Mechanical Properties of Fluids – Complete Formula Sheet (JEE Main Only)
1. Basic Definitions
- Fluid: Substance that can flow (liquids + gases)
- Density (ρ): Mass / Volume
- Relative density: Density of substance / Density of water
ρ = m / V
2. Pressure in Fluids
Pressure:
P = F / A
Pressure at depth h:
P = P₀ + ρgh
- Independent of container shape
- Same at same depth
3. Pascal’s Law
- Pressure applied to confined fluid is transmitted equally
Hydraulic lift:
F₂ / F₁ = A₂ / A₁
4. Buoyancy & Archimedes’ Principle
Buoyant force:
FB = ρfluid g Vdisplaced
- Acts vertically upward
- Independent of depth
5. Floatation Conditions
- Floating body: Weight = Buoyant force
- Fraction submerged = ρbody / ρfluid
Apparent weight:
Wapparent = mg − FB
6. Continuity Equation
A₁v₁ = A₂v₂
- Valid for incompressible fluids
- Velocity ↑ when area ↓
7. Bernoulli’s Theorem
P + ½ρv² + ρgh = constant
- Valid for steady, incompressible, non-viscous flow
- Explains lift in aeroplanes
8. Applications of Bernoulli
- Venturimeter
- Atomiser & spray gun
- Blood flow in arteries
9. Viscosity
Viscous force:
F = η A (dv/dx)
Coefficient of viscosity (η):
- Liquids → η decreases with temperature
- Gases → η increases with temperature
10. Stokes’ Law
F = 6π η r v
Terminal velocity:
vt = (2r²(ρ − σ)g) / (9η)
- Small spherical body
- Laminar flow
11. Reynolds Number
R = (ρvd) / η
- R < 2000 → Laminar flow
- R > 3000 → Turbulent flow
12. Surface Tension
T = F / L
- Liquids try to minimize surface area
- Surface energy = T × area
Excess pressure:
Drop: ΔP = 2T / r
Soap bubble: ΔP = 4T / r
13. Capillarity
h = (2T cosθ) / (ρgr)
- θ < 90° → Rise (water)
- θ > 90° → Depression (mercury)
14. JEE Main Question Profiling
| Question Type | JEE Focus | Common Trap |
|---|---|---|
| Pressure vs depth | P = ρgh | Ignoring atmospheric pressure |
| Buoyancy | Volume displaced logic | Using body volume incorrectly |
| Bernoulli MCQs | Energy conservation | Applying with viscosity |
| Continuity | Area–velocity relation | Assuming compressibility |
| Stokes / terminal velocity | η, r² dependence | Wrong density difference |
| Surface tension | 2T vs 4T confusion | Mixing drop & bubble |
15. JEE Main Weightage Insight
- 1–2 questions almost every year
- Formula + concept dominant
- Bernoulli & viscosity are favourites
StudyBeacon • JEE Main Physics • Fluids Master Sheet
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