Mechanical Properties of Fluids: NEET and JEE Main 2027 Notes, PDF

Mechanical Properties of Fluids is Chapter 9 of NCERT Class 11 Physics and part of Unit 7, Properties of Solids and Liquids, in both the NEET UG and JEE Main syllabi. These notes cover pressure, Pascal’s law, streamline flow, the equation of continuity, Bernoulli’s principle, viscosity, Stokes’ law and surface tension, with a free PDF.

Mechanical Properties of Fluids Notes for NEET and JEE Main

Section-wise key points from NCERT Chapter 9, formula tables, high-yield facts and common mistakes for 2027 revision.

Mechanical Properties of Fluids at a Glance

Topics follow the NEET UG 2026 syllabus released by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus published by NTA. Both stay the reference until the 2027 syllabi are out. Full lists: NEET syllabus and JEE Main syllabus.

What is a fluid and what is pressure?

Liquids and gases can flow, so they are called fluids. A fluid has no definite shape and offers very little resistance to shear stress.

• Solids and liquids have a fixed volume and low compressibility; a gas fills its whole container.
• The shearing stress of fluids is about a million times smaller than that of solids.
• A fluid at rest exerts a force normal to any surface in contact with it.
• Pressure P = F/A, where F is the normal force. Pressure is a scalar; SI unit pascal (Pa) = N m⁻²; dimensions [ML⁻¹T⁻²].
• Density ρ = m/V; SI unit kg m⁻³. Water at 4 °C has density 1.0 × 10³ kg m⁻³.
• Relative density is density divided by the density of water at 4 °C and has no unit (aluminium: 2.7).

Pascal’s Law and Variation of Pressure with Depth

Pascal’s law: pressure in a fluid at rest is the same at all points at the same height, and a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the container walls.

• Pressure at a point in a fluid at rest acts equally in all directions.
• Pressure at depth h in a liquid open to the atmosphere: P = Pa + ρgh. The excess P − Pa = ρgh is the gauge pressure.
• Pressure depends on the height of the liquid column, not on the base area or shape of the vessel (hydrostatic paradox).
• Mercury barometer (Torricelli): Pa = ρgh, with about 76 cm of mercury at sea level. A drop of 10 mm or more signals an approaching storm.
• Open-tube manometer measures gauge pressure; use oil for small differences and mercury for large ones.
• Tyre pressure gauges and blood pressure gauges (sphygmomanometers) read gauge pressure.
• At 10 m below a lake surface the pressure is about 2 atm; at 1 km in the sea it is about 100 atm more than at the surface.

Hydraulic Machines

• Hydraulic lift: a small force F₁ on a piston of area A₁ supports F₂ = F₁(A₂/A₁) on a larger piston of area A₂; A₂/A₁ is the mechanical advantage.
• Hydraulic brakes: pedal force moves the master piston, and the pressure is transmitted through brake oil equally to all four wheels.

Streamline Flow and the Equation of Continuity

Flow is steady when the velocity of each fluid particle passing a given point stays constant in time. The path of a particle in steady flow is a streamline.

• A streamline’s tangent at any point gives the direction of fluid velocity there; two streamlines never cross.
• Equation of continuity for an incompressible fluid: Av = constant. It expresses conservation of mass; Av is the volume flow rate.
• The fluid speeds up where the pipe narrows and the streamlines crowd together.
• Steady flow happens at low speeds. Above a limiting value, the critical speed, flow becomes turbulent, as in white-water rapids.
• In laminar flow, velocities at different points may differ in size but are parallel.

Bernoulli’s Principle and Its Applications

Bernoulli’s principle (Daniel Bernoulli, 1738): along a streamline, P + ½ρv² + ρgh is constant. It is conservation of energy for a fluid in steady flow.

• It assumes a non-viscous, incompressible fluid in steady (streamline) flow; it does not hold for turbulent flow.
• Viscosity converts some kinetic energy into heat, so with viscous drag the downstream pressure is lower than the equation predicts.
• For a fluid at rest it reduces to P₁ − P₂ = ρg(h₂ − h₁).
• Torricelli’s law: speed of efflux from a hole at depth h in an open tank, v = √(2gh), the same as for a freely falling body.
• If the tank pressure P is much larger than Pa, the efflux speed is set by the pressure, as in rocket propulsion.
• Dynamic lift acts on an aeroplane wing, a hydrofoil or a spinning ball moving through a fluid.
• Magnus effect: a spinning ball drags air with it, so streamlines crowd on one side, creating a pressure difference and a lift that bends its path.
• An aerofoil makes the air flow faster above the wing than below, giving an upward lift that balances the plane’s weight.

Viscosity, Stokes’ Law and Terminal Velocity

Viscosity is the internal friction between layers of a fluid in relative motion. The coefficient of viscosity η is the ratio of shearing stress to strain rate.

• SI unit: poiseuille (Pl); also N s m⁻² or Pa s. Dimensions [ML⁻¹T⁻¹].
• In laminar flow through a tube, the layer along the axis moves fastest and the layer at the wall is at rest.
• Viscosity of liquids decreases as temperature rises; viscosity of gases increases.
• Blood is more viscous than water, and the relative viscosity of blood stays constant between 0 °C and 37 °C.
• Stokes’ law: viscous drag on a sphere of radius a moving with speed v is F = 6πηav.
• Terminal velocity is reached when viscous drag plus buoyancy balances the weight: v_t = 2a²(ρ − σ)g/(9η), where ρ is the density of the sphere and σ that of the fluid.
• Terminal velocity varies as the square of the radius and inversely as the viscosity.

Surface Tension, Angle of Contact and Capillary Rise

Molecules at a liquid surface have extra energy compared with those inside, so a liquid tends to have the least surface area possible. Surface tension S is the surface energy per unit area, equal to the force per unit length acting in the plane of the interface.

• A molecule at the surface has roughly half the binding of one inside; the energy to bring it to the surface is roughly half the heat of evaporation (about 40 kJ/mol for water).
• For a film on a wire frame with a sliding bar of length l: S = F/2l, because the film has two surfaces.
• Surface tension usually falls as temperature rises.
• Surface energy belongs to the interface between two materials, at least one of them a fluid, and depends on both.
• Free drops and bubbles are spherical (when gravity can be neglected) because a sphere has the least area for a given volume.

Angle of Contact

• Angle of contact θ is the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
• Balance of interfacial tensions: S_la cos θ + S_sl = S_sa.
• θ is obtuse when S_sl > S_la (water on a lotus leaf or waxy surface, mercury on any surface): the liquid does not wet the solid.
• θ is acute when S_sl < S_la (water on glass or plastic, kerosene on almost anything): the liquid wets and spreads.
• Soaps, detergents and dyes are wetting agents that make θ small; waterproofing agents make it large.

• The concave side of a curved liquid surface is always at higher pressure than the convex side.
• Capillary rise: h = 2S cos θ/(ρga), where a is the tube radius. Rise is larger in a thinner tube.
• For water in a glass capillary of radius 0.05 cm, the rise is about 2.98 cm.
• If the meniscus is convex (cos θ negative, as for mercury in glass), the liquid level falls in the capillary.

Most-asked Facts for NEET and JEE Main: Mechanical Properties of Fluids

Revise these one-line facts from the NCERT chapter just before the exam.

• Pressure is a scalar; 1 atm = 1.013 × 10⁵ Pa, 1 bar = 10⁵ Pa, 1 torr = 133 Pa.
• P = Pa + ρgh; gauge pressure = ρgh.
• Liquid pressure depends on depth, not on the shape of the vessel (hydrostatic paradox).
• Hydraulic lift: F₂ = F₁(A₂/A₁).
• Continuity equation Av = constant follows from conservation of mass.
• Bernoulli: P + ½ρv² + ρgh = constant along a streamline, for steady non-viscous incompressible flow.
• Torricelli’s speed of efflux: v = √(2gh).
• Lift on a spinning ball is the Magnus effect.
• Viscosity SI unit poiseuille (Pa s); dimensions [ML⁻¹T⁻¹].
• Liquid viscosity falls with temperature; gas viscosity rises.
• Stokes’ law F = 6πηav; terminal velocity ∝ a².
• Surface tension falls with temperature.
• Excess pressure: drop 2S/r, soap bubble 4S/r.
• Capillary rise h = 2S cos θ/(ρga); mercury shows capillary depression.
• Water on a lotus leaf has an obtuse angle of contact; water on glass has an acute one.

Common Mistakes to Avoid

Watch for these mix-ups when you answer questions on this chapter.

• Writing excess pressure in a soap bubble as 2S/r. A soap bubble has two surfaces, so it is 4S/r; an air bubble inside a liquid is 2S/r.
• Using S = F/l for a soap film on a frame. The film has two surfaces, so S = F/2l.
• Saying viscosity of all fluids falls with temperature. It falls for liquids but rises for gases.
• Applying Bernoulli’s equation to turbulent or highly viscous flow. It holds for steady, non-viscous, incompressible flow.
• Thinking liquid pressure at the bottom depends on the vessel’s shape or base area. It depends only on the depth.
• Treating pressure as a vector. The force in its definition is the normal component, and pressure has no direction.
• Forgetting that terminal velocity depends on the difference in densities (ρ − σ) and on a².
• Expecting mercury to rise in a glass capillary. Its angle of contact is obtuse, so it is depressed.

Mechanical Properties of Fluids Notes PDF and Related Pages

Download the AglaSem notes for Mechanical Properties of Fluids (key notes on properties of matter covering elasticity, surface tension, pressure, Bernoulli’s theorem and viscosity, with important questions and answers) free: View PDF

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• Source text: NCERT Chapter 9 (NCERT, Class 11 Physics Part II)

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