📚 Key Concepts
Pressure and density in fluidsPascal's lawHydrostatic pressureBuoyancy and Archimedes' principleStreamline flow and turbulent flowBernoulli's principleViscosity and Stokes' lawSurface tension and capillarity
🎯 Key Formulas
Pressure in fluid: P = ρhgPascal's law: P₁ = P₂ (pressure transmission)Buoyant force: F = ρVg (density × volume × g)Bernoulli's equation: P + (1/2)ρv² + ρgh = constantStokes' law: F = 6πηrvSurface tension: T = F/LExcess pressure inside bubble: P = 4T/RReynolds number: Re = ρvd/η
⚠️ Common Mistakes to Avoid
Confusing gauge and absolute pressureWrong application of Bernoulli's principleIncorrect understanding of streamlinesMixing up laminar and turbulent flowWrong units in viscosity calculationsForgetting atmospheric pressure in calculations
📖 Knowledge Prerequisites
Basic mechanics conceptsUnderstanding of forcesVector algebraDensity and pressure conceptsBasic calculus for derivations
💡 Tips for Students
Visualize fluid flow patternsUnderstand pressure acts in all directionsRemember Bernoulli's principle assumptionsPractice drawing streamlinesLearn practical applicationsConnect theory with daily life examples
👉 Practice Recommedations
Calculate hydrostatic pressure at different depthsSolve problems on buoyancyApply Bernoulli's equation in various scenariosWork on viscosity problemsPractice surface tension calculationsSpecial Notes:
- Fluids can be liquids or gases
- Pressure in fluids depends on depth
- Flow can be steady or unsteady
- Surface tension explains many natural phenomena
- Viscosity affects fluid motion differently at different scales
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