# Mechanical Properties of Fluids > Mechanical Properties of Fluids for NEET-UG Physics — Pascal's law, Bernoulli's theorem, viscosity, Stokes' law and surface tension from NCERT. - Canonical URL: https://prepelephant.com/topics/neet-ug/physics/mechanical-properties-of-fluids - Exam / course: NEET-UG · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Mechanical Properties of Fluids", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/mechanical-properties-of-fluids ## Direct answer Fluids cannot be pulled, only pushed — which is why pressure, a scalar acting equally in all directions, replaces force throughout fluid mechanics. The chapter runs on four pillars: Pascal's law for enclosed fluids, Archimedes for buoyancy, Bernoulli's P + ½ρv^2 + ρgh = constant for streamline flow of an ideal fluid, and the viscous-surface pair of Stokes' law and surface tension. Terminal velocity, capillary rise and the excess pressure inside drops and bubbles are where NEET-UG places its numericals. ## What you must remember - Pressure at depth h: P = P_atm + ρgh, with 1 atm = 1.013 × 10^5 Pa — equivalently 76 cm of mercury or about 10.3 m of water. - Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished everywhere — the hydraulic lift multiplies force by the area ratio A2/A1. - Archimedes: upthrust equals the weight of displaced fluid; a floating body displaces exactly its own weight of fluid. - Bernoulli (streamline, incompressible, non-viscous): P + ½ρv^2 + ρgh = constant — faster flow means lower pressure, which explains aerofoil lift, the spinning ball's swing and the atomiser. - Torricelli's theorem: efflux speed under a head h is sqrt(2gh). - Stokes' law F = 6πηrv gives terminal velocity v_t = 2r^2(ρ - σ)g/(9η); viscosity of liquids falls with temperature (gases rise); water at 20 °C has η ≈ 1 × 10^-3 Pa s. - Reynolds number R_e = ρvD/η: pipe flow is streamline below about 2000 and turbulent above about 3000. - Surface tension S (N/m) is also energy per unit area; capillary rise h = 2S cosθ/(rρg); excess pressure is 2S/r in a liquid drop but 4S/r in a soap bubble, which has two surfaces. ## A typical exam case: terminal velocity Consider a mist droplet of radius 5 × 10^-5 m falling in air (η ≈ 1.8 × 10^-5 Pa s). At terminal velocity, weight balances the Stokes drag plus buoyancy, giving v_t = 2r^2ρg/9η = 2 × (5 × 10^-5)^2 × 1000 × 9.8/(9 × 1.8 × 10^-5) ≈ 0.3 m/s — a gentle drift. Scale the radius up tenfold and the terminal velocity grows a hundredfold, past 30 m/s, which is why large raindrops must break apart in flight; rain arrives as droplets because v_t grows as r^2, and any drop big enough to fall dangerously shatters first. This single scaling argument also answers the exam's standard question: what happens to terminal velocity when the radius doubles? Quadruples — provided viscosity and densities are unchanged. The same ledger governs the capillary: h = 2S cosθ/(rρg) says a narrower tube gives a higher column, water-glass has an acute contact angle (near 0°, cos θ ≈ 1) so water climbs, while mercury-glass is obtuse (about 135°) and the column depresses. Detergent enters by lowering S, which is precisely how it helps water wet into fabric gaps that plain water cannot penetrate. ## Where students slip Bernoulli's equation is licensed only for streamline flow of a non-viscous, incompressible fluid along a tube of flow — applying it across a suddenly opened tap or through a turbulent section is out of contract. The soap-bubble factor of two is the most-looted error: a bubble has an inner and an outer surface, so its excess pressure is 4S/r, double a drop's 2S/r, and the exam restates this nearly every year in some form. In capillary questions, students quote the rise formula but forget that the meniscus angle decides the sign — cos θ negative means depression, not rise. Pascal-law problems trip on which piston the effort and load sit: the force multiplies by the area ratio, but the work does not multiply, because the small piston travels proportionally farther. Finally, viscosity questions punish "thicker flows slower in summer": liquids flow easier when hot (η falls), while gases become more viscous. ## Frequently asked questions ### Why is the pressure inside a soap bubble twice that inside a liquid drop of the same radius? A soap bubble has two surfaces, inner and outer, each contributing 2S/r; total excess pressure is therefore 4S/r against the drop's 2S/r. ### How does terminal velocity depend on droplet radius? v_t = 2r^2(ρ - σ)g/9η grows as the square of the radius: double the radius and the terminal velocity quadruples, assuming η and the densities stay fixed. ### Why does water rise in a glass capillary but mercury depress? Water-glass contact angle is acute (nearly 0°), making cos θ positive and the rise real; mercury-glass angle is obtuse (about 135°), so cos θ is negative and the meniscus is pushed down. ### State Bernoulli's principle and its conditions. Along a streamline of a steady, incompressible, non-viscous flow, P + ½ρv^2 + ρgh stays constant; the trade between pressure and speed explains lift and venturi behaviour. ### What does the Reynolds number tell you? R_e = ρvD/η compares inertial to viscous effects: below roughly 2000 pipe flow is laminar, above roughly 3000 it is turbulent, with a transition band between.