Class 11 Physics: Mechanical Properties of Fluids Notes

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1. Introduction

• Fluids include liquids and gases that flow and take the shape of their container.
• Mechanical properties describe how fluids respond to forces.

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2. Pressure in Fluids

• Definition: Force exerted per unit area on a surface.

$$P = \frac{F}{A}$$P=AF​

Where:

• $F$F = force normal to surface
• $A$A = area
• Pascal’s Law: Pressure applied at any point in a confined incompressible fluid is transmitted equally in all directions.

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3. Variation of Pressure with Depth

• Pressure at depth $h$h in a fluid of density $\rho$ρ under gravity $g$g:

$$P = P_0 + \rho g h$$P=P0​+ρgh

Where $P_0$P0​ = surface pressure.

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4. Upthrust and Buoyancy

• Upthrust (Buoyant Force): Net upward force exerted by a fluid on a submerged object.
• Archimedes’ Principle: Upthrust = Weight of fluid displaced.

$$F_b = \rho_{fluid} g V_{displaced}$$Fb​=ρfluid​gVdisplaced​

• Relative density:

$$\text{Relative Density} = \frac{\rho_{object}}{\rho_{fluid}}$$Relative Density=ρfluid​ρobject​​

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5. Viscosity

• Definition: Property of a fluid that resists relative motion between its layers.
• Viscous Force (Friction in Fluids):

$$F = \eta A \frac{v}{d}$$F=ηAdv​

Where:

• $\eta$η = coefficient of viscosity
• $A$A = area of layer
• $v$v = relative velocity
• $d$d = distance between layers
• Stokes’ Law: Viscous force on a sphere moving in fluid:

$$F = 6 \pi \eta r v$$F=6πηrv

• Poiseuille’s Law: Flow rate through a pipe:

$$Q = \frac{\pi r^4 (P_1 – P_2)}{8 \eta L}$$Q=8ηLπr4(P1​−P2​)​

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6. Surface Tension

• Definition: Energy required to increase surface area by unit amount or force along a line of unit length.
• Symbol: $\gamma$γ
• Surface Energy:

$$W = \gamma \Delta A$$W=γΔA

• Effects: formation of droplets, capillary rise, soap bubbles.

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7. Compressibility

• Definition: Measure of change in volume under applied pressure.

$$K = -\frac{\Delta P}{\Delta V / V}$$K=−ΔV/VΔP​

• Bulk Modulus (K): Resistance of fluid to compression.

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8. Key Points

• Fluids cannot resist shear stress, only pressure.
• Pressure increases with depth in a fluid.
• Viscosity and surface tension are key mechanical properties.
• Archimedes’ principle explains buoyancy.
• Bulk modulus measures incompressibility.