Mechanical Properties of Fluids

A fluid is anything that cannot sustain a shearing stress — which is exactly the property Chapter 8 said solids possess — and that one sentence generates this entire chapter. It opens with pressure, a scalar despite being built from a force, and Pascal's law, which transmits an applied pressure undiminished through an enclosed fluid and so lets a car be lifted by a foot on a pedal. Pressure grows with depth as $P = P_a + \rho g h$, giving the hydrostatic paradox, the mercury barometer and the distinction between gauge and absolute pressure. Archimedes' principle then explains why anything floats: the upthrust equals the weight of fluid displaced, so a floating body sinks to exactly the fraction $\frac{\rho_{\text{body}}}{\rho_{\text{fluid}}}$ of its volume. Set the fluid moving and conservation of mass becomes the equation of continuity $A_1v_1 = A_2v_2$, while conservation of energy becomes Bernoulli's principle $P + \frac{1}{2}\rho v^2 + \rho g h =$ constant — from which follow the speed of efflux $v = \sqrt{2gh}$, the Venturi meter, the swerve of a spun cricket ball and the lift on an aircraft wing. Real fluids resist through viscosity, giving Stokes' law and the terminal velocity $v_t \propto r^2$ that keeps dust airborne and raindrops survivable, Poiseuille's law with its startling fourth power of the radius, and the Reynolds number that decides whether a flow is smooth or turbulent. The chapter closes on surface tension: surface energy, the angle of contact, the excess pressure $\frac{2S}{r}$ inside a drop against $\frac{4S}{r}$ inside a bubble, and the capillary rise $h = \frac{2S\cos\theta}{r\rho g}$ that carries water to the top of a tree. Topics the rationalised syllabus trimmed — Archimedes' principle and floatation, the Venturi meter, Poiseuille's law and the Reynolds number — are restored in full, because Boards, JEE Main and NEET ask about them every single year. Dedicated JEE and NEET Corners follow, each with a full-length exam-pattern practice drill.