JEE/NEET Physics · Mechanical Properties of Fluids series · Part 7 of 7 · All parts →
- Seven parts on one card — statics, motion and surfaces of fluids
- P = P₀ + ρgh · Pascal F₁/A₁ = F₂/A₂ · Archimedes F_B = ρ_f V g
- A₁v₁ = A₂v₂ · Bernoulli P + ½ρv² + ρgh = const · Torricelli √(2gh)
- Stokes 6πηrv · terminal v_t = 2r²g(ρ−σ)/9η
- T = F/ℓ · ΔP = 2T/r (4T/r bubble) · capillary h = 2T cosθ/(rρg)
The final card of the Mechanical Properties of Fluids series — seven parts on one revision sheet, plus the plumbing, aviation and medicine that run on them.
- The master formula card
- The one-rule-per-part recap
- Fluids in the wide world
- Final practice set
- Recap
The Master Formula Card
| What | Formula | Remember |
|---|---|---|
| Pressure | P = F/A | perpendicular push |
| Hydrostatic | P = P₀ + ρgh | depth × density only |
| Pascal | F₁/A₁ = F₂/A₂ | liquid lever |
| Archimedes | F_B = ρ_f V g | fluid’s density! |
| Floatation | displaced weight = own weight | density decides |
| Continuity | A₁v₁ = A₂v₂ | flow booked |
| Bernoulli | P + ½ρv² + ρgh = const | fast ↔ thin |
| Torricelli | v = √(2gh) | free-fall speed |
| Viscosity | F = ηA dv/dx | internal friction |
| Stokes | F = 6πηrv | small + slow only |
| Terminal velocity | v_t = 2r²g(ρ−σ)/9η | r² rules |
| Surface tension | T = F/ℓ = energy/area | inward pull |
| Drop/bubble | ΔP = 2T/r · 4T/r | bubble doubled |
| Capillarity | h = 2T cosθ/(rρg) | narrow = higher |
The One-Rule-Per-Part Recap
1: depth times density is all. 2: enclosed fluids broadcast pressure intact. 3: you float if you displace your weight before you sink your volume. 4: speed is bought with pressure. 5: drag grows until it matches gravity — the terminal ceiling. 6: surfaces cost energy and pull inward.
Fluids in the Wide World
- Every city’s water supply is this series plumbed together: rooftop/tower pressure (ρgh), pipe sizing (continuity), pump hydraulics (Pascal).
- Flight itself — wings, propellers, and jet intakes are Bernoulli machines with Newton’s third law as co-pilot.
- Weather and oceans — atmospheric pressure maps, storm surges (ρgh), cloud droplet physics (surface tension) — the chapter running at planetary scale.
- Human circulation — blood pressure (mmHg = ρgh units), viscosity’s role in heart strain, capillary action in the finest vessels: medicine as fluid mechanics.
- Sport engineering — cricket ball swing, golf ball dimples, swimsuit drag: millions spent tuning viscosity and boundary layers.
Solids sit where you put them; fluids GO everywhere — through pipes, lungs, engines, clouds, veins. A substance with no shape of its own will fill any container, push every wall, and flow down every gradient: controlling that restless behaviour IS civilization’s plumbing, aviation, and medicine.
One day of your life: shower (Bernoulli + pressure), breakfast pours (viscosity), brakes on the commute (Pascal), blood pressure check (ρgh in mmHg), rain on the way home (terminal velocity + surface tension). Five chapters, one Tuesday.
Map the series on one tank of water: arrows for pressure on the walls (Part 1), a piston on top (Part 2), a floating block (Part 3), an outlet jet (Part 4), a falling drop beside it (Part 5), a meniscus curve at the top (Part 6). One picture holds all seven parts.
Practice set (answers hidden — try first)
(NEET-level) Gauge pressure at 20 m depth in water =
(JEE Main-level) A₁=10 cm², v₁=2; A₂=5 cm² → v₂ =
(NEET-level) Object ρ=500 floats in water: submerged fraction =
(JEE Main-level) Soap bubble r=2 cm, T=0.03: ΔP =
(NEET-level) Torricelli speed from h=0.8 m (g=10) =
- pressure trio (P₀+ρgh, Pascal, buoyancy)
- flow trio (continuity, Bernoulli, Torricelli)
- viscosity trio (Newton, Stokes, terminal)
- surface trio (T, ΔP, capillarity)
- density decides floating; r² decides falling
- 🔁 the 14-row master card
- 🔁 one rule per part
- 🔁 fluids = the functional half of matter
- 🧠 Full-card chant: ‘depth, broadcast, displace, trade, drag, skin’.
- 🏠 Daily: city water = this series, plumbed.
- 🏠 Daily: blood pressure is ρgh in mmHg.
Quick revision
- Seven parts on one card — statics, motion and surfaces of fluids
- P = P₀ + ρgh · Pascal F₁/A₁ = F₂/A₂ · Archimedes F_B = ρ_f V g
- A₁v₁ = A₂v₂ · Bernoulli P + ½ρv² + ρgh = const · Torricelli √(2gh)
- Stokes 6πηrv · terminal v_t = 2r²g(ρ−σ)/9η
- T = F/ℓ · ΔP = 2T/r (4T/r bubble) · capillary h = 2T cosθ/(rρg)
- The one-rule-per-part recap
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