Pressure: P = F/A (scalar). Unit: Pascal (Pa) = N/m²

Atmospheric pressure: 1 atm = 1.013 × 10⁵ Pa ≈ 10⁵ Pa

Hydrostatic pressure: P = P₀ + ρgh (depth h below surface)

Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and to the walls.

Buoyant force: F_b = ρ_fluid V_immersed g

Apparent weight: W_app = mg – F_b

Floatation condition: ρ_body ≤ ρ_fluid → fraction immersed = ρ_body/ρ_fluid

Viscous force (Newtonian fluid): F = η A (dv/dy) → η = coefficient of viscosity (Pa·s)

Stokes' law: Drag force on a sphere moving in fluid: F_d = 6πηrv

Terminal velocity: v_t = (2r²(ρ–σ)g)/(9η) (ρ = density of sphere, σ = density of fluid)

Excess pressure inside a bubble:
For soap bubble (2 surfaces): ΔP = 4γ/R
For liquid drop (1 surface): ΔP = 2γ/R
For air bubble in liquid: ΔP = 2γ/R

Capillary rise: h = (2γ cosθ)/(ρgr)
For water (θ ≈ 0°): h = 2γ/(ρgr)
For mercury (θ > 90°): depression.

💡 NEET TIPS & SHORTCUTS

• Pressure at same horizontal level in a static fluid is equal.
• Bernoulli's equation is valid for steady, incompressible, non‑viscous flow.
• Venturi meter and pitot tube are direct applications.
• For floating body, weight of body = weight of displaced liquid.

⚠️ COMMON MISTAKES

• Applying Bernoulli without checking assumptions (compressibility, viscosity).
• Confusing absolute pressure with gauge pressure.
• Forgetting that surface tension decreases with temperature.
• Using wrong formula for excess pressure in different bubbles.

Pressure at depth: P = P₀ + ρgh

Buoyant force: F_b = ρ_l V_imm g

Continuity: A₁v₁ = A₂v₂

Bernoulli: P + ½ρv² + ρgh = const

Stokes' law: F = 6πηrv

Capillary rise: h = 2γcosθ/(ρgr)