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Cheat sheet · Class 11 · CBSE · Science Physics

Mechanical Properties of Fluids cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 11 · Physics

Cheat sheet

Chapter 9Mechanical Properties of Fluids

Pressure + KE + PE per volume = constant (Bernoulli).

1. Pressure

P=Pa+ρghP = P_a + \rho g h
  • Pascal's law: pressure applied to an enclosed fluid is transmitted equally (hydraulic lift, brakes).
  • Gauge pressure = P − Pₐ.

2. Flow

A1v1=A2v2A_1v_1 = A_2v_2 (continuity)
P+12ρv2+ρgh=constP + \tfrac12\rho v^2 + \rho g h = \text{const}

Torricelli: speed of efflux v=2ghv = \sqrt{2gh}.

Applications: lift on aeroplane wings, atomiser, blowing-off roofs.

3. Viscosity

F=ηAdvdxF = \eta A\dfrac{dv}{dx}F=6πηrvF = 6\pi\eta r v (Stokes)
vt=2r2(ρ−σ)g9ηv_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}

Reynolds number Re=ρvdηR_e = \dfrac{\rho v d}{\eta}; laminar below ~1000, turbulent above ~2000.

4. Surface Tension

S=FlS = \dfrac{F}{l}h=2Scos⁡θρgrh = \dfrac{2S\cos\theta}{\rho g r}
  • Excess pressure: drop 2S/r, bubble 4S/r.
  • Acute contact angle ⇒ liquid wets the surface and rises (water–glass); obtuse ⇒ falls (mercury).

5. Key Points

  • Viscosity of liquids falls with temperature; of gases it rises.
  • Surface tension falls as temperature rises.
  • Detergents lower surface tension.
  • Faster flow ⇒ lower pressure.

Remember: P = ρgh | A₁v₁ = A₂v₂ | Bernoulli | Stokes | capillary rise

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