Properties of Matter and Fluid Mechanics

Properties of matter explain how solids deform and fluids flow. NDA tests elasticity, Pascal's law, buoyancy, Bernoulli, and applications like hydraulic systems.

Elasticity

• Stress = Force / Area. SI: N/m² = Pa.
• Strain = change in dimension / original dimension. Dimensionless.
• Hooke's Law: Within elastic limit, stress ∝ strain. Stress = E × strain.
• Young's modulus (Y): Longitudinal stress/strain. Steel ≈ 200 GPa.
• Bulk modulus (K): Volume stress/strain.
• Shear modulus (G): Shearing stress/strain.
• Poisson's ratio: Lateral strain / longitudinal strain (≈ 0.3 for most materials).

Pascal's Law and Hydraulic Systems

Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and the container walls.

• Hydraulic press: small force on small piston → large force on large piston.
• F₁/A₁ = F₂/A₂. Mechanical advantage = A₂/A₁.
• Applications: Hydraulic brakes, hydraulic lifts, jack-up systems.

Archimedes' Principle and Buoyancy

Archimedes' Principle: An object immersed in a fluid experiences an upward force (buoyancy) equal to the weight of the fluid it displaces.

F_buoyancy = ρ × V × g, where ρ is fluid density, V is displaced volume.

• Float: If buoyancy ≥ weight, object floats.
• Sink: If buoyancy < weight, object sinks.
• Density: Object floats if its density < fluid density. Ice (density 0.92) floats on water.
• Ships float because their average density (including air-filled hull) is less than water.

Surface Tension, Viscosity, Capillary

• Surface tension: Force per unit length at fluid surface (N/m). Caused by cohesive forces. Why water droplets are spherical; small insects walk on water.
• Viscosity: Resistance to flow. Honey is more viscous than water. SI: Pa·s. Stokes' law for sphere falling in viscous fluid: F = 6πηrv.
• Capillary action: Liquid rises (or falls) in a narrow tube due to surface tension. Water rises (adhesion > cohesion); mercury falls (cohesion > adhesion).
• Examples: Plants drawing water up roots/stems; sponge absorbing water; oil rising in lamp wick.

Bernoulli's Principle

For an ideal fluid (incompressible, non-viscous): along a streamline,

P + ½ρv² + ρgh = constant

• Higher velocity ↔ lower pressure.
• Applications:
  • Aircraft lift (faster air over curved upper wing → lower pressure → lift).
  • Atomiser, spray gun.
  • Venturimeter (measures flow rate).
  • Magnus effect (spinning ball curving).

NDA PYQ Examples

Frequently Asked Questions

Why are water droplets spherical?

Surface tension. A liquid surface acts like a stretched elastic film, trying to minimise surface area. The sphere has the minimum surface area for a given volume, so small drops naturally form spheres.

Why does a deep sea diver get an ear ache?

Water pressure increases with depth (P = ρgh). The unequal pressure on the ear drum (high outside, normal inside) can cause pain or damage. Divers equalise by pinching nose and blowing gently.

How do airplanes generate lift?

Bernoulli's principle. Wing shape (airfoil) makes air travel faster over the top than the bottom. Faster flow → lower pressure on top. Pressure difference pushes wing up = lift.

Why is mercury used in barometers?

Mercury is very dense (13.6 g/cc), so atmospheric pressure can be balanced by a column only ~76 cm high (vs ~10 m for water). Mercury also doesn't evaporate easily and is opaque, making the meniscus easy to read.

What is viscosity?

Resistance to flow. Honey is highly viscous (flows slowly); water has low viscosity. Viscosity decreases with temperature in liquids (warm honey flows easier) and increases with temperature in gases.

Related Topics

NDA PhysicsLaws of Motion NDA PhysicsHeat & Thermodynamics NDA PhysicsWork Energy Power NDA PhysicsAtmospheric Structure NDAPhysics — Full Syllabus