Q1. In a hydraulic lift the small piston has area 0.01 m² and the large one 0.5 m². What force on the small piston lifts a 5000 N load?
Pascal's law: F₁/A₁ = F₂/A₂
F₁ = F₂ × A₁/A₂ = 5000 × 0.01/0.5
F₁ = 100 N
Mechanical Properties of Fluids — Class 11
From hydraulic lifts to aeroplane wings, fluids follow a few neat laws. Compute pressure at depth and master buoyancy and Bernoulli.
Pressure in a fluidPressure increases with depth: P = ρgh (plus atmospheric pressure). It acts equally in all directions.
Pascal's lawPressure applied to an enclosed fluid is transmitted undiminished — the basis of the hydraulic lift and brakes.
Archimedes' principleA body in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces.
Bernoulli & viscosityBernoulli: faster fluid ⇒ lower pressure (aeroplane lift). Viscosity is a fluid's internal friction.
Fluid-pressure calculator Interactive
Find the pressure at a given depth in a fluid of known density (g = 9.8 m/s²).
Pressure, P = ρgh—Pa
This is the pressure due to the fluid alone; add atmospheric pressure (≈1.01×10⁵ Pa) for the absolute pressure.
Numericals practice Interactive
Pressure and buoyancy problems with steps.
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Solved numericals
Q2. Why does an aeroplane wing generate lift?
Air moves faster over the curved top than the flatter bottom.
By Bernoulli's principle, faster flow means lower pressure on top.
The higher pressure below pushes the wing up (lift).
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Pressure at depth | P = ρ g h | pascal (Pa) |
| Pascal's law (hydraulic) | F₁/A₁ = F₂/A₂ | — |
| Buoyant force | F_B = ρ_fluid × V × g | N |
| Bernoulli's equation | P + ½ρv² + ρgh = constant | — |
Common mistakes & exam wins
- Fluid pressure depends only on depth and density, not on the shape of the container.
- A hydraulic lift multiplies force via Pascal's law (small area in, large area out).
- Bernoulli: where a fluid moves faster, its pressure is lower.
- A body floats when the buoyant force equals its weight (its average density ≤ fluid density).
Frequently asked questions
How does pressure vary with depth in a fluid?
It increases linearly with depth: P = ρgh, where ρ is the density and h the depth below the surface.
What is Archimedes' principle?
A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.
What is Bernoulli's principle?
For a flowing fluid, where the speed is higher the pressure is lower (P + ½ρv² + ρgh is constant).