Schooling · Class 11 · Physics · Mechanical Properties of Fluids · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-II
Mechanical Properties of Fluids: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Pressure in a fluid
- Pascal's law
- Archimedes' principle
- Equation of continuity
- Bernoulli's principle
- Viscosity
- Surface tension
- Formulas and facts
- Pressure at depth h
- Pascal's law application
- Buoyant force
- Equation of continuity
- Bernoulli's equation
- Stokes' law for viscous drag
- Terminal velocity of a sphere
- Worked examples
- Pressure at depth in a lake
- Hydraulic lift
- Speed of water through a pipe
- Watch out for
- Forgetting to add atmospheric…
- Thinking buoyant force depends on…
- Applying Bernoulli's equation to…
- Confusing speed increase with…
- Using diameter instead of radius in…
What this chapter is about
This chapter extends your study of matter by examining how fluids — liquids and gases — behave under various conditions. While solids have definite shape and resist deformation, fluids flow and take the shape of their container. You will learn how pressure acts within fluids, why objects float or sink, and how fluids move through pipes and around obstacles.
Key ideas
- Pressure in a fluid acts equally in all directions at a point and increases with depth. At depth h below the surface, pressure P = P₀ + ρgh, where P₀ is atmospheric pressure, ρ is fluid density, and g is acceleration due to gravity.
- Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls of the container. This principle enables hydraulic lifts and brakes.
- Archimedes' principle states that when a body is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced. An object floats when the buoyant force equals its weight.
- Equation of continuity for incompressible fluid flow: A₁v₁ = A₂v₂, where A is cross-sectional area and v is flow speed. This means fluid speeds up when passing through a narrower section.
- Bernoulli's principle states that for steady, non-viscous, incompressible flow, the sum P + ½ρv² + ρgh remains constant along a streamline. Where speed increases, pressure decreases.
- Viscosity is the internal friction in a fluid that opposes relative motion between its layers. The coefficient of viscosity η has SI unit Pa·s (pascal-second).
- Surface tension is the property of a liquid surface that makes it behave like a stretched elastic membrane. It arises from unbalanced molecular forces at the surface and has SI unit N/m.
- Capillary rise occurs when adhesive forces between liquid and tube walls exceed cohesive forces within the liquid, causing the liquid to rise in a narrow tube. The height of rise h = 2S cos θ / (ρgr), where S is surface tension, θ is contact angle, and r is tube radius.
Formulas and facts to remember
- Pressure at depth h: P = P₀ + ρgh (P₀ is surface pressure, ρ is fluid density)
- Pascal's law application: F₁/A₁ = F₂/A₂ (force multiplication in hydraulic systems)
- Buoyant force: F_b = ρ_fluid × V_displaced × g (Archimedes' principle)
- Equation of continuity: A₁v₁ = A₂v₂ (for incompressible fluids)
- Bernoulli's equation: P + ½ρv² + ρgh = constant (along a streamline)
- Stokes' law for viscous drag: F = 6πηrv (on a sphere of radius r moving at speed v through fluid of viscosity η)
- Terminal velocity of a sphere: v_t = 2r²(ρ_sphere − ρ_fluid)g / 9η
- Capillary rise: h = 2S cos θ / (ρgr) (S is surface tension, θ is contact angle, r is tube radius)
Common mistakes
- Forgetting to add atmospheric pressure when calculating total pressure at depth → The formula P = P₀ + ρgh gives absolute pressure; gauge pressure is just ρgh.
- Thinking buoyant force depends on the object's density → Buoyant force depends only on the volume of fluid displaced and the fluid's density, not the object's material.
- Applying Bernoulli's equation to viscous or turbulent flow → Bernoulli's principle applies only to ideal, steady, non-viscous, incompressible flow along a streamline.
- Confusing speed increase with pressure increase in flowing fluids → In horizontal flow, where speed increases, pressure decreases (not increases).
- Using diameter instead of radius in capillary rise formula → The formula h = 2S cos θ / (ρgr) requires radius r, so divide the given diameter by 2.
Quick revision
- Pressure in a fluid at depth h: P = P₀ + ρgh; acts equally in all directions.
- Buoyant force equals weight of displaced fluid; object floats when this equals object's weight.
- Continuity: fluid speeds up in narrow sections (A₁v₁ = A₂v₂).
- Bernoulli: fast-moving fluid has lower pressure than slow-moving fluid at same height.
- Viscosity is internal friction in fluids; terminal velocity is reached when drag equals net weight.
- Surface tension causes liquids to minimise surface area; capillary rise occurs in narrow tubes.