, so the net force on them is zero.

9.6.3

Angle of Contact

When a liquid meets a solid surface, the liquid surface near the wall is generally curved. This curvature is not accidental — it arises from the competition between adhesive forces (liquid–solid) and…

9.6.4

Drops and Bubbles

Why does a small drop of water form a perfect sphere, while a larger puddle flattens out? The answer lies in surface tension.

9.6.5

Capillary Rise

When a narrow tube (a capillary) is dipped into a liquid, the liquid either rises or falls inside the tube relative to the surrounding liquid surface.

Summary

- Fluids can flow: unlike a solid, a fluid (liquid or gas) has no fixed shape of its own and takes the shape of its container.

Points to Ponder

1. Pressure is a scalar quantity. The common description "force per unit area" can mislead you into thinking pressure is a vector.

Exercises

+Show 20 questions20 questions
  1. 9.1Explain why (a) The blood pressure in humans is greater at the feet than at the brain. (b) Atmospheric pressure at a height of about $6\ \te…Free
  2. 9.2Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute. (b) Water on a clean glass su…Free
  3. 9.3Fill in the blanks using the word(s) from the list appended with each statement: (a) Surface tension of liquids generally ... with temperatu…Free
  4. 9.4Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it. (b) When we try to close a water tap with our fing…Preview
  5. 9.5A $50\ \text{kg}$ girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter $1.0\ \text{cm}$. What is the…Preview
  6. 9.6Torricelli's barometer used mercury. Pascal duplicated it using French wine of density $984\ \text{kg m}^{-3}$. Determine the height of the…Preview
  7. 9.7A vertical off-shore structure is built to withstand a maximum stress of $10^{9}\ \text{Pa}$. Is the structure suitable for putting up on to…Preview
  8. 9.8A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000\ \text{kg}$. The area of cross-section of the piston carry…Preview
  9. 9.9A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with $10.0\ \text{cm}$…Preview
  10. 9.10In the previous problem, if $15.0\ \text{cm}$ of water and spirit each are further poured into the respective arms of the tube, what is the…Preview
  11. 9.11Can Bernoulli's equation be used to describe the flow of water through a rapid in a river? Explain.Preview
  12. 9.12Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation? Explain.Preview
  13. 9.13Glycerine flows steadily through a horizontal tube of length $1.5\ \text{m}$ and radius $1.0\ \text{cm}$. If the amount of glycerine collect…Preview
  14. 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\ \text{m s}^…Preview
  15. 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? ![Fig 9.20 -- Two di…Preview
  16. 9.16The cylindrical tube of a spray pump has a cross-section of $8.0\ \text{cm}^{2}$ one end of which has $40$ fine holes each of diameter $1.0\…Preview
  17. 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…Preview
  18. 9.18Figure 9.21 (a) shows a thin liquid film supporting a small weight = 4.5 x 10^-2 N. What is the weight supported by a film of the same liqui…Preview
  19. 9.19What is the pressure inside the drop of mercury of radius $3.00\ \text{mm}$ at room temperature? Surface tension of mercury at that temperat…Preview
  20. 9.20What is the excess pressure inside a bubble of soap solution of radius $5.00\ \text{mm}$, given that the surface tension of soap solution at…Preview

Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

+Show 23 questions23 questions
  1. Q1A tall cylinder is filled with viscous oil. A round pebble is dropped from the top of the cylinder with zero initial velocity, so it falls d…Free
  2. Q2Consider four flow-line diagrams of a fluid: (a) a set of smooth, nearly parallel curved lines all bending the same way, with arrows along t…Free
  3. Q3Along a streamline (a) the velocity of a fluid particle remains constant. (b) the velocity of all fluid particles crossing a given position…Free
  4. Q4An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the veloc…Preview
  5. Q5The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A…Preview
  6. Q6For a surface molecule (Note: more than one of the given options may be correct.) (a) the net force on it is zero. (b) there is a net downwa…Preview
  7. Q7Pressure is a scalar quantity because (Note: more than one of the given options may be correct.) (a) it is the ratio of force to area and bo…Preview
  8. Q8A wooden block with a coin placed on its top floats in water in a container. The vertical distance $l$ is the depth of the block that lies s…Preview
  9. Q9With increase in temperature, the viscosity of (Note: more than one of the given options may be correct.) (a) gases decreases. (b) liquids i…Preview
  10. Q10Streamline flow is more likely for liquids with (Note: more than one of the given options may be correct.) (a) high density. (b) high viscos…Preview
  11. Q11Is viscosity a vector?Preview
  12. Q12Is surface tension a vector?Preview
  13. Q13Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is $\rho_i…Preview
  14. Q14A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $M$ and density $\rho$ is suspended by…Preview
  15. Q15A cubical block of density $\rho$ is floating on the surface of water. Out of its height $L$, fraction $x$ is submerged in water. The vessel…Preview
  16. Q16The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius $r = 2.5\times 10^{-5}$ m. The surfac…Preview
  17. Q17The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle $…Preview
  18. Q18Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of m…Preview
  19. Q19If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius $R$, break int…Preview
  20. Q20The sufrace tension and vapour pressure of water at 20°C is $7.28\times 10^{-2}$ Nm$^{-1}$ and $2.33\times 10^{3}$ Pa, respectively. What is…Preview
  21. Q21(a) Pressure decreases as one ascends the atmosphere. If the density of air is $\rho$, what is the change in pressure d$p$ over a differenti…Preview
  22. Q22Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with incre…Preview
  23. Q23A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outs…Preview