FSc Part 1 Physics Chapter 5 Complete Guide Book — Solids and Fluid Dynamics

Pick up a piece of quartz, a window pane and a plastic bottle. All three are solids, but inside they are put together in very different ways — and that hidden arrangement decides whether the thing is hard, melts sharply, or bends instead of breaking. This chapter starts there, because nearly everything that follows (stretching, breaking, floating, flowing) comes back to how the atoms sit next to each other.

Crystalline solids have their atoms, molecules or ions arranged in a regular pattern that repeats over the whole crystal — what the book calls long-range order. Metals and ceramics are the everyday examples. The atoms are not frozen still: each one vibrates about a fixed point, and the vibration grows as the temperature rises. Strong cohesive forces hold the pattern in place, until at one sharp temperature the vibrations win, the order collapses all at once, and the solid melts. That is why every crystalline solid has a definite melting point — quartz, calcite, sugar, mica and diamond are the book's examples. Scientists study these patterns with X-ray diffraction (XRD) and transmission electron microscopy (TEM).

Amorphous (glassy) solids have no regular arrangement at all. The word itself means "without form". Think of them as a liquid whose disordered structure got frozen in place. Ordinary glass is the classic case: heat it and it does not melt at one temperature, it softens gradually into a paste and then into a very thick liquid at almost 800 °C. So amorphous solids have no definite melting point. Plastic, glass and fused silicon belong here.

Polymeric solids sit in between — partly ordered, partly not. Polymers are huge chain molecules built when small molecules join together (polymerization). Plastics and synthetic rubbers are polymers, and so are natural materials: polythene, polystyrene and nylon are named in the book, and natural rubber in its pure state is a hydrocarbon, (C₅H₈)_n. Polymers are light for their strength — a lower specific gravity than even the lightest metals — which is why a plastic bucket can be both light and tough.

📌 Book note: the margin box on page 88 contrasts glassy and crystalline order side by side, and a second box shows the sodium chloride (NaCl) crystal lattice — sodium and chlorine ions locked in a repeating cage. That cage picture is the whole idea of a crystal in one drawing.

Squeeze a soft rubber ball in your hand and it flattens; open your hand and it pops back to a sphere. Pull a rubber band and it gets longer; let go and it returns. The book starts with these two homely experiments because they contain the whole subject: when an outside force acts on a body, its shape, length or volume changes. That change is called deformation.

Look closer, at the level of atoms. In a crystalline solid the atoms sit in a regular order, held by forces between neighbours. Push or pull the solid and the atoms are dragged slightly away from their equilibrium positions — the solid is now in a state of stress. Take the force away, and if it was not too large, the atoms slide back and the body regains its original shape. That ability to come back is elasticity. The book's Figure 5.2 shows the same story in a single unit cell: unstretched, stretched outward, squeezed inward, and back to normal once the force is removed.

Two things are worth noticing already. First, deformation is not damage: a stretched rubber band is deformed, not broken. Second, there is a limit — "provided the external force was not too great". Past that limit the atoms do not find their way home, and the change becomes permanent. That limit, and what happens beyond it, is the subject of section 5.5.

Engineers do not just say "this rod stretched a lot". They measure two numbers, because a thick rod and a thin wire pulled by the same force behave very differently. The first number is stress: the force applied per unit area, σ = F/A. Its SI unit is the newton per square metre (N m⁻²), which has its own name, the pascal (Pa). Stress is named by what it changes: if it changes length it is tensile stress (pulling), if it changes volume it is volume stress, and if it changes shape it is shear stress.

The second number is strain: how big the deformation is compared with the original size. For a stretch in one dimension, strain ε = change in length (ΔL) ÷ original length (L_o). Because it is a length divided by a length, strain has no units — it is just a ratio, often a small decimal like 0.004. Pulling gives tensile strain; squeezing gives compressive strain. Squeezing a block from all sides gives volumetric strain, ΔV/V_o. And if one face of a block slides sideways by Δx while the faces are y apart, the shear strain is γ = Δx/y = tan θ, which for small angles is just θ itself (in radians).

Now the key ratio. Within the elastic limit, stress divided by strain is constant for a given material. For stretching, that constant is Young's modulus, Y = tensile stress ÷ tensile strain = (F/A) ÷ (ΔL/L_o). It has the same unit as stress, N m⁻², and it is a measure of stiffness: steel (Y ≈ 200 × 10⁹ N m⁻²) is far stiffer than bone (15 × 10⁹) or ice (14 × 10⁹). The book's Table 5.1 lists Young's, bulk and shear moduli side by side — notice that liquids like water and mercury have zero Young's and shear moduli: you cannot stretch a liquid like a wire, because it has no fixed shape to hold.

📌 Book note: Young's modulus is named after the 19th-century British scientist Thomas Young, but the book points out the concept itself was developed in 1727 by Leonhard Euler.

Formulas are only useful if you can measure the numbers that go into them, and the book gives one complete experiment for this: Searle's apparatus. Two wires of the same material, same length and same diameter hang from a rigid support — a reference wire and a test wire. Each carries a horizontal bar (frame) at its lower end. A constant weight hangs from the reference bar and a hanger from the test bar, so both wires stay stretched and free of kinks before you start.

The procedure, step by step: (1) measure the original length L_o with a metre scale; (2) measure the wire's diameter d at several points with a screw gauge and take the average — several points matter, because a wire is never perfectly uniform; (3) level the spirit level with the micrometer screw and note that reading as your reference; (4) add a weight to the test wire — it stretches, so the spirit level tilts; (5) turn the micrometer until the level is horizontal again, and subtract the first reading from the second to get the extension ΔL; (6) work out stress = weight ÷ area = mg ÷ πr² and strain = ΔL ÷ L_o; (7) repeat with heavier loads; (8) plot stress against strain. The graph is a straight line, and its slope is Young's modulus. That last step is the elegant part: instead of trusting one measurement, you let a whole line of measurements speak.

📌 Brain teaser (book, p. 92): a steel rod and a rubber band are pulled by the same force — which stretches more? The rubber band, by far: its Young's modulus is tiny next to steel's, so the same stress produces a far bigger strain.

Stretch a metal wire slowly in a testing machine, measuring the stress at every step, and plot stress against strain. You get the most important graph in this chapter — the book's Figure 5.5, the stress–strain curve of a typical ductile material. Read it from left to right like a story.

From the origin O to point A, stress rises in a straight line with strain: this is the proportional limit (σ_p), the greatest stress a material can take without losing straight-line proportionality. Here Hooke's law holds — stress is directly proportional to strain (or, for a spring, force to extension). From A to B the line bends: stress and strain are no longer proportional, but if you unload anywhere up to B, the curve is retraced and the material returns to its original state. The region OB is the elastic region, and point B is the yield point; the stress there is the elastic limit (σ_e).

Push past B and the story changes. The material is permanently changed — it will not recover its shape when the stress is removed. This is plastic deformation, the region from B to C. Point C is the ultimate tensile strength (UTS, σ_u): the maximum stress the material can withstand, its nominal strength. Past C, the material breaks at point D, the fracture stress (σ_f).

Materials that go through a long plastic region before breaking are ductile — lead, copper and wrought iron. Materials that snap just after the elastic limit are brittle — glass and high-carbon steel, and also beryllium, bismuth and chromium. That one distinction explains why a copper wire can be drawn thin but a glass rod cannot.

Worked example 5.1 (book): a steel wire 12 mm in diameter, 11 m long between a log and a tractor, pulled with 10,000 N. Radius r = 6 × 10⁻³ m, so area A = πr² = 3.14 × (6 × 10⁻³)² = 1.13 × 10⁻⁴ m². Stress σ = F/A = 10,000 ÷ 1.13 × 10⁻⁴ ≈ 88.46 × 10⁶ N m⁻². With E = 200 × 10⁹ N m⁻², strain = stress ÷ E = 88.46 × 10⁶ ÷ 200 × 10⁹ = 4.4 × 10⁻⁴. Extension ΔL = strain × L_o = 4.4 × 10⁻⁴ × 11 = 4.84 × 10⁻³ m — less than 5 mm over 11 metres, which is exactly why steel is trusted for towing.

Stretch a spring and let go: it snaps back and can do work on its way. Where did that energy come from? From you — the work you did stretching it is not lost, it is stored inside the material as strain energy (elastic potential energy), equal to the gain in potential energy of the molecules pushed away from their mean positions.

The derivation is short and worth following once. A spring stretched by x within its elastic limit obeys Hooke's law, F = kx, so the force grows steadily from 0 to F as you stretch. The average force during the stretch is therefore F/2, and work = average force × distance = (F/2) × x = ½Fx. Since F = kx, this is also ½kx². The book shows the same result as the area of the triangle OPQ under the force–extension graph — and the learning outcome reminds you that this works generally: the area under a force–extension graph is the work done stretching the material, and within the proportionality limit it equals the elastic potential energy stored, E_p = ½kx².

📌 Book note (For your information, p. 94): the work done in stretching a material equals the average force applied multiplied by the distance moved — which is exactly why the graph's area, not just its height, is the quantity that matters.

Drop a mug full of water into a bucket and it feels light while it is under water, heavy the moment you lift it out. An air-filled balloon released under water shoots straight to the surface. More than two thousand years ago Archimedes noticed the same thing and gave it a name: the upthrust of the liquid — an upward force on anything immersed in it, which makes the object seem to lose weight.

Archimedes' principle: when an object is totally or partially immersed in a liquid, an upthrust acts on it equal to the weight of the fluid it displaces. The book proves it with a cylinder of area A and height h, its top at depth h₁ and bottom at h₂. Liquid pressure grows with depth (P = ρgh), so the bottom face is pushed up harder than the top face is pushed down: F₂ − F₁ = ρgh₂A − ρgh₁A = ρgA(h₂ − h₁) = ρgAh = ρgV. And ρgV is exactly the weight of the displaced liquid. So upthrust = ρgV — one short formula, and it works for gases too.

Floatation follows at once. An object sinks if its weight is greater than the upthrust, and floats if its weight is equal to or less than the upthrust. A floating object displaces a fluid whose weight equals the weight of the object — the principle of floatation. The book's applications make the point concrete: (1) a hot-air balloon rises because its average density is less than the surrounding air, and the pilot controls the rise by varying the hot air; (2) a wooden block floats because an equal volume of water weighs more than the block; (3) ships and boats are shaped so that the water they displace weighs as much as the whole loaded ship — they sink only if their total weight exceeds the upthrust; (4) a submarine fills tanks with seawater to grow heavier and dive, and empties them to rise again.

Worked example 5.2 (book): a wooden cube of side 10 cm = 0.1 m, fully dipped in water. Volume V = (0.1)³ = 1 × 10⁻³ m³. Upthrust = ρgV = 1000 × 9.8 × 1 × 10⁻³ = 9.8 N.

Worked example 5.3 (book): an empty meteorological balloon weighs 80 N and holds 10 m³ of hydrogen (density 0.09 kg m⁻³; air 1.3 kg m⁻³). Upthrust = weight of air displaced = 1.3 × 9.8 × 10 = 127.4 N. Weight of the hydrogen itself = 0.09 × 10 × 9.8 = 8.82 N. So the balloon can lift, besides its own weight, w₂ = 127.4 − 80 − 8.82 = 38.58 N of instruments.

📌 Book notes: Archimedes was born about 287 BC in Syracuse on the island of Sicily. And the margin teaser asks why a heavy steel ship floats while a small rock sinks — the answer is shape, not weight: the ship's hollow hull displaces an enormous weight of water, the rock displaces almost none.

Solids stretch; fluids flow — and flowing fluids can behave in two very different ways. Watch water in a smooth pipe and then water tumbling over rocks, and you have already seen both. The book sorts flow into streamline (laminar) and turbulent flow, then defines the simplified fluid that the rest of the chapter's mathematics will assume.

In streamline or laminar flow, every particle that passes a given point follows exactly the same path as the particles that passed that point before it. The smooth path is called a streamline, and the tangent to a streamline at any point gives the direction of flow there. Two streamlines can never cross — if they did, a particle at the crossing would have to choose two directions at once, which is impossible. The book's example makes it concrete: on a streamline PQR, the speeds at P, Q and R may differ (v₁, v₂, v₃), but if the speed at each fixed point does not change with time, the flow is steady.

Turbulent flow is the opposite: irregular, unsteady flow, where the velocity changes abruptly and the exact path of a particle cannot be followed. Above a certain speed the smooth motion breaks down into eddies and whirlpools, and the particles' paths keep changing. If two streamlines crossed, the flow would stop being steady and become turbulent — that is the book's own test for it.

An ideal fluid is then defined as a fluid that satisfies three conditions: (1) it is non-viscous — no friction between neighbouring layers; (2) it is incompressible — its density stays constant; (3) its motion is steady. No real fluid is ideal — the book is honest about that in section 5.15 — but assuming one lets us derive two exact laws, continuity and Bernoulli, which real flows follow closely enough to be useful.

📌 Book note: the margin pictures make the idea memorable — a Formula One car and a dolphin both have streamlined bodies, shaped so the fluid slides past them smoothly instead of breaking into drag-making eddies.

Before Bernoulli comes a simpler law, and it is just conservation of mass wearing a pipe's clothes. First, the rate of flow: the volume of fluid passing any section of a pipe per unit time. If fluid of speed v flows for time t, it covers length ℓ = vt, so the volume passed is A × ℓ = Avt, and the rate of flow is Avt ÷ t = Av, measured in m³ s⁻¹ (sometimes litres per second).

Now take a pipe of non-uniform size and watch a short interval Δt. At the wide lower end (area A₁, speed v₁) the fluid advances Δx₁ = v₁Δt, so the mass entering is Δm₁ = A₁v₁Δt × ρ₁. At the narrow upper end the mass leaving is Δm₂ = A₂v₂Δt × ρ₂. For steady flow of an incompressible fluid, mass is conserved — what enters in Δt must leave in Δt — so Δm₁ = Δm₂, giving A₁v₁ρ₁ = A₂v₂ρ₂. Density is constant, so it cancels, and we get the equation of continuity: A₁v₁ = A₂v₂. In words: the rate of flow in equals the rate of flow out. This equation, the book notes, is why a tap's falling stream gets thinner as it speeds up — the same volume per second must squeeze through a smaller area, so it moves faster (the margin "Tidbits" picture on page 101 shows exactly this).

Worked example 5.4 (book): a hose of internal diameter 20 mm discharges 30 kg of water in 60 s. Radius r = 0.02 ÷ 2 = 0.01 m; area A = πr² = 3.14 × (0.01)² = 3.14 × 10⁻⁴ m². Mass per second = 30 ÷ 60 = 0.5 kg s⁻¹. From ρAv = mass per second, v = 0.5 ÷ (1000 × 3.14 × 10⁻⁴) = 0.5 ÷ 0.314 = 1.6 m s⁻¹.

📌 Book notes: Euler obtained the continuity equation for an incompressible fluid in 1752, and the book lists where it is applied — blood flow in arteries and veins, water flow in rivers and pipes, and air flow in duct and ventilation systems.

Here is the whole continuity equation in one garden trick. Take a rubber pipe with water flowing through it and squeeze the end with your fingers. The cross-sectional area through which the water flows falls, and — by A₁v₁ = A₂v₂ — the velocity must rise to keep the same flow rate. The jet shoots farther, not because you pushed harder, but because the same water now has less room to get through.

The book states it in one line, but it is worth pausing on why it never fails: the water behind cannot pile up inside the pipe (it is incompressible), and it cannot vanish, so every cubic centimetre that enters per second must leave per second. Narrow the exit and the only freedom left is speed. The same reasoning explains the thumb over a garden hose in Figure 5.16, the tap stream getting thinner as it falls, and — turned around — why a river speeds up where its bed narrows.

Continuity was conservation of mass. Bernoulli's equation is conservation of energy, and it is the fundamental equation of fluid dynamics: it relates pressure to fluid speed and height. Its statement, in the book's words: the sum of pressure, kinetic energy per unit volume and potential energy per unit volume of an ideal fluid throughout steady flow remains constant — that is, P + ½ρv² + ρgh = constant.

The derivation repays a careful read, because every step is an idea you already know. Take an ideal (incompressible, non-viscous, steady) fluid flowing through a pipe of varying cross-section and height. The fluid behind pushes the front fluid with force P₁A₁ through distance Δx₁, doing work W₁ = P₁A₁Δx₁; the fluid ahead resists, so W₂ = −P₂A₂Δx₂. Net work W = P₁A₁Δx₁ − P₂A₂Δx₂. By continuity, A₁v₁t = A₂v₂t = V (the same volume), so W = (P₁ − P₂)V = (P₁ − P₂)m/ρ. This work goes into changing the fluid's kinetic energy (½mv₂² − ½mv₁²) and gravitational potential energy (mgh₂ − mgh₁). Equate them, divide by m/ρ, rearrange, and out comes P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂. Nothing new was invented — work, kinetic energy and potential energy were simply kept honest in a moving fluid.

For a horizontal pipe the height terms cancel, leaving the slogan version: where speed is high, pressure is low (P + ½ρv² = constant). Nearly every application in the next section is that one sentence, dressed up.

📌 Brain teaser (book, p. 102): how does the shape of a curveball in baseball relate to Bernoulli's principle? The spinning ball drags air faster on one side than the other — faster air, lower pressure, and the pressure difference pushes the ball sideways into its curve. Section 5.12 gives the cricket version of the same story.

Bernoulli's equation earns its keep in devices you have seen. (1) Aeroplane wings: a wing deflects the air so that streamlines crowd closer above the wing than below it. Where streamlines are closer, the speed is faster — and where speed is faster, pressure is lower. The wing is therefore pushed upward by the pressure difference, and that push is the lift of an aeroplane.

(2) Swing of a ball: throw or kick a ball with spin — or, as a cricket bowler does, polish one side smooth and leave the other rough — and the air moves faster over one side than the other. Faster air means lower pressure, slower air higher pressure, and the difference drives a sideways force, the Magnus effect, which makes the ball curve in the air.

(3) Filter pump: a jet of water from a tap is forced through a constriction in the centre of the pump, so it flows faster there and the pressure drops. Air is therefore sucked in from a side tube, and air and water are expelled together below.

(4) Carburetor: a car engine's carburetor uses a Venturi duct to feed the right air–petrol mixture to the cylinders. Air drawn through the duct moves very fast at the narrow part, pressure falls there, and a side inlet fed with petrol lets petrol vapour be drawn into the air stream.

(5) Paint sprayer / atomizer: a stream of air passing over a tube dipped in liquid makes the liquid rise in the tube — squeeze the rubber ball of an atomizer, air rushes through the narrow aperture at high speed, pressure falls, and atmospheric pressure pushes the perfume up into the jet.

(6) Venturi relation: for a horizontal pipe with wide area A₁ and narrow area A₂, Bernoulli gives P₁ − P₂ = ½ρ(v₂² − v₁²). Continuity gives v₁ = A₂v₂/A₁, and since A₂ is much smaller than A₁, v₁ is small enough to neglect, leaving P₁ − P₂ = ½ρv₂² — the Venturi relation, used in a Venturi meter to measure the speed of a liquid flow from a pressure difference read on a manometer.

(7) Torricelli's theorem: take a large tank with a small orifice. The top surface falls so slowly that its speed v₁ is effectively zero, and both surfaces are at atmospheric pressure, so Bernoulli reduces to v₂ = √[2g(h₁ − h₂)]. The speed of efflux equals the speed a body gains falling through the height (h₁ − h₂) under gravity. The book adds two honest footnotes: if the orifice points upward, the jet's kinetic energy would lift it back to the tank's level, and in practice viscous losses alter the result somewhat.

📌 Book note (Interesting Information, p. 105): the horizontal-pipe slogan in one line — "where speed is high, the pressure will be low", P + ½ρv² = constant.

Real fluids are not ideal: their layers drag on each other. That internal friction is viscosity — a measure of how much force is needed to slide one layer of liquid over another. Substances that do not flow easily, like thick tar and honey, have large coefficients of viscosity (η, Greek eta); substances that flow easily, like water, have small ones. The book's table at 30 °C puts numbers on the feeling: air 0.019, acetone 0.295, methanol 0.510, benzene 0.564, water 0.801, ethanol 1.000, plasma 1.6 and glycerin 6.29 (all × 10⁻³ N s m⁻²) — glycerin is about eight times as viscous as water.

Since liquids and gases both have non-zero viscosity, a force is always needed to move an object through them. Even air's tiny viscosity makes a large retarding force on a fast car — stick your hand out of a fast car's window and you feel it at once. An object moving through a fluid feels a retarding force called drag force, which grows as the object's speed grows.

For most shapes the exact drag is hard to calculate, but for a sphere moving slowly there is an exact result, Stokes' law: the drag force F on a sphere of radius r moving with speed v through a fluid of viscosity η is F = 6πηrv. Notice what it says: drag is proportional to size, to viscosity and to speed — double any one of them and the drag doubles. At high speeds this simple proportionality breaks down, and the book says so plainly.

📌 Book notes: a chimney works best when it is tall and exposed to air currents, which reduce the pressure at the top and force the upward flow of smoke — Bernoulli again, in a brick tower. And the "Do you know?" box is a warning in disguise: small viscosities at high speeds still make large forces.

Watch a fog droplet fall. It does not keep accelerating like a stone in a vacuum — it quickly settles to one steady speed and falls at that speed all the way down. That speed is its terminal velocity, and Stokes' law explains it in three lines.

On the droplet two forces act: weight downward and drag upward. The net force is weight − drag force. As the droplet speeds up under gravity, the drag (6πηrv) grows with speed, until it becomes equal to the weight. Then the net force is zero, acceleration stops, and the droplet falls with constant speed — the terminal velocity v_t. Setting drag equal to weight: 0 = mg − 6πηrv_t, so v_t = mg ÷ 6πηr. The droplet's mass is ρV with V = (4/3)πr³, so substituting gives the book's final form: v_t = 2gr²ρ ÷ 9η. Read it carefully: terminal velocity grows with the square of the radius — a droplet twice as wide falls four times as fast — and falls as viscosity rises.

Worked example 5.5 (book): a tiny water droplet of radius 0.010 cm = 1.0 × 10⁻⁴ m falling through air (η = 19 × 10⁻⁶ kg m⁻¹ s⁻¹, ρ = 1000 kg m⁻³). v_t = 2 × 9.8 × (1.0 × 10⁻⁴)² × 1000 ÷ (9 × 19 × 10⁻⁶) = 1.96 × 10⁻⁴ ÷ 1.71 × 10⁻⁴ = 1.1 m s⁻¹. That slow, gentle fall is why fog hangs in the air instead of hammering down like rain.

This short section is the book's honesty box. An ideal fluid — no viscosity, incompressible — cannot exist in practice; it is a model. Real fluids are all the fluids we actually meet: water, diesel, petrol, honey, kerosene oil, castor oil — every one of them has viscosity. More viscosity can be found in real life than in water: honey, for example, is far more viscous than water.

The comparison matters because Bernoulli's equation, as the book states it here, says the speed of a fluid rises when its potential energy or its static pressure falls. Real fluids do not face that trade cleanly: they lose energy to viscous friction, they have a viscous flow rather than a non-viscous one, and — unlike the ideal model — real fluids are also subject to surface tension. Ideal fluids are incompressible and are not subjected to surface tension in this model. So whenever you apply Bernoulli to a real pipe, a real wing or a real river, remember you are using a beautiful approximation, and viscous losses are the price of the approximation. The book gives no example of an ideal fluid, for the simple reason that none exists.

Now the strangest corner of the chapter. Superfluidity is the property of fluids with zero viscosity — flow without any friction at all. A substance showing it is a superfluid: it flows without losing kinetic energy, squeezes through incredibly narrow spaces without resistance, and once it starts moving it keeps moving past any obstacle.

Superfluidity appears only at extremely low temperatures. The most studied example is superfluid helium-4, which changes from an ordinary liquid to a superfluid just below its boiling point of −452 °F (−269 °C, or 4 K). Below that temperature it looks like a normal clear liquid but has no viscosity: a vortex set spinning in it keeps spinning indefinitely, because there is no friction to slow it down.

In fluid dynamics, a vortex is a region in which the flow revolves around an axial line, straight or curved; vortices are generally created at a moving boundary under frictionless conditions, and they move with the fluid and are dispersed by the action of viscosity — which is why, in a superfluid, they never disperse.

Applications are few so far, but serious ones: superfluid helium-4 serves as a coolant for high-field magnets; both helium-3 and helium-4 are used in advanced particle detectors; research on superfluidity helps us understand superconductivity; and liquid helium's great thermal conductivity makes it valuable in cryogenic applications, including cooling superconducting magnets, scientific research and medical uses, plus leak testing in industry and the production of electronic and optical products.

📌 Book notes (Tidbits, p. 108): parachutes increase air resistance (drag) by creating a large surface area, which counteracts gravity and slows the fall so people can land safely. And superfluids can "climb" up the walls and over the edges of containers — because they feel no friction like normal fluids do, nothing holds the creeping film back.

This chapter has two halves that share one habit of mind: relate what you can measure to what must stay constant. In solids, the measured pair is stress and strain, and their ratio — Young's modulus — tells you how stiff a material is; the stress–strain curve then tells you where Hooke's law stops, where permanent change starts, and where the material breaks. Stretching stores energy (½kx²), and Searle's experiment shows how the modulus is actually measured. In fluids, the conserved quantities are mass (continuity, Av = constant) and energy (Bernoulli, P + ½ρv² + ρgh = constant); Archimedes' upthrust ρgV explains floating, Stokes' drag 6πηrv explains why droplets stop accelerating, and superfluids show what happens when viscosity itself vanishes.

Topics covered, with links:

• 5.1 — Classification of Solids
• 5.2 — Deformation in Solids
• 5.3 — Stress, Strain and Young's Modulus
• 5.4 — Determination of Young's Modulus of a Wire
• 5.5 — Elastic Deformation, Plastic Deformation and Elastic Limit
• 5.6 — Strain Energy in Deformed Materials
• 5.7 — Archimedes' Principle and Floatation
• 5.8 — Steady, Non-viscous and Ideal Fluid
• 5.9 — Equation of Continuity
• 5.10 — Increase in Flow Velocity
• 5.11 — Bernoulli's Equation
• 5.12 — Uses of Bernoulli's Equation
• 5.13 — Viscous Drag and Stokes' Law
• 5.14 — Terminal Velocity
• 5.15 — Real Fluids are Viscous Fluids
• 5.16 — Superfluids
• Official exercise — 12 MCQs, 11 short, 6 constructed-response, 8 comprehensive, 8 numericals, all solved

Revision guidance: first, write the seven formulas from memory — σ = F/A, ε = ΔL/L_o, Y = stress/strain, E_p = ½kx², upthrust = ρgV, Av = constant, P + ½ρv² + ρgh = constant, F = 6πηrv, v_t = 2gr²ρ/9η. Then practise the two graph questions (stress–strain regions, force–extension area) and the two "why" questions examiners love (why pressure falls in a uniform pipe, why a ship floats and a rock sinks). Finish with the numericals that combine two ideas — continuity into Bernoulli (5.6), and Stokes into terminal velocity (5.8).