Chapter 3: Fluid Statics

3.1 Fluid Statics: Pressure & Buoyancy

3.2 Surface Tension & Surface Energy

3.3 Angle of Contact & Capillarity
Angle of contact (θ): Angle between solid surface & tangent to liquid surface at point of contact.
Acute (wetting liquid, e.g. water-glass).
Obtuse (non-wetting, e.g. mercury-glass).
Capillarity: Rise or fall of liquid in a capillary tube.

• Applications:
  • Rise of ink in pen.
  • Rise of oil in wick of lamp.
  • Water supply in plant stem.

3.4 Fluid Dynamics: Viscosity

3.5 Poiseuille’s Formula

3.6 Stokes’ Law

3.7 Equation of Continuity

3.8 Bernoulli’s Equation

Important Questions and Answers in Short

Q1. Define pressure in a fluid.
👉 Pressure at depth h: P = hρg.

Q2. State Archimedes’ principle.
👉 Body immersed in fluid loses weight = weight of displaced fluid.

Q3. Define surface tension.
👉 Force per unit length acting along liquid surface.

Q4. What is surface energy?
👉 Energy per unit area of surface.

Q5. Define angle of contact.
👉 Angle between tangent to liquid surface & solid surface at point of contact.

Q6. State Newton’s law of viscosity.
👉 It states that shear stress in a fluid is directly proportional to the velocity gradient (rate of shear strain).

Q7. State Stokes’ law.
👉 Viscous drag: F = 6πηrv.

Q12. State Bernoulli’s theorem.
👉 It states that for the steady flow of an incompressible, non-viscous fluid, the total mechanical energy along a streamline remains constant, i.e. P + ½ρv² + ρgh = constant.

Q13. Give two applications of Bernoulli’s theorem.
👉 Lift of airplane, atomizer spray.

✅ Formula Sheet (Quick Revision):

• Pressure: P = hρg
• Buoyancy: F = ρVg
• Surface tension: T = F/L
• Capillarity: h = 2T cosθ / (ρgr)
• Viscosity law: F = ηA dv/dx
• Poiseuille’s: V = πPr⁴ / (8ηl)
• Stokes’ law: F = 6πηrv, v_t = (2/9)(r²(ρ–σ)g/η)
• Continuity: A₁v₁ = A₂v₂
• Bernoulli: P + ½ρv² + ρgh = constant