Complete revision notes and formulas for Mechanical Properties of Fluids (Class 11). Curated for JEE, NEET, AP Physics, SAT, and CUET. Tap any topic to open the live simulation and full PYQ set.
P = P₀ + ρgh — see pressure grow linearly with depth in any fluid.
Pressure in a static fluid increases linearly with depth: P = P₀ + ρgh.
Independent of container shape — pressure depends only on vertical depth.
P₀ is the pressure at the surface (usually atmospheric, 101.3 kPa).
h = depth below the surface.
1 m of water adds ~9800 Pa (~10% of atmospheric pressure).
Submarines must withstand huge ΔP at deep ocean (~1000 atm at 10 km).
F₁/A₁ = F₂/A₂ — small input force lifts a heavy load via large piston.
Pressure applied to an enclosed fluid is transmitted equally in all directions.
Hydraulic lift: small input force F₁ on small area A₁ produces large output F₂ on large area A₂.
Mechanical advantage = A₂/A₁; conservation of volume → input distance × A₁ = output distance × A₂.
Same pressure throughout.
Energy is conserved: small force × large distance = large force × small distance.
Hydraulic brakes, jacks, presses all rely on Pascal's law.
F_b = ρ_fluid V_disp g — sink, float, suspend depending on density.
Buoyant force F_b = weight of displaced fluid = ρ_fluid · V_displaced · g.
Floats if ρ_object < ρ_fluid; sinks if ρ_object > ρ_fluid; suspends if equal.
When floating, the fraction submerged equals ρ_object / ρ_fluid.
Acts upward through center of buoyancy.
Fraction submerged when floating.
Apparent weight in fluid = true weight − F_b.
Iceberg: ~89% submerged in seawater (ρ_ice/ρ_seawater ≈ 920/1025).
Compare 4 materials in one fluid — see who floats by density rule.
A solid object's behavior depends only on the density ratio with the fluid.
Wood (ρ ≈ 600) floats in water; iron (ρ ≈ 7800) sinks.
Ice floats on water because ice (920) is less dense than water (1000) — unusual property.
Strictly less than for floating.
Hollow shapes (boats, balloons) effectively reduce average density via trapped air.
Mercury (13,600 kg/m³) is dense enough that iron, lead, and even gold can float on it.
Re = ρvD/η — sweep velocity to cross from laminar to turbulent flow.
Reynolds number Re = ρvD/η classifies flow regime.
Re < 2000 → laminar (smooth streamlines). Re > 4000 → turbulent (chaotic eddies).
Between 2000–4000 → transitional regime, sensitive to disturbances.
Dimensionless number.
Higher viscosity (η) → lower Re → more laminar.
Larger pipe diameter or faster flow → higher Re → more turbulent.
A₁v₁ = A₂v₂ — pipe narrows; particles speed up. Live volume flow rate.
For incompressible fluid in steady flow: A₁v₁ = A₂v₂ along any streamtube.
Volume flow rate Q = Av is constant — conservation of mass.
Narrowing the pipe forces the fluid to speed up.
Volume flow conserved.
For compressible flow.
A river speeds up where it narrows — continuity in action.
Same idea: covering part of a hose nozzle makes water shoot farther.
P + ½ρv² + ρgh = const — manometers show pressure drop where speed is high.
Along a streamline of an ideal fluid: P + ½ρv² + ρgh = constant.
Energy interpretation: pressure energy + kinetic energy + gravitational PE per unit volume is conserved.
Faster flow ↔ lower pressure (where elevation is constant).
Along a streamline, ideal fluid.
Assumes incompressible, non-viscous, steady flow.
Used to derive Torricelli's law for efflux: v = √(2gh).
Pipe with throat — flow accelerates, pressure plummets. Used in flow meters.
Fluid speeds up through a constriction (continuity), so its pressure drops there (Bernoulli).
Used in carburetors, atomizers, flow meters, aspirators.
ΔP = ½ρ(v₂² − v₁²) > 0 between main and throat.
Throat is at lower P.
If A₂/A₁ = 1/2, then v₂ = 2v₁ and pressure drops by 1.5 ρv₁².
Strong winds blowing past a chimney create suction that draws smoke up.
Curved airfoil — air on top is faster, pressure lower → net upward force.
Curved upper surface forces air to travel a longer path → higher speed → lower pressure (Bernoulli).
Net pressure difference × wing area = lift force, perpendicular to airflow.
L = ½ρv²C_L A — depends on airspeed squared and angle of attack.
C_L grows with angle of attack until stall.
Doubling airspeed quadruples lift — but also drag.
Above stall angle (~15–18°), flow separates and lift collapses.
F_drag = 6πηrv — viscous drag on a sphere through fluid.
A small sphere of radius r moving slowly through a viscous fluid experiences drag F = 6πηrv.
Valid for low Reynolds numbers (smooth, laminar flow).
Drag is linear in v — unlike high-speed drag (∝ v²).
Spherical object, slow flow.
Used to determine viscosity (Stokes' viscometer).
Used in Millikan oil-drop experiment to measure electron charge.
Sphere in viscous fluid — accelerates until weight = buoyancy + drag at v_t.
A sphere falling through fluid accelerates until weight = buoyancy + drag, then v = constant.
Terminal velocity v_t = 2r²(ρ_s − ρ_f)g / (9η).
Larger or denser objects have higher v_t; thicker fluids slow them down.
From Stokes' law balance.
Skydiver in spread-eagle: v_t ≈ 55 m/s; head-down: ~90 m/s.
Raindrops reach v_t ≈ 9 m/s (otherwise they'd be lethal!).
h = 2T cosθ/(ρgr) — narrow tube pulls liquid up by surface tension.
In a narrow tube, surface tension pulls liquid up against gravity.
Rise height h = 2T cosθ / (ρgr) — narrower tube → higher rise.
θ = contact angle (small for water-glass; large/obtuse for mercury, which depresses).
h is positive (rise) when cosθ > 0.
Plants use capillary action to draw water up roots and stems.
Mercury in glass shows capillary depression (cosθ < 0).
Excess pressure inside drops/bubbles — ΔP = 2T/R (drop), 4T/R (bubble).
Surface tension T (N/m) is the force per unit length acting along a surface, minimising area.
Excess pressure inside a liquid drop: ΔP = 2T/R.
Excess pressure inside a soap bubble: ΔP = 4T/R (two surfaces).
Single surface.
Two surfaces (inner + outer).
Smaller drops/bubbles have higher internal pressure — that's why two soap bubbles touching cause the smaller to push into the larger.
Water striders walk on water by exploiting surface tension.
Mechanical Properties of Fluids on sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs). Free physics revision for Class 11, JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT Subject Physics, and CUET-UG.