By going through these CBSE Class 11 Physics Notes Chapter 10 Mechanical Properties of Fluids, students can recall all the concepts quickly.

## Mechanical Properties of Fluids Notes Class 11 Physics Chapter 10

→ Fluids are substances that can flow e.g. liquids and gases. Fluids don’t possess a definite shape.

→ When a liquid is in equilibrium, the force acting on its surface is perpendicular everywhere.

→ In a liquid, the pressure is the same at the same horizontal level.

→ The pressure at any point in the liquid depends on the depth (h). below the surface, the density of liquid and acceleration due to gravity.

→ Pressure is the same in all directions.

→ If two drops of the same volume but different densities are mixed together, then the density of the mixture is the arithmetic mean of their densities i.e. ρ = \(\frac{\rho_{1}+\rho_{2}}{2}\)

→ The upthrust on a body immersed in a liquid depends only on the volume of the body and is independent of the mass, density or shape of the body.

→ The weight of the plastic bag full of air is the same as that of the empty bag because the upthrust is equal to the weight of the air enclosed.

→ The wooden rod can’t float vertically in a pond of water because the centre of gravity lies above the metacentre.

→ The cross-section of the water stream from a tap decreases as it goes down in accordance with the equation of continuity.

→ The loss in weight of a body = Weight of the fluid displaced by the body.

→ Upthrust = Weight of the liquid displaced.

→ The floating body is in stable equilibrium when the metacentre is above the C.G. (C.G. is below the centre of buoyancy).

→ The floating body is in unstable equilibrium when the metacentre lies below the C.G. (i.e. C.G. is above the centre of buoyancy).

→ The floating body is in the neutral equilibrium when the C.G. coincides with the metacentre {i.e. C.G. coincides with the C.B.).

→ When a gale blows over a roof, the force on the roof is upwards.

→ If a beaker is filled with a liquid of density ρ up to height h, then the mean pressure on the walls of the beaker is \(\frac{\mathrm{h} \rho \mathrm{g}}{2}\)

→ The viscosity of liquids decreases with the rise in temperature i.e.

η ∝ \(\frac{1}{\sqrt{\mathrm{T}}}\)

→ The viscosity of gases increases with the rise in temperature i.e.

η ∝ \(\sqrt{T}\)

→ The streamlined or turbulent nature of flow depends on the velocity of flow of the liquid.

→ Streamline flow is also called laminar flow.

→ Reynolds number is low for liquids of higher viscosity.

→ N_{R} < 2000 for streamline flow.

→ N_{R} > 3000 for turbulent flow.

→ N_{R} lies between 2000 and 3000 for unstable flow.

→ Viscosity is due to the transport of momentum.

→ Bernoulli’s theorem is based on the conservation of energy.

→ Bernoulli’s theorem is strictly applicable to non-viscous fluids.

→ Viscosity arises out of tangential dragging force acting on the fluid layer.

→ Grease is more viscous than honey.

→ The coefficient of viscosity is measured in Nm^{-2}.

→ Stake’s law can be used to find the size of tiny spherical objects.

→ The flow of fluid under pressure may be zig-zag or in parallel layers of slow velocity in which the velocity vector is parallel at each point of the fluid.

→ The flow of fluid whose velocity varies from point to point is called turbulent flow.

→ The flow of fluid whose velocity at every point remains constant is called streamline flow.

→ For streamline flow, conservation of energy law-holds good and this law is known as Bernoulli’s Theorem.

→ A large number of phenomena like the flow of fluids through constructed pipes, the flight of planes, birds, burners, filter pumps and many other devices work on the principle of Bernoulli’s theorem.

→ The flow of fluids through pipes and capillaries is described by Poiseuille’s formula.

→ Pascal’s law accounts for the Principle of transmission of pressure in fluids.

→ The equation of continuity always holds good which is A_{1}v_{1} = A_{2}v_{2}. . The force acting per unit length of the imaginary line drawn on the liquid surface parallel to the surface is called the force of surface tension.

→ Due to surface tension, free surfaces of fluids tend to have minimum surface and so, the liquid drops tend to be spherical and also bubbles are formed in such a film.

→ The free surface has surface energy per unit area equal to surface tension.

→ Free surfaces in tubes, pipes of negligible bore tend to be concave sides which forces the liquid to rise in the capillary.

→ There is the force of pressure inside a soap bubble equal to \(\frac{4 \mathrm{~T}}{\mathrm{R}}\) due to two surfaces in the bubble.

→ Practical use of surface tension made in the capillary rise of liquids f (rise of ink in fountain pen) and cleaning of other stains by detergents.

→ Molecular forces don’t obey the inverse square law.

→ Molecular forces are of electrical origin.

→ Work done in forming a soap bubble of radius R is 8πR^{2}T, where T = surface tension.

→ The angle of contact increases with the rise in temperature and it decreases with the addition of soluble impurities.

→ The angle of contact is independent of the angle of inclination of the walls.

→ The materials used for waterproofing increase’s the angle of contact e as well as the surface tension.

→ Detergents decrease both the angle of contact as well as surface tension.

→ Surface tension does not depend on the area of the surface.

→ When there is no external force, the shape of a liquid is determined by the surface tension of the liquid.

→ Soap helps in better cleaning of clothes because it reduces the surface tension of the liquid.

→ A liquid having an obtuse angle of contact does not wet the walls of containing vessel.

→When force of adhesion is less than \(\frac{1}{\sqrt{2}}\) times the force of cohesion (F_{A} < \(\frac{\mathrm{F}_{\mathrm{c}}}{\sqrt{2}}\)) the liquid does not wet the walls of vessel and meniscus is convex.

→ The height of a liquid column in a capillary tube is inversely proportional to acceleration due to gravity.

→ Energy is released when the liquid drops merge into each other to form a larger drop.

→ The liquid rises in a capillary tube when angle of contact is acute and F_{A} > \(\frac{\mathrm{F}_{\mathrm{c}}}{\sqrt{2}}\)

→ The surface tension of molten cadmium increases with the increase in temperature.

→ Surface tension is numerically equal to surface energy.

→ Surface energy is the potential energy of the surface molecules per unit area.

→ The surface tension of lubricants, paints, antiseptics should below so that they may spread easily.

→ C.G.S. and S.L units of rare poise (dyne s cm^{-2} or g cm^{-1} s^{-1} ) and decompose (Nsm^{-2} or kg m^{-1} s^{-1}) respectively.

→ 1 decapoise= 10 poise..

→ Thrust: It ¡s defined as the total force exerted by the fluid on any surface in contact.

→ Atmospheric Pressure: It is defined as the weight of a column of air of unit cross-sectional area extending from that point to the top of the atmosphere.

= 1.013 × 10^{5} Pa = 76cm of Hg column.

→ Gauge pressure: It is the difference between absolute pressure and atmospheric pressure.

→Archimede’s Principle: It states that when a body is dipped wholly or partially in a fluid, it loses its weight.

→Surface Tension: It is the property of the liquid by virtue of which the free surface of the liquid at rest tends to have minimum area and as such ft behaves like a stretched elastic membrane.

→ Poiseuille’s Formula: According to it, the volume of the fluids flowing through ¡h pipe-isdireçly pLoportona1 to the pressure difference across the ends of the pipe and fourth power of the radius, it is inversely proportional to the coefficient of viscosity and length of the pipe.

i.e. mathematically. V = \(\frac{\pi}{8} \frac{\mathrm{pr}^{4}}{\eta l}\)

→ 1 Torr: It is the pressure exerted by a mercury column of 1 mm in height.

→ Law of Floatation: It states that a body floats in a fluid if the weight of the fluid displaced by the immersed portion of the body is equal to the weight of the body.

i.e V_{1 }ρ_{1 }g =V_{2} ρ_{2} g

or

\(\frac{\rho_{1}}{\rho_{2}}=\frac{V_{2}}{V_{1}}\)

or

\(\frac{\text { density of solid }}{\text { density of liquid }}=\frac{\text { Volume of immersed part of solid }}{\text { Total volume of solid }}\)

→ Force of Cohesion: It is the force of attraction between the molecules of the same substance or the same kind.

→ Force of adhesion: It is the force of attraction between the molecules of different substances.

→ The angle of Contact: It is defined as the angle at which the tangent to the liquid surface at the point of contact makes with the solid surface inside the liquid.

→ Capillarity: It is the phenomenon of rising or fall of a liquid in a capillary tube.

→ Jurin’s Law: It states that the liquid rises more in a narrow tube and lesser in a wider tube.

→ Viscosity: It is the property of fluid layers to oppose the relative motion among them.

→ Coefficient of Viscosity: It is defined as the tangential force required per unit area of the fluid surface to maintain a unit velocity gradient between two adjacent layers.

→ Stoke’s Law: It states that the viscous drag on a spherical body of radius r moving with terminal velocity v_{T} in a fluid of viscosity r| is given by F – 6πηrv_{T}.

→ Central line: The line joining the C.G. and centre of buoyancy is called the Central line.

→ Metacentre: It is defined as the point where the vertical line through the centre of buoyancy intersects the central line.

→ Terminal Velocity: It is defined as the constant velocity attained by a spherical body falling through a viscous medium when the net force on it is zero.

→ Pascal’s Law: It states that in an enclosed fluid, the increased pressure is transmitted equally in all possible directions if the effect of gravity is neglected.

→ Streamline: It is defined as the path straight or curved, the tangent to which at any point gives the direction of flow of the liquid at ‘ that point.

→ Tube of flow: It is a bundle of streamlines having the same velocity of liquid elements over any cross-section perpendicular to the direction of flow.

→ Streamline flow: The flow of a liquid is said to streamline flow or steady flow if all its particles pass through a given point with the same velocity.

→ Turbulent flow: The flow of a liquid in which the velocity of all particles crossing a given point is not the same and the motion of fluid becomes disorderly is called turbulent flow,

→ Laminar flow: The flow is said to be laminar if the liquid flows over a horizontal surface in the form of layers of different velocities.

→ Critical velocity: It is defined as the maximum velocity of a liquid or fluid up to which the flow is streamlined and above which it is turbulent.

→ Reynolds’ number: It is a pure number that tells about the type of flow. It is the ratio of inertial force and the viscous force for a fluid in motion.

→ Equation of Continuity: It expresses the law of conservation of ‘ mass in fluid dynamics.

i. e. a_{1}v_{1} =a_{2}v_{2} .

→ Bernoulli’s Theorem: It states that the total energy (sum of pressure energy, K..E. and P.E.) per unit mass is always constant for an ideal fluid.

i.e. \(\frac{\mathrm{P}}{\mathrm{\rho}}\) + gh + \(\frac{1}{2}\) v^{2} = constant

→ Surface film: It is the topmost layer of the liquid at rest with a thickness equal to the molecular range.

**Important Formulae:**

→ Pressure is given by P = \(\frac{F}{A}\).

→ Pressure exerted by a liquid column.

P = hρg

→ Downward acceleration of a body falling down in a fluid

(i.e. effective value of g) is

a = (\(\frac{\text { density of body }-\text { density of fluid }}{\text { density of body }}\))g

→ Pascal’s law, \(\frac{\mathrm{F}_{1}}{\mathrm{a}_{1}}=\frac{\mathrm{F}_{2}}{\mathrm{a}_{2}}\) = Constant.

→ Surface tension, T = \(\frac{F}{l}=\frac{\text { Force }}{\text { Length }}\).

→ Excess of pressure inside an air bubble is

p_{i} – p_{o} = \(\frac{2 \mathrm{~T}}{\mathrm{R}}\)

→ Excess of pressure inside a soap bubble is

p_{i} – p_{o} = \(\frac{4 \mathrm{~T}}{\mathrm{R}}\)

And inside a liquid drop,

p_{i} – p_{o} = \(\frac{2 \mathrm{~T}}{\mathrm{R}}\)

→ Ascent formula is h = \(\frac{2T cosθ}{rρg}\)

→ Shape of drops is decided by using

cos θ = \(\frac{\mathrm{T}_{\mathrm{SA}}-\mathrm{T}_{\mathrm{SL}}}{\mathrm{T}_{\mathrm{LA}}}\)

→ Viscous force is given by

F = – η A \(\frac{\mathrm{d} \mathrm{v}}{\mathrm{dx}}\)

→ Volume of liquid flowing per second is given by

V = \(\frac{\pi \mathrm{pr}^{4}}{8 \eta l}\)

→ Terminal velocity is given by

VT = \(\frac{2}{9} \frac{r^{2}}{\eta}\)(ρ – σ)g

where ρ = density of body

σ = density of liquid (fluid).

→ P + ρgh + \(\) ρv^{2} = constant.

If h = constant, Then

P_{1} + \(\) ρv_{1}^{2} = P_{2} + \(\) ρv_{2}^{2}.

→ The weight of the aircraft is balanced by the upward lifting force due to pressure difference

Let mg = Δp × A

or

mg = \(\frac{1}{2}\) ρ(v_{1}^{2} – v_{2}^{2}) × A.

→ Inertial force = (avρ)v = av^{2}ρ

→ Viscous force = \(\frac{ηav}{D}\).