JEE/NEET Physics · Mechanical Properties of Fluids series · Part 1 of 7 · All parts →
- Pressure = force per area, P = F/A — fluids push perpendicular to every surface they touch
- In a liquid at rest: P = P₀ + ρgh — depth is the only thing that matters
- Same depth → same pressure, regardless of container shape (hydrostatic paradox)
- Density ρ = mass/volume; water ≈ 1000 kg/m³; mercury ≈ 13,600
- Gauge pressure vs absolute: add atmospheric P₀ ≈ 1.01×10⁵ Pa for absolute
A dam wall holds back a lake — but the water only pushes on the bottom few metres with any seriousness. Why? Because pressure in a liquid comes from the weight of the water ABOVE you, and nothing else. Part 1 of the Mechanical Properties of Fluids series.
- Pressure: the perpendicular push
- The ρgh rule
- The shape paradox
- Gauge vs absolute
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Pressure: The Perpendicular Push
Fluids can’t hold a sideways shear — so their push on any surface is always perpendicular to it, in every direction at once. Divide by area and you have pressure, in pascals: a fluid presses with the same intensity on the floor, the walls, and your ears at any given depth.
The ρgh Rule
Descend in a liquid and you carry the weight of all the liquid above you:
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| P | pressure at depth h | Pa (1 atm ≈ 1.01×10⁵ Pa) |
| ρ | density of the liquid | kg/m³; water 1000, mercury 13,600 |
| g | gravity | 9.8 m/s² |
| h | vertical depth below the surface | m — only depth matters |
The Shape Paradox
A thin tube and a wide tank, both filled to 1 m: same pressure at the bottom. The tank has more water, but pressure cares only about the COLUMN HEIGHT above the point, not the total volume. Water finds its level — connected vessels always equalize.
Gauge vs Absolute
Pressure gauges read the excess over atmospheric (gauge). The true, absolute pressure adds P₀. Tyre gauge reading 220 kPa means ~320 kPa absolute. Water’s ρgh adds to whatever presses on its surface.
Solved Examples
P = 10⁵ + 1000×10×2 = 1.2×10⁵ Pa.
Gauge part: 0.2 atm per 2 m — every 10 m of water ≈ one atmosphere. ✔
Answer: 1.2×10⁵ Pa
Average pressure (triangle): ρg(h/2) = 25,000 Pa over area 10×5 = 50 m².
F = 25,000 × 50 = 1.25×10⁶ N — pressure grows linearly with depth, so use the average. ✔
Answer: 1.25 MN
P = 10⁵ + (1000×10×1) + (800×10×1).
= 10⁵ + 10⁴ + 8000 = 1.18×10⁵ Pa — each layer adds its own ρgh, stacked like floors. ✔
Answer: 1.18×10⁵ Pa
- Using volume or container shape. Pressure at a point depends only on depth, density and surface pressure — not on the amount of water.
- Measuring h diagonally. h is the VERTICAL depth, never the slant distance along a tilted wall.
- Gauge vs absolute mix-ups. Decide once per problem whether the question wants the excess (gauge) or the true total.
- Forgetting layers add. Multiple liquids stack: each contributes its own ρg×(its own thickness).
This Physics in Your Daily Life
- Scuba divers add one atmosphere every 10 m — at 30 m you’re squeezed by 4 atmospheres: dive tables and decompression stops are ρgh scheduling.
- Water tanks on rooftops — height IS pressure: municipal supply ‘pressure’ is just the tank’s elevation in disguise (ρgh in the plumbing).
- Dams are thick at the bottom, thin at the top — the triangular pressure profile drawn in concrete.
- Ear-popping in deep pools — your eardrum is a pressure sensor reporting ρgh directly.
- Blood pressure cuffs — measured in mm of mercury: a density-and-height unit (ρgh) still running modern medicine.
Imagine standing under a column of water reaching to the surface: only that column’s weight presses on your head — the lake’s width is irrelevant. Your shoulders don’t feel the water ten metres away; they feel only what’s stacked above them. Pressure is a per-area inheritance from above.
10 m of water: P = 1000×10×10 = 10⁵ Pa — one atmosphere exactly. 10 m of mercury (13.6× denser): 13.6 atm. 10 m of air (~1.2 kg/m³): a mere 120 Pa. Same depth, wildly different inheritance: density is the whole difference.
Picture pressure arrows on a submerged box: all pointing perpendicular into the faces — top arrows short, bottom arrows long, side arrows growing downward. The arrow-length profile is a triangle: zero at the surface, ρgh at the bottom.
Practice set (answers hidden — try first)
(NEET-level) Gauge pressure 5 m under water (g=10):
(JEE Main-level) Pressure at the bottom of 2 m mercury (ρ=13,600): gauge =
(NEET-level) Two tanks, same liquid, same depth, different shapes: bottom pressure is
(Concept) Fluid pressure on a wall acts:
(JEE Main-level) Water fills 3/4 of a 4 m tank: bottom gauge pressure =
- P = F/A, perpendicular to every surface
- P = P₀ + ρgh — depth, density, that’s all
- shape-independent (hydrostatic paradox)
- 10 m water ≈ 1 atm
- layers stack their own ρgh
- 🔁 pressure perpendicular everywhere
- 🔁 P = P₀ + ρgh
- 🔁 container shape irrelevant
- 🧠 Chant: ‘depth times density times g’.
- 🧠 Diver rule: ’10 metres = 1 atmosphere’.
- 🏠 Daily: rooftop tanks = pressure stored as height.
- 🏠 Daily: dam walls are triangles in concrete.
Quick revision
- Pressure = force per area, P = F/A — fluids push perpendicular to every surface they touch
- In a liquid at rest: P = P₀ + ρgh — depth is the only thing that matters
- Same depth → same pressure, regardless of container shape (hydrostatic paradox)
- Density ρ = mass/volume; water ≈ 1000 kg/m³; mercury ≈ 13,600
- Gauge pressure vs absolute: add atmospheric P₀ ≈ 1.01×10⁵ Pa for absolute
- Pressure: the perpendicular push
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